id	sid	tid	token	lemma	pos
easat-3999	1	1	edelweiss	edelweiss	PROPN
easat-3999	1	2	applied	apply	VERB
easat-3999	1	3	science	science	NOUN
easat-3999	1	4	and	and	CCONJ
easat-3999	1	5	technology	technology	NOUN
easat-3999	1	6	issn	issn	PROPN
easat-3999	1	7	:	:	PUNCT
easat-3999	1	8	2576	2576	NUM
easat-3999	1	9	-	-	SYM
easat-3999	1	10	8484	8484	NUM
easat-3999	1	11	vol	vol	NOUN
easat-3999	1	12	.	.	PROPN
easat-3999	1	13	8	8	NUM
easat-3999	1	14	,	,	PUNCT
easat-3999	1	15	no	no	INTJ
easat-3999	1	16	.	.	NOUN
easat-3999	1	17	6	6	NUM
easat-3999	1	18	,	,	PUNCT
easat-3999	1	19	9356	9356	NUM
easat-3999	1	20	-	-	SYM
easat-3999	1	21	9375	9375	NUM
easat-3999	1	22	2024	2024	NUM
easat-3999	1	23	publisher	publisher	NOUN
easat-3999	1	24	:	:	PUNCT
easat-3999	1	25	learning	learn	VERB
easat-3999	1	26	gate	gate	NOUN
easat-3999	1	27	doi	doi	PROPN
easat-3999	1	28	:	:	PUNCT
easat-3999	1	29	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	1	30	©	©	PROPN
easat-3999	1	31	2024	2024	NUM
easat-3999	1	32	by	by	ADP
easat-3999	1	33	the	the	DET
easat-3999	1	34	author	author	NOUN
easat-3999	1	35	;	;	PUNCT
easat-3999	1	36	licensee	licensee	PROPN
easat-3999	1	37	learning	learning	NOUN
easat-3999	1	38	gate	gate	NOUN
easat-3999	1	39	©	©	PROPN
easat-3999	1	40	2024	2024	NUM
easat-3999	1	41	by	by	ADP
easat-3999	1	42	the	the	DET
easat-3999	1	43	author	author	NOUN
easat-3999	1	44	;	;	PUNCT
easat-3999	1	45	licensee	licensee	PROPN
easat-3999	1	46	learning	learn	VERB
easat-3999	1	47	gate	gate	NOUN
easat-3999	1	48	*	*	PUNCT
easat-3999	1	49	correspondence	correspondence	NOUN
easat-3999	1	50	:	:	PUNCT
easat-3999	2	1	challoumis_constantinos@yahoo.com	challoumis_constantinos@yahoo.com	X
easat-3999	2	2	panphysics	panphysic	NOUN
easat-3999	2	3	enopiisis	enopiisis	NOUN
easat-3999	2	4	constantinos	constantino	NOUN
easat-3999	2	5	challoumis1	challoumis1	VERB
easat-3999	2	6	*	*	PROPN
easat-3999	2	7	1national	1national	NUM
easat-3999	2	8	and	and	CCONJ
easat-3999	2	9	kapodistrian	kapodistrian	ADJ
easat-3999	2	10	university	university	PROPN
easat-3999	2	11	of	of	ADP
easat-3999	2	12	athens	athens	PROPN
easat-3999	2	13	,	,	PUNCT
easat-3999	2	14	greece	greece	PROPN
easat-3999	2	15	;	;	PUNCT
easat-3999	2	16	challoumis_constantinos@yahoo.com	challoumis_constantinos@yahoo.com	X
easat-3999	2	17	(	(	PUNCT
easat-3999	2	18	c.c	c.c	PROPN
easat-3999	2	19	.	.	PROPN
easat-3999	2	20	)	)	PUNCT
easat-3999	2	21	.	.	PUNCT
easat-3999	3	1	abstract	abstract	ADV
easat-3999	3	2	:	:	PUNCT
easat-3999	3	3	this	this	DET
easat-3999	3	4	paper	paper	NOUN
easat-3999	3	5	examines	examine	VERB
easat-3999	3	6	desmos	desmo	NOUN
easat-3999	3	7	(	(	PUNCT
easat-3999	3	8	or	or	CCONJ
easat-3999	3	9	bond	bond	NOUN
easat-3999	3	10	)	)	PUNCT
easat-3999	3	11	and	and	CCONJ
easat-3999	3	12	its	its	PRON
easat-3999	3	13	implications	implication	NOUN
easat-3999	3	14	compared	compare	VERB
easat-3999	3	15	to	to	ADP
easat-3999	3	16	the	the	DET
easat-3999	3	17	literature	literature	PROPN
easat-3999	3	18	review	review	PROPN
easat-3999	3	19	.	.	PUNCT
easat-3999	4	1	it	it	PRON
easat-3999	4	2	focuses	focus	VERB
easat-3999	4	3	on	on	ADP
easat-3999	4	4	the	the	DET
easat-3999	4	5	parameter	parameter	NOUN
easat-3999	4	6	n	n	CCONJ
easat-3999	4	7	,	,	PUNCT
easat-3999	4	8	which	which	PRON
easat-3999	4	9	characterizes	characterize	VERB
easat-3999	4	10	how	how	SCONJ
easat-3999	4	11	the	the	DET
easat-3999	4	12	effective	effective	ADJ
easat-3999	4	13	force	force	NOUN
easat-3999	4	14	or	or	CCONJ
easat-3999	4	15	interaction	interaction	NOUN
easat-3999	4	16	between	between	ADP
easat-3999	4	17	celestial	celestial	ADJ
easat-3999	4	18	bodies	body	NOUN
easat-3999	4	19	changes	change	VERB
easat-3999	4	20	with	with	ADP
easat-3999	4	21	distance	distance	NOUN
easat-3999	4	22	.	.	PUNCT
easat-3999	5	1	by	by	ADP
easat-3999	5	2	analyzing	analyze	VERB
easat-3999	5	3	cosmic	cosmic	ADJ
easat-3999	5	4	phenomena	phenomenon	NOUN
easat-3999	5	5	such	such	ADJ
easat-3999	5	6	as	as	ADP
easat-3999	5	7	mercury	mercury	NOUN
easat-3999	5	8	’s	’s	PART
easat-3999	5	9	precession	precession	NOUN
easat-3999	5	10	and	and	CCONJ
easat-3999	5	11	hubble	hubble	NOUN
easat-3999	5	12	's	's	PART
easat-3999	5	13	expansion	expansion	NOUN
easat-3999	5	14	,	,	PUNCT
easat-3999	5	15	derived	derive	VERB
easat-3999	5	16	that	that	DET
easat-3999	5	17	variable	variable	NOUN
easat-3999	5	18	n	n	NOUN
easat-3999	5	19	is	be	AUX
easat-3999	5	20	approximately	approximately	ADV
easat-3999	5	21	1.10	1.10	NUM
easat-3999	5	22	.	.	PUNCT
easat-3999	6	1	this	this	DET
easat-3999	6	2	value	value	NOUN
easat-3999	6	3	indicates	indicate	VERB
easat-3999	6	4	a	a	DET
easat-3999	6	5	deviation	deviation	NOUN
easat-3999	6	6	from	from	ADP
easat-3999	6	7	the	the	DET
easat-3999	6	8	classical	classical	ADJ
easat-3999	6	9	law	law	NOUN
easat-3999	6	10	,	,	PUNCT
easat-3999	6	11	suggesting	suggest	VERB
easat-3999	6	12	a	a	DET
easat-3999	6	13	more	more	ADV
easat-3999	6	14	gradual	gradual	ADJ
easat-3999	6	15	weakening	weakening	NOUN
easat-3999	6	16	of	of	ADP
easat-3999	6	17	forces	force	NOUN
easat-3999	6	18	with	with	ADP
easat-3999	6	19	distance	distance	NOUN
easat-3999	6	20	.	.	PUNCT
easat-3999	7	1	notably	notably	ADV
easat-3999	7	2	,	,	PUNCT
easat-3999	7	3	the	the	DET
easat-3999	7	4	bond	bond	NOUN
easat-3999	7	5	model	model	NOUN
easat-3999	7	6	provides	provide	VERB
easat-3999	7	7	a	a	DET
easat-3999	7	8	different	different	ADJ
easat-3999	7	9	perspective	perspective	NOUN
easat-3999	7	10	on	on	ADP
easat-3999	7	11	energy	energy	NOUN
easat-3999	7	12	interactions	interaction	NOUN
easat-3999	7	13	,	,	PUNCT
easat-3999	7	14	as	as	SCONJ
easat-3999	7	15	it	it	PRON
easat-3999	7	16	predicts	predict	VERB
easat-3999	7	17	higher	high	ADJ
easat-3999	7	18	effective	effective	ADJ
easat-3999	7	19	energies	energy	NOUN
easat-3999	7	20	for	for	ADP
easat-3999	7	21	the	the	DET
easat-3999	7	22	earth	earth	NOUN
easat-3999	7	23	-	-	PUNCT
easat-3999	7	24	moon	moon	NOUN
easat-3999	7	25	system	system	NOUN
easat-3999	7	26	compared	compare	VERB
easat-3999	7	27	to	to	ADP
easat-3999	7	28	the	the	DET
easat-3999	7	29	moon	moon	NOUN
easat-3999	7	30	-	-	PUNCT
easat-3999	7	31	sun	sun	NOUN
easat-3999	7	32	system	system	NOUN
easat-3999	7	33	,	,	PUNCT
easat-3999	7	34	contrary	contrary	ADV
easat-3999	7	35	to	to	ADP
easat-3999	7	36	literature	literature	NOUN
easat-3999	7	37	review	review	NOUN
easat-3999	7	38	predictions	prediction	NOUN
easat-3999	7	39	.	.	PUNCT
easat-3999	8	1	in	in	ADP
easat-3999	8	2	that	that	DET
easat-3999	8	3	way	way	NOUN
easat-3999	8	4	explains	explain	VERB
easat-3999	8	5	why	why	SCONJ
easat-3999	8	6	the	the	DET
easat-3999	8	7	moon	moon	NOUN
easat-3999	8	8	is	be	AUX
easat-3999	8	9	a	a	DET
easat-3999	8	10	satellite	satellite	NOUN
easat-3999	8	11	and	and	CCONJ
easat-3999	8	12	not	not	PART
easat-3999	8	13	a	a	DET
easat-3999	8	14	planet	planet	NOUN
easat-3999	8	15	,	,	PUNCT
easat-3999	8	16	something	something	PRON
easat-3999	8	17	that	that	PRON
easat-3999	8	18	is	be	AUX
easat-3999	8	19	not	not	PART
easat-3999	8	20	plausible	plausible	ADJ
easat-3999	8	21	to	to	PART
easat-3999	8	22	be	be	AUX
easat-3999	8	23	explained	explain	VERB
easat-3999	8	24	in	in	ADP
easat-3999	8	25	the	the	DET
easat-3999	8	26	current	current	ADJ
easat-3999	8	27	literature	literature	PROPN
easat-3999	8	28	review	review	NOUN
easat-3999	8	29	.	.	PUNCT
easat-3999	9	1	this	this	DET
easat-3999	9	2	finding	finding	NOUN
easat-3999	9	3	aligns	align	VERB
easat-3999	9	4	with	with	ADP
easat-3999	9	5	observed	observe	VERB
easat-3999	9	6	cosmic	cosmic	ADJ
easat-3999	9	7	expansion	expansion	NOUN
easat-3999	9	8	and	and	CCONJ
easat-3999	9	9	offers	offer	VERB
easat-3999	9	10	a	a	DET
easat-3999	9	11	refined	refined	ADJ
easat-3999	9	12	view	view	NOUN
easat-3999	9	13	of	of	ADP
easat-3999	9	14	gravitational	gravitational	ADJ
easat-3999	9	15	dynamics	dynamic	NOUN
easat-3999	9	16	.	.	PUNCT
easat-3999	10	1	also	also	ADV
easat-3999	10	2	,	,	PUNCT
easat-3999	10	3	the	the	DET
easat-3999	10	4	elliptical	elliptical	ADJ
easat-3999	10	5	forms	form	NOUN
easat-3999	10	6	on	on	ADP
easat-3999	10	7	cosmos	cosmo	NOUN
easat-3999	10	8	are	be	AUX
easat-3999	10	9	the	the	DET
easat-3999	10	10	prove	prove	NOUN
easat-3999	10	11	of	of	ADP
easat-3999	10	12	rotation	rotation	NOUN
easat-3999	10	13	of	of	ADP
easat-3999	10	14	gravity	gravity	NOUN
easat-3999	10	15	from	from	ADP
easat-3999	10	16	desmos	desmo	NOUN
easat-3999	10	17	impact	impact	NOUN
easat-3999	10	18	.	.	PUNCT
easat-3999	11	1	something	something	PRON
easat-3999	11	2	that	that	PRON
easat-3999	11	3	show	show	VERB
easat-3999	11	4	the	the	DET
easat-3999	11	5	way	way	NOUN
easat-3999	11	6	to	to	PART
easat-3999	11	7	control	control	VERB
easat-3999	11	8	and	and	CCONJ
easat-3999	11	9	create	create	VERB
easat-3999	11	10	gravity	gravity	NOUN
easat-3999	11	11	.	.	PUNCT
easat-3999	12	1	also	also	ADV
easat-3999	12	2	,	,	PUNCT
easat-3999	12	3	in	in	ADP
easat-3999	12	4	that	that	DET
easat-3999	12	5	way	way	NOUN
easat-3999	12	6	is	be	AUX
easat-3999	12	7	explained	explain	VERB
easat-3999	12	8	that	that	SCONJ
easat-3999	12	9	there	there	ADV
easat-3999	12	10	the	the	DET
easat-3999	12	11	dark	dark	ADJ
easat-3999	12	12	matter	matter	NOUN
easat-3999	12	13	is	be	AUX
easat-3999	12	14	a	a	DET
easat-3999	12	15	space	space	NOUN
easat-3999	12	16	-	-	PUNCT
easat-3999	12	17	time	time	NOUN
easat-3999	12	18	and	and	CCONJ
easat-3999	12	19	energy	energy	NOUN
easat-3999	12	20	effect	effect	NOUN
easat-3999	12	21	from	from	ADP
easat-3999	12	22	equations	equation	NOUN
easat-3999	12	23	of	of	ADP
easat-3999	12	24	desmos	desmos	NOUN
easat-3999	12	25	(	(	PUNCT
easat-3999	12	26	bond	bond	NOUN
easat-3999	12	27	)	)	PUNCT
easat-3999	12	28	.	.	PUNCT
easat-3999	13	1	keywords	keyword	NOUN
easat-3999	13	2	:	:	PUNCT
easat-3999	13	3	bond	bond	NOUN
easat-3999	13	4	,	,	PUNCT
easat-3999	13	5	cosmic	cosmic	ADJ
easat-3999	13	6	expansion	expansion	NOUN
easat-3999	13	7	,	,	PUNCT
easat-3999	13	8	desmos	desmo	NOUN
easat-3999	13	9	,	,	PUNCT
easat-3999	13	10	gravitational	gravitational	ADJ
easat-3999	13	11	interactions	interaction	NOUN
easat-3999	13	12	,	,	PUNCT
easat-3999	13	13	gravity	gravity	NOUN
easat-3999	13	14	,	,	PUNCT
easat-3999	13	15	hubble	hubble	ADJ
easat-3999	13	16	constant	constant	ADJ
easat-3999	13	17	,	,	PUNCT
easat-3999	13	18	mercury	mercury	NOUN
easat-3999	13	19	's	's	PART
easat-3999	13	20	precession	precession	NOUN
easat-3999	13	21	,	,	PUNCT
easat-3999	13	22	modified	modify	VERB
easat-3999	13	23	gravity	gravity	NOUN
easat-3999	13	24	,	,	PUNCT
easat-3999	13	25	parametern	parametern	NOUN
easat-3999	13	26	.	.	PUNCT
easat-3999	14	1	1	1	X
easat-3999	14	2	.	.	X
easat-3999	14	3	introduction	introduction	NOUN
easat-3999	14	4	in	in	ADP
easat-3999	14	5	the	the	DET
easat-3999	14	6	classical	classical	ADJ
easat-3999	14	7	dynamics	dynamic	NOUN
easat-3999	14	8	of	of	ADP
easat-3999	14	9	the	the	DET
easat-3999	14	10	interaction	interaction	NOUN
easat-3999	14	11	of	of	ADP
easat-3999	14	12	heavenly	heavenly	ADJ
easat-3999	14	13	bodies	body	NOUN
easat-3999	14	14	,	,	PUNCT
easat-3999	14	15	together	together	ADV
easat-3999	14	16	with	with	ADP
easat-3999	14	17	the	the	DET
easat-3999	14	18	cosmic	cosmic	ADJ
easat-3999	14	19	expansion	expansion	NOUN
easat-3999	14	20	,	,	PUNCT
easat-3999	14	21	hitherto	hitherto	NOUN
easat-3999	14	22	,	,	PUNCT
easat-3999	14	23	it	it	PRON
easat-3999	14	24	was	be	AUX
easat-3999	14	25	explained	explain	VERB
easat-3999	14	26	by	by	ADP
easat-3999	14	27	classical	classical	ADJ
easat-3999	14	28	gravity	gravity	NOUN
easat-3999	14	29	,	,	PUNCT
easat-3999	14	30	where	where	SCONJ
easat-3999	14	31	the	the	DET
easat-3999	14	32	strengths	strength	NOUN
easat-3999	14	33	fall	fall	VERB
easat-3999	14	34	off	off	ADP
easat-3999	14	35	like	like	ADP
easat-3999	14	36	the	the	DET
easat-3999	14	37	square	square	NOUN
easat-3999	14	38	of	of	ADP
easat-3999	14	39	distance	distance	NOUN
easat-3999	14	40	between	between	ADP
easat-3999	14	41	masses	masse	NOUN
easat-3999	14	42	.	.	PUNCT
easat-3999	15	1	recent	recent	ADJ
easat-3999	15	2	observations	observation	NOUN
easat-3999	15	3	combined	combine	VERB
easat-3999	15	4	with	with	ADP
easat-3999	15	5	alternative	alternative	ADJ
easat-3999	15	6	models	model	NOUN
easat-3999	15	7	seem	seem	VERB
easat-3999	15	8	to	to	PART
easat-3999	15	9	point	point	VERB
easat-3999	15	10	out	out	ADP
easat-3999	15	11	deficiencies	deficiency	NOUN
easat-3999	15	12	in	in	ADP
easat-3999	15	13	the	the	DET
easat-3999	15	14	classical	classical	ADJ
easat-3999	15	15	interpretation	interpretation	NOUN
easat-3999	15	16	of	of	ADP
easat-3999	15	17	cosmic	cosmic	ADJ
easat-3999	15	18	phenomena	phenomenon	NOUN
easat-3999	15	19	.	.	PUNCT
easat-3999	16	1	desmos	desmos	PROPN
easat-3999	16	2	model	model	NOUN
easat-3999	16	3	introduces	introduce	VERB
easat-3999	16	4	a	a	DET
easat-3999	16	5	parameter	parameter	NOUN
easat-3999	16	6	n	n	CCONJ
easat-3999	16	7	that	that	PRON
easat-3999	16	8	changes	change	VERB
easat-3999	16	9	the	the	DET
easat-3999	16	10	rate	rate	NOUN
easat-3999	16	11	at	at	ADP
easat-3999	16	12	which	which	PRON
easat-3999	16	13	forces	force	NOUN
easat-3999	16	14	weaken	weaken	VERB
easat-3999	16	15	with	with	ADP
easat-3999	16	16	distance	distance	NOUN
easat-3999	16	17	.	.	PUNCT
easat-3999	17	1	in	in	ADP
easat-3999	17	2	this	this	DET
easat-3999	17	3	paper	paper	NOUN
easat-3999	17	4	.	.	PUNCT
easat-3999	18	1	it	it	PRON
easat-3999	18	2	has	have	AUX
easat-3999	18	3	explored	explore	VERB
easat-3999	18	4	how	how	SCONJ
easat-3999	18	5	"	"	PUNCT
easat-3999	18	6	n	n	CCONJ
easat-3999	18	7	"	"	PUNCT
easat-3999	18	8	really	really	ADV
easat-3999	18	9	affects	affect	VERB
easat-3999	18	10	a	a	DET
easat-3999	18	11	host	host	NOUN
easat-3999	18	12	of	of	ADP
easat-3999	18	13	cosmic	cosmic	ADJ
easat-3999	18	14	phenomena	phenomenon	NOUN
easat-3999	18	15	including	include	VERB
easat-3999	18	16	the	the	DET
easat-3999	18	17	precession	precession	NOUN
easat-3999	18	18	of	of	ADP
easat-3999	18	19	mercury	mercury	NOUN
easat-3999	18	20	's	's	PART
easat-3999	18	21	orbit	orbit	NOUN
easat-3999	18	22	and	and	CCONJ
easat-3999	18	23	the	the	DET
easat-3999	18	24	hubble	hubble	ADJ
easat-3999	18	25	expansion	expansion	NOUN
easat-3999	18	26	,	,	PUNCT
easat-3999	18	27	and	and	CCONJ
easat-3999	18	28	how	how	SCONJ
easat-3999	18	29	the	the	DET
easat-3999	18	30	new	new	ADJ
easat-3999	18	31	model	model	NOUN
easat-3999	18	32	of	of	ADP
easat-3999	18	33	gravitation	gravitation	NOUN
easat-3999	18	34	proposed	propose	VERB
easat-3999	18	35	the	the	DET
easat-3999	18	36	bond	bond	NOUN
easat-3999	18	37	model	model	NOUN
easat-3999	18	38	and	and	CCONJ
easat-3999	18	39	the	the	DET
easat-3999	18	40	way	way	NOUN
easat-3999	18	41	that	that	PRON
easat-3999	18	42	affects	affect	VERB
easat-3999	18	43	energy	energy	NOUN
easat-3999	18	44	interactions	interaction	NOUN
easat-3999	18	45	between	between	ADP
easat-3999	18	46	celestial	celestial	ADJ
easat-3999	18	47	bodies	body	NOUN
easat-3999	18	48	.	.	PUNCT
easat-3999	19	1	i	i	PRON
easat-3999	19	2	take	take	VERB
easat-3999	19	3	special	special	ADJ
easat-3999	19	4	note	note	NOUN
easat-3999	19	5	that	that	SCONJ
easat-3999	19	6	the	the	DET
easat-3999	19	7	effective	effective	ADJ
easat-3999	19	8	energy	energy	NOUN
easat-3999	19	9	between	between	ADP
easat-3999	19	10	the	the	DET
easat-3999	19	11	earth	earth	NOUN
easat-3999	19	12	and	and	CCONJ
easat-3999	19	13	moon	moon	NOUN
easat-3999	19	14	in	in	ADP
easat-3999	19	15	the	the	DET
easat-3999	19	16	bond	bond	NOUN
easat-3999	19	17	model	model	NOUN
easat-3999	19	18	is	be	AUX
easat-3999	19	19	greater	great	ADJ
easat-3999	19	20	than	than	ADP
easat-3999	19	21	between	between	ADP
easat-3999	19	22	the	the	DET
easat-3999	19	23	moon	moon	NOUN
easat-3999	19	24	and	and	CCONJ
easat-3999	19	25	sun	sun	NOUN
easat-3999	19	26	,	,	PUNCT
easat-3999	19	27	on	on	ADP
easat-3999	19	28	the	the	DET
easat-3999	19	29	contrary	contrary	NOUN
easat-3999	19	30	to	to	ADP
easat-3999	19	31	the	the	DET
easat-3999	19	32	classical	classical	ADJ
easat-3999	19	33	expectation	expectation	NOUN
easat-3999	19	34	,	,	PUNCT
easat-3999	19	35	as	as	SCONJ
easat-3999	19	36	there	there	PRON
easat-3999	19	37	is	be	VERB
easat-3999	19	38	the	the	DET
easat-3999	19	39	opposite	opposite	ADJ
easat-3999	19	40	result	result	NOUN
easat-3999	19	41	.	.	PUNCT
easat-3999	20	1	this	this	DET
easat-3999	20	2	contrast	contrast	NOUN
easat-3999	20	3	effectively	effectively	ADV
easat-3999	20	4	underscores	underscore	VERB
easat-3999	20	5	how	how	SCONJ
easat-3999	20	6	gravitational	gravitational	ADJ
easat-3999	20	7	forces	force	NOUN
easat-3999	20	8	are	be	AUX
easat-3999	20	9	perceived	perceive	VERB
easat-3999	20	10	rather	rather	ADV
easat-3999	20	11	differently	differently	ADV
easat-3999	20	12	in	in	ADP
easat-3999	20	13	the	the	DET
easat-3999	20	14	two	two	NUM
easat-3999	20	15	models	model	NOUN
easat-3999	20	16	.	.	PUNCT
easat-3999	21	1	desmos	desmos	NOUN
easat-3999	21	2	is	be	AUX
easat-3999	21	3	fundamentally	fundamentally	ADV
easat-3999	21	4	shows	show	VERB
easat-3999	21	5	that	that	SCONJ
easat-3999	21	6	the	the	DET
easat-3999	21	7	cosmos	cosmos	PROPN
easat-3999	21	8	is	be	AUX
easat-3999	21	9	based	base	VERB
easat-3999	21	10	on	on	ADP
easat-3999	21	11	bond	bond	NOUN
easat-3999	21	12	,	,	PUNCT
easat-3999	21	13	where	where	SCONJ
easat-3999	21	14	is	be	AUX
easat-3999	21	15	not	not	PART
easat-3999	21	16	an	an	DET
easat-3999	21	17	attractive	attractive	ADJ
easat-3999	21	18	power	power	NOUN
easat-3999	21	19	but	but	CCONJ
easat-3999	21	20	a	a	DET
easat-3999	21	21	connection	connection	NOUN
easat-3999	21	22	of	of	ADP
easat-3999	21	23	bodies	body	NOUN
easat-3999	21	24	,	,	PUNCT
easat-3999	21	25	because	because	SCONJ
easat-3999	21	26	it	it	PRON
easat-3999	21	27	is	be	AUX
easat-3999	21	28	based	base	VERB
easat-3999	21	29	on	on	ADP
easat-3999	21	30	energy	energy	NOUN
easat-3999	21	31	,	,	PUNCT
easat-3999	21	32	something	something	PRON
easat-3999	21	33	that	that	PRON
easat-3999	21	34	explains	explain	VERB
easat-3999	21	35	the	the	PRON
easat-3999	21	36	in	in	ADP
easat-3999	21	37	many	many	ADJ
easat-3999	21	38	cases	case	NOUN
easat-3999	21	39	the	the	DET
easat-3999	21	40	planets	planet	NOUN
easat-3999	21	41	are	be	AUX
easat-3999	21	42	rotating	rotate	VERB
easat-3999	21	43	around	around	ADP
easat-3999	21	44	not	not	PART
easat-3999	21	45	the	the	DET
easat-3999	21	46	center	center	NOUN
easat-3999	21	47	of	of	ADP
easat-3999	21	48	a	a	DET
easat-3999	21	49	sun	sun	NOUN
easat-3999	21	50	,	,	PUNCT
easat-3999	21	51	but	but	CCONJ
easat-3999	21	52	around	around	ADP
easat-3999	21	53	of	of	ADP
easat-3999	21	54	the	the	DET
easat-3999	21	55	united	united	PROPN
easat-3999	21	56	point	point	PROPN
easat-3999	21	57	of	of	ADP
easat-3999	21	58	space	space	NOUN
easat-3999	21	59	-	-	PUNCT
easat-3999	21	60	time	time	NOUN
easat-3999	21	61	and	and	CCONJ
easat-3999	21	62	movement	movement	NOUN
easat-3999	21	63	of	of	ADP
easat-3999	21	64	bodies	body	NOUN
easat-3999	21	65	through	through	ADP
easat-3999	21	66	their	their	PRON
easat-3999	21	67	aggregate	aggregate	ADJ
easat-3999	21	68	energy	energy	NOUN
easat-3999	21	69	.	.	PUNCT
easat-3999	22	1	using	use	VERB
easat-3999	22	2	other	other	ADJ
easat-3999	22	3	words	word	NOUN
easat-3999	22	4	energy	energy	NOUN
easat-3999	22	5	permits	permit	VERB
easat-3999	22	6	also	also	ADV
easat-3999	22	7	the	the	DET
easat-3999	22	8	dark	dark	ADJ
easat-3999	22	9	energy	energy	NOUN
easat-3999	22	10	as	as	SCONJ
easat-3999	22	11	there	there	PRON
easat-3999	22	12	is	be	VERB
easat-3999	22	13	not	not	PART
easat-3999	22	14	a	a	DET
easat-3999	22	15	direct	direct	ADJ
easat-3999	22	16	mass	mass	NOUN
easat-3999	22	17	,	,	PUNCT
easat-3999	22	18	but	but	CCONJ
easat-3999	22	19	the	the	DET
easat-3999	22	20	bond	bond	NOUN
easat-3999	22	21	of	of	ADP
easat-3999	22	22	the	the	DET
easat-3999	22	23	energy	energy	NOUN
easat-3999	22	24	units	unit	NOUN
easat-3999	22	25	.	.	PUNCT
easat-3999	23	1	2	2	X
easat-3999	23	2	.	.	X
easat-3999	23	3	literature	literature	PROPN
easat-3999	23	4	review	review	PROPN
easat-3999	23	5	cosmology	cosmology	NOUN
easat-3999	23	6	is	be	AUX
easat-3999	23	7	the	the	DET
easat-3999	23	8	scientific	scientific	ADJ
easat-3999	23	9	study	study	NOUN
easat-3999	23	10	of	of	ADP
easat-3999	23	11	the	the	DET
easat-3999	23	12	large	large	ADJ
easat-3999	23	13	-	-	PUNCT
easat-3999	23	14	scale	scale	NOUN
easat-3999	23	15	properties	property	NOUN
easat-3999	23	16	of	of	ADP
easat-3999	23	17	the	the	DET
easat-3999	23	18	universe	universe	NOUN
easat-3999	23	19	as	as	ADP
easat-3999	23	20	a	a	DET
easat-3999	23	21	whole	whole	NOUN
easat-3999	23	22	.	.	PUNCT
easat-3999	24	1	it	it	PRON
easat-3999	24	2	endeavors	endeavor	VERB
easat-3999	24	3	to	to	PART
easat-3999	24	4	use	use	VERB
easat-3999	24	5	the	the	DET
easat-3999	24	6	scientific	scientific	ADJ
easat-3999	24	7	method	method	NOUN
easat-3999	24	8	to	to	PART
easat-3999	24	9	understand	understand	VERB
easat-3999	24	10	the	the	DET
easat-3999	24	11	origin	origin	NOUN
easat-3999	24	12	,	,	PUNCT
easat-3999	24	13	evolution	evolution	NOUN
easat-3999	24	14	,	,	PUNCT
easat-3999	24	15	and	and	CCONJ
easat-3999	24	16	ultimate	ultimate	ADJ
easat-3999	24	17	fate	fate	NOUN
easat-3999	24	18	of	of	ADP
easat-3999	24	19	the	the	DET
easat-3999	24	20	entire	entire	ADJ
easat-3999	24	21	universe	universe	NOUN
easat-3999	24	22	.	.	PUNCT
easat-3999	25	1	like	like	ADP
easat-3999	25	2	any	any	DET
easat-3999	25	3	field	field	NOUN
easat-3999	25	4	of	of	ADP
easat-3999	25	5	science	science	NOUN
easat-3999	25	6	,	,	PUNCT
easat-3999	25	7	cosmology	cosmology	NOUN
easat-3999	25	8	involves	involve	VERB
easat-3999	25	9	the	the	DET
easat-3999	25	10	formation	formation	NOUN
easat-3999	25	11	of	of	ADP
easat-3999	25	12	theories	theory	NOUN
easat-3999	25	13	or	or	CCONJ
easat-3999	25	14	hypotheses	hypothesis	NOUN
easat-3999	25	15	about	about	ADP
easat-3999	25	16	the	the	DET
easat-3999	25	17	universe	universe	NOUN
easat-3999	25	18	,	,	PUNCT
easat-3999	25	19	which	which	PRON
easat-3999	25	20	make	make	VERB
easat-3999	25	21	specific	specific	ADJ
easat-3999	25	22	predictions	prediction	NOUN
easat-3999	25	23	for	for	ADP
easat-3999	25	24	phenomena	phenomenon	NOUN
easat-3999	25	25	that	that	PRON
easat-3999	25	26	can	can	AUX
easat-3999	25	27	be	be	AUX
easat-3999	25	28	tested	test	VERB
easat-3999	25	29	with	with	ADP
easat-3999	25	30	observations	observation	NOUN
easat-3999	25	31	.	.	PUNCT
easat-3999	26	1	9357	9357	NUM
easat-3999	26	2	edelweiss	edelweiss	PROPN
easat-3999	26	3	applied	apply	VERB
easat-3999	26	4	science	science	NOUN
easat-3999	26	5	and	and	CCONJ
easat-3999	26	6	technology	technology	NOUN
easat-3999	26	7	issn	issn	PROPN
easat-3999	26	8	:	:	PUNCT
easat-3999	26	9	2576	2576	NUM
easat-3999	26	10	-	-	SYM
easat-3999	26	11	8484	8484	NUM
easat-3999	26	12	vol	vol	NOUN
easat-3999	26	13	.	.	PROPN
easat-3999	26	14	8	8	NUM
easat-3999	26	15	,	,	PUNCT
easat-3999	26	16	no	no	INTJ
easat-3999	26	17	.	.	NOUN
easat-3999	27	1	6	6	NUM
easat-3999	27	2	:	:	SYM
easat-3999	27	3	9356	9356	NUM
easat-3999	27	4	-	-	SYM
easat-3999	27	5	9375	9375	NUM
easat-3999	27	6	,	,	PUNCT
easat-3999	27	7	2024	2024	NUM
easat-3999	27	8	doi	doi	NOUN
easat-3999	27	9	:	:	PUNCT
easat-3999	27	10	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	27	11	©	©	PROPN
easat-3999	27	12	2024	2024	NUM
easat-3999	27	13	by	by	ADP
easat-3999	27	14	the	the	DET
easat-3999	27	15	author	author	NOUN
easat-3999	27	16	;	;	PUNCT
easat-3999	27	17	licensee	licensee	PROPN
easat-3999	27	18	learning	learning	NOUN
easat-3999	27	19	gate	gate	NOUN
easat-3999	27	20	depending	depend	VERB
easat-3999	27	21	on	on	ADP
easat-3999	27	22	the	the	DET
easat-3999	27	23	outcome	outcome	NOUN
easat-3999	27	24	of	of	ADP
easat-3999	27	25	the	the	DET
easat-3999	27	26	observations	observation	NOUN
easat-3999	27	27	,	,	PUNCT
easat-3999	27	28	the	the	DET
easat-3999	27	29	theories	theory	NOUN
easat-3999	27	30	will	will	AUX
easat-3999	27	31	be	be	AUX
easat-3999	27	32	abandoned	abandon	VERB
easat-3999	27	33	,	,	PUNCT
easat-3999	27	34	revised	revise	VERB
easat-3999	27	35	,	,	PUNCT
easat-3999	27	36	or	or	CCONJ
easat-3999	27	37	extended	extend	VERB
easat-3999	27	38	to	to	PART
easat-3999	27	39	accommodate	accommodate	VERB
easat-3999	27	40	the	the	DET
easat-3999	27	41	data	datum	NOUN
easat-3999	27	42	.	.	PUNCT
easat-3999	28	1	today	today	NOUN
easat-3999	28	2	,	,	PUNCT
easat-3999	28	3	technology	technology	NOUN
easat-3999	28	4	allows	allow	VERB
easat-3999	28	5	us	we	PRON
easat-3999	28	6	to	to	PART
easat-3999	28	7	test	test	VERB
easat-3999	28	8	a	a	DET
easat-3999	28	9	significant	significant	ADJ
easat-3999	28	10	number	number	NOUN
easat-3999	28	11	of	of	ADP
easat-3999	28	12	these	these	DET
easat-3999	28	13	predictions	prediction	NOUN
easat-3999	28	14	,	,	PUNCT
easat-3999	28	15	leading	lead	VERB
easat-3999	28	16	to	to	ADP
easat-3999	28	17	our	our	PRON
easat-3999	28	18	current	current	ADJ
easat-3999	28	19	understanding	understanding	NOUN
easat-3999	28	20	of	of	ADP
easat-3999	28	21	cosmological	cosmological	ADJ
easat-3999	28	22	mechanisms	mechanism	NOUN
easat-3999	28	23	that	that	PRON
easat-3999	28	24	shaped	shape	VERB
easat-3999	28	25	the	the	DET
easat-3999	28	26	universe	universe	NOUN
easat-3999	28	27	.	.	PUNCT
easat-3999	29	1	these	these	DET
easat-3999	29	2	advances	advance	NOUN
easat-3999	29	3	have	have	AUX
easat-3999	29	4	been	be	AUX
easat-3999	29	5	met	meet	VERB
easat-3999	29	6	,	,	PUNCT
easat-3999	29	7	in	in	ADP
easat-3999	29	8	turn	turn	NOUN
easat-3999	29	9	,	,	PUNCT
easat-3999	29	10	by	by	ADP
easat-3999	29	11	the	the	DET
easat-3999	29	12	development	development	NOUN
easat-3999	29	13	of	of	ADP
easat-3999	29	14	new	new	ADJ
easat-3999	29	15	technologies	technology	NOUN
easat-3999	29	16	to	to	PART
easat-3999	29	17	survey	survey	VERB
easat-3999	29	18	still	still	ADV
easat-3999	29	19	larger	large	ADJ
easat-3999	29	20	swaths	swath	NOUN
easat-3999	29	21	of	of	ADP
easat-3999	29	22	the	the	DET
easat-3999	29	23	universe	universe	NOUN
easat-3999	29	24	in	in	ADP
easat-3999	29	25	the	the	DET
easat-3999	29	26	ongoing	ongoing	ADJ
easat-3999	29	27	quest	quest	NOUN
easat-3999	29	28	to	to	PART
easat-3999	29	29	understand	understand	VERB
easat-3999	29	30	cosmological	cosmological	ADJ
easat-3999	29	31	structure	structure	NOUN
easat-3999	29	32	formation	formation	NOUN
easat-3999	29	33	.	.	PUNCT
easat-3999	30	1	although	although	SCONJ
easat-3999	30	2	the	the	DET
easat-3999	30	3	questions	question	NOUN
easat-3999	30	4	of	of	ADP
easat-3999	30	5	what	what	PRON
easat-3999	30	6	the	the	DET
easat-3999	30	7	universe	universe	NOUN
easat-3999	30	8	is	be	AUX
easat-3999	30	9	made	make	VERB
easat-3999	30	10	of	of	ADP
easat-3999	30	11	,	,	PUNCT
easat-3999	30	12	how	how	SCONJ
easat-3999	30	13	old	old	ADJ
easat-3999	30	14	it	it	PRON
easat-3999	30	15	is	be	AUX
easat-3999	30	16	,	,	PUNCT
easat-3999	30	17	and	and	CCONJ
easat-3999	30	18	how	how	SCONJ
easat-3999	30	19	it	it	PRON
easat-3999	30	20	will	will	AUX
easat-3999	30	21	end	end	VERB
easat-3999	30	22	are	be	AUX
easat-3999	30	23	ancient	ancient	ADJ
easat-3999	30	24	,	,	PUNCT
easat-3999	30	25	it	it	PRON
easat-3999	30	26	was	be	AUX
easat-3999	30	27	only	only	ADV
easat-3999	30	28	with	with	ADP
easat-3999	30	29	the	the	DET
easat-3999	30	30	development	development	NOUN
easat-3999	30	31	of	of	ADP
easat-3999	30	32	modern	modern	ADJ
easat-3999	30	33	scientific	scientific	ADJ
easat-3999	30	34	tools	tool	NOUN
easat-3999	30	35	that	that	PRON
easat-3999	30	36	progress	progress	NOUN
easat-3999	30	37	began	begin	VERB
easat-3999	30	38	to	to	PART
easat-3999	30	39	be	be	AUX
easat-3999	30	40	made	make	VERB
easat-3999	30	41	in	in	ADP
easat-3999	30	42	finding	find	VERB
easat-3999	30	43	answers	answer	NOUN
easat-3999	30	44	.	.	PUNCT
easat-3999	31	1	indeed	indeed	ADV
easat-3999	31	2	,	,	PUNCT
easat-3999	31	3	at	at	ADP
easat-3999	31	4	various	various	ADJ
easat-3999	31	5	times	time	NOUN
easat-3999	31	6	in	in	ADP
easat-3999	31	7	history	history	NOUN
easat-3999	31	8	,	,	PUNCT
easat-3999	31	9	the	the	DET
easat-3999	31	10	scientific	scientific	ADJ
easat-3999	31	11	consensus	consensus	NOUN
easat-3999	31	12	on	on	ADP
easat-3999	31	13	these	these	DET
easat-3999	31	14	questions	question	NOUN
easat-3999	31	15	shifted	shift	VERB
easat-3999	31	16	dramatically	dramatically	ADV
easat-3999	31	17	from	from	ADP
easat-3999	31	18	the	the	DET
easat-3999	31	19	theories	theory	NOUN
easat-3999	31	20	of	of	ADP
easat-3999	31	21	a	a	DET
easat-3999	31	22	very	very	ADV
easat-3999	31	23	old	old	ADJ
easat-3999	31	24	,	,	PUNCT
easat-3999	31	25	steady	steady	ADJ
easat-3999	31	26	-	-	PUNCT
easat-3999	31	27	state	state	NOUN
easat-3999	31	28	universe	universe	NOUN
easat-3999	31	29	to	to	ADP
easat-3999	31	30	those	those	PRON
easat-3999	31	31	of	of	ADP
easat-3999	31	32	a	a	DET
easat-3999	31	33	universe	universe	NOUN
easat-3999	31	34	extending	extend	VERB
easat-3999	31	35	far	far	ADV
easat-3999	31	36	back	back	ADV
easat-3999	31	37	into	into	ADP
easat-3999	31	38	the	the	DET
easat-3999	31	39	past	past	NOUN
easat-3999	31	40	,	,	PUNCT
easat-3999	31	41	where	where	SCONJ
easat-3999	31	42	the	the	DET
easat-3999	31	43	galaxies	galaxy	NOUN
easat-3999	31	44	appeared	appear	VERB
easat-3999	31	45	to	to	PART
easat-3999	31	46	be	be	AUX
easat-3999	31	47	receding	recede	VERB
easat-3999	31	48	from	from	ADP
easat-3999	31	49	one	one	NUM
easat-3999	31	50	another	another	DET
easat-3999	31	51	in	in	ADP
easat-3999	31	52	the	the	DET
easat-3999	31	53	aftermath	aftermath	NOUN
easat-3999	31	54	of	of	ADP
easat-3999	31	55	a	a	DET
easat-3999	31	56	violent	violent	ADJ
easat-3999	31	57	cosmic	cosmic	ADJ
easat-3999	31	58	explosion	explosion	NOUN
easat-3999	31	59	.	.	PUNCT
easat-3999	32	1	this	this	DET
easat-3999	32	2	picture	picture	NOUN
easat-3999	32	3	was	be	AUX
easat-3999	32	4	further	far	ADV
easat-3999	32	5	refined	refine	VERB
easat-3999	32	6	and	and	CCONJ
easat-3999	32	7	developed	develop	VERB
easat-3999	32	8	to	to	PART
easat-3999	32	9	account	account	VERB
easat-3999	32	10	for	for	ADP
easat-3999	32	11	the	the	DET
easat-3999	32	12	large	large	ADJ
easat-3999	32	13	-	-	PUNCT
easat-3999	32	14	scale	scale	NOUN
easat-3999	32	15	properties	property	NOUN
easat-3999	32	16	—	—	PUNCT
easat-3999	32	17	such	such	ADJ
easat-3999	32	18	as	as	ADP
easat-3999	32	19	the	the	DET
easat-3999	32	20	expansion	expansion	NOUN
easat-3999	32	21	rate	rate	NOUN
easat-3999	32	22	,	,	PUNCT
easat-3999	32	23	age	age	NOUN
easat-3999	32	24	,	,	PUNCT
easat-3999	32	25	and	and	CCONJ
easat-3999	32	26	density	density	NOUN
easat-3999	32	27	structures	structure	NOUN
easat-3999	32	28	—	—	PUNCT
easat-3999	32	29	that	that	SCONJ
easat-3999	32	30	we	we	PRON
easat-3999	32	31	observe	observe	VERB
easat-3999	32	32	today	today	NOUN
easat-3999	32	33	.	.	PUNCT
easat-3999	33	1	some	some	PRON
easat-3999	33	2	of	of	ADP
easat-3999	33	3	these	these	DET
easat-3999	33	4	developments	development	NOUN
easat-3999	33	5	in	in	ADP
easat-3999	33	6	physical	physical	ADJ
easat-3999	33	7	cosmology	cosmology	NOUN
easat-3999	33	8	will	will	AUX
easat-3999	33	9	be	be	AUX
easat-3999	33	10	the	the	DET
easat-3999	33	11	subject	subject	NOUN
easat-3999	33	12	of	of	ADP
easat-3999	33	13	the	the	DET
easat-3999	33	14	present	present	ADJ
easat-3999	33	15	lecture	lecture	NOUN
easat-3999	33	16	.	.	PUNCT
easat-3999	34	1	ancient	ancient	ADJ
easat-3999	34	2	greece	greece	PROPN
easat-3999	34	3	is	be	AUX
easat-3999	34	4	rightly	rightly	ADV
easat-3999	34	5	celebrated	celebrate	VERB
easat-3999	34	6	for	for	ADP
easat-3999	34	7	the	the	DET
easat-3999	34	8	combative	combative	ADJ
easat-3999	34	9	spirit	spirit	NOUN
easat-3999	34	10	of	of	ADP
easat-3999	34	11	intellectual	intellectual	ADJ
easat-3999	34	12	inquiry	inquiry	NOUN
easat-3999	34	13	that	that	PRON
easat-3999	34	14	defined	define	VERB
easat-3999	34	15	its	its	PRON
easat-3999	34	16	philosophers	philosopher	NOUN
easat-3999	34	17	,	,	PUNCT
easat-3999	34	18	states	state	NOUN
easat-3999	34	19	,	,	PUNCT
easat-3999	34	20	and	and	CCONJ
easat-3999	34	21	everyday	everyday	ADJ
easat-3999	34	22	citizens	citizen	NOUN
easat-3999	34	23	.	.	PUNCT
easat-3999	35	1	pretence	pretence	NOUN
easat-3999	35	2	and	and	CCONJ
easat-3999	35	3	speculation	speculation	NOUN
easat-3999	35	4	were	be	AUX
easat-3999	35	5	encouraged	encourage	VERB
easat-3999	35	6	,	,	PUNCT
easat-3999	35	7	and	and	CCONJ
easat-3999	35	8	argument	argument	NOUN
easat-3999	35	9	was	be	AUX
easat-3999	35	10	held	hold	VERB
easat-3999	35	11	as	as	ADP
easat-3999	35	12	an	an	DET
easat-3999	35	13	active	active	ADJ
easat-3999	35	14	ingredient	ingredient	NOUN
easat-3999	35	15	of	of	ADP
easat-3999	35	16	progress	progress	NOUN
easat-3999	35	17	.	.	PUNCT
easat-3999	36	1	perplexity	perplexity	NOUN
easat-3999	36	2	also	also	ADV
easat-3999	36	3	abounded	abound	VERB
easat-3999	36	4	in	in	ADP
easat-3999	36	5	the	the	DET
easat-3999	36	6	faces	face	NOUN
easat-3999	36	7	of	of	ADP
easat-3999	36	8	these	these	DET
easat-3999	36	9	thinkers	thinker	NOUN
easat-3999	36	10	,	,	PUNCT
easat-3999	36	11	given	give	VERB
easat-3999	36	12	the	the	DET
easat-3999	36	13	reach	reach	NOUN
easat-3999	36	14	and	and	CCONJ
easat-3999	36	15	power	power	NOUN
easat-3999	36	16	of	of	ADP
easat-3999	36	17	the	the	DET
easat-3999	36	18	phenomena	phenomenon	NOUN
easat-3999	36	19	that	that	PRON
easat-3999	36	20	surrounded	surround	VERB
easat-3999	36	21	them	they	PRON
easat-3999	36	22	,	,	PUNCT
easat-3999	36	23	and	and	CCONJ
easat-3999	36	24	because	because	SCONJ
easat-3999	36	25	there	there	PRON
easat-3999	36	26	was	be	VERB
easat-3999	36	27	no	no	DET
easat-3999	36	28	distinct	distinct	ADJ
easat-3999	36	29	profession	profession	NOUN
easat-3999	36	30	of	of	ADP
easat-3999	36	31	science	science	NOUN
easat-3999	36	32	.	.	PUNCT
easat-3999	37	1	how	how	SCONJ
easat-3999	37	2	were	be	AUX
easat-3999	37	3	matters	matter	NOUN
easat-3999	37	4	formed	form	VERB
easat-3999	37	5	and	and	CCONJ
easat-3999	37	6	where	where	SCONJ
easat-3999	37	7	did	do	AUX
easat-3999	37	8	they	they	PRON
easat-3999	37	9	go	go	VERB
easat-3999	37	10	?	?	PUNCT
easat-3999	38	1	what	what	PRON
easat-3999	38	2	were	be	AUX
easat-3999	38	3	the	the	DET
easat-3999	38	4	eternal	eternal	ADJ
easat-3999	38	5	,	,	PUNCT
easat-3999	38	6	underlying	underlying	ADJ
easat-3999	38	7	elements	element	NOUN
easat-3999	38	8	of	of	ADP
easat-3999	38	9	reality	reality	NOUN
easat-3999	38	10	?	?	PUNCT
easat-3999	39	1	what	what	PRON
easat-3999	39	2	was	be	AUX
easat-3999	39	3	the	the	DET
easat-3999	39	4	ordered	ordered	ADJ
easat-3999	39	5	basis	basis	NOUN
easat-3999	39	6	of	of	ADP
easat-3999	39	7	the	the	DET
easat-3999	39	8	cosmos	cosmos	PROPN
easat-3999	39	9	?	?	PUNCT
easat-3999	40	1	what	what	PRON
easat-3999	40	2	was	be	AUX
easat-3999	40	3	the	the	DET
easat-3999	40	4	nature	nature	NOUN
easat-3999	40	5	of	of	ADP
easat-3999	40	6	the	the	DET
easat-3999	40	7	stars	star	NOUN
easat-3999	40	8	,	,	PUNCT
easat-3999	40	9	especially	especially	ADV
easat-3999	40	10	the	the	DET
easat-3999	40	11	wandering	wander	VERB
easat-3999	40	12	ones	one	NOUN
easat-3999	40	13	?	?	PUNCT
easat-3999	41	1	what	what	PRON
easat-3999	41	2	were	be	AUX
easat-3999	41	3	their	their	PRON
easat-3999	41	4	distances	distance	NOUN
easat-3999	41	5	and	and	CCONJ
easat-3999	41	6	their	their	PRON
easat-3999	41	7	impacts	impact	NOUN
easat-3999	41	8	on	on	ADP
easat-3999	41	9	the	the	DET
easat-3999	41	10	human	human	ADJ
easat-3999	41	11	condition	condition	NOUN
easat-3999	41	12	?	?	PUNCT
easat-3999	42	1	remarkable	remarkable	ADJ
easat-3999	42	2	theories	theory	NOUN
easat-3999	42	3	emerged	emerge	VERB
easat-3999	42	4	through	through	ADP
easat-3999	42	5	evolving	evolve	VERB
easat-3999	42	6	traditions	tradition	NOUN
easat-3999	42	7	of	of	ADP
easat-3999	42	8	logic	logic	NOUN
easat-3999	42	9	that	that	PRON
easat-3999	42	10	,	,	PUNCT
easat-3999	42	11	studied	study	VERB
easat-3999	42	12	today	today	NOUN
easat-3999	42	13	,	,	PUNCT
easat-3999	42	14	are	be	AUX
easat-3999	42	15	much	much	ADV
easat-3999	42	16	more	more	ADV
easat-3999	42	17	wide	wide	ADV
easat-3999	42	18	-	-	PUNCT
easat-3999	42	19	ranging	range	VERB
easat-3999	42	20	and	and	CCONJ
easat-3999	42	21	powerful	powerful	ADJ
easat-3999	42	22	than	than	ADP
easat-3999	42	23	usually	usually	ADV
easat-3999	42	24	appreciated	appreciate	VERB
easat-3999	42	25	.	.	PUNCT
easat-3999	43	1	to	to	PART
easat-3999	43	2	cite	cite	VERB
easat-3999	43	3	one	one	NUM
easat-3999	43	4	example	example	NOUN
easat-3999	43	5	,	,	PUNCT
easat-3999	43	6	euclidean	euclidean	ADJ
easat-3999	43	7	geometry	geometry	NOUN
easat-3999	43	8	at	at	ADP
easat-3999	43	9	first	first	ADJ
easat-3999	43	10	glance	glance	NOUN
easat-3999	43	11	may	may	AUX
easat-3999	43	12	appear	appear	VERB
easat-3999	43	13	to	to	ADP
easat-3999	43	14	concern	concern	NOUN
easat-3999	43	15	only	only	ADV
easat-3999	43	16	dry	dry	ADJ
easat-3999	43	17	images	image	NOUN
easat-3999	43	18	on	on	ADP
easat-3999	43	19	charts	chart	NOUN
easat-3999	43	20	of	of	ADP
easat-3999	43	21	lines	line	NOUN
easat-3999	43	22	,	,	PUNCT
easat-3999	43	23	circles	circle	NOUN
easat-3999	43	24	,	,	PUNCT
easat-3999	43	25	triangles	triangle	NOUN
easat-3999	43	26	,	,	PUNCT
easat-3999	43	27	pentagons	pentagon	NOUN
easat-3999	43	28	,	,	PUNCT
easat-3999	43	29	and	and	CCONJ
easat-3999	43	30	other	other	ADJ
easat-3999	43	31	shapes	shape	NOUN
easat-3999	43	32	.	.	PUNCT
easat-3999	44	1	however	however	ADV
easat-3999	44	2	,	,	PUNCT
easat-3999	44	3	its	its	PRON
easat-3999	44	4	reasoning	reasoning	NOUN
easat-3999	44	5	is	be	AUX
easat-3999	44	6	also	also	ADV
easat-3999	44	7	indispensable	indispensable	ADJ
easat-3999	44	8	for	for	ADP
easat-3999	44	9	comprehending	comprehend	VERB
easat-3999	44	10	the	the	DET
easat-3999	44	11	patterns	pattern	NOUN
easat-3999	44	12	and	and	CCONJ
easat-3999	44	13	symmetries	symmetry	NOUN
easat-3999	44	14	of	of	ADP
easat-3999	44	15	electrostatics	electrostatic	NOUN
easat-3999	44	16	,	,	PUNCT
easat-3999	44	17	magnetostatics	magnetostatic	NOUN
easat-3999	44	18	,	,	PUNCT
easat-3999	44	19	the	the	DET
easat-3999	44	20	refractions	refraction	NOUN
easat-3999	44	21	of	of	ADP
easat-3999	44	22	lenses	lense	NOUN
easat-3999	44	23	and	and	CCONJ
easat-3999	44	24	mirrors	mirror	NOUN
easat-3999	44	25	,	,	PUNCT
easat-3999	44	26	the	the	DET
easat-3999	44	27	visual	visual	ADJ
easat-3999	44	28	experience	experience	NOUN
easat-3999	44	29	of	of	ADP
easat-3999	44	30	moving	move	VERB
easat-3999	44	31	trains	train	NOUN
easat-3999	44	32	or	or	CCONJ
easat-3999	44	33	riding	ride	VERB
easat-3999	44	34	on	on	ADP
easat-3999	44	35	atomic	atomic	ADJ
easat-3999	44	36	nuclei	nucleus	NOUN
easat-3999	44	37	,	,	PUNCT
easat-3999	44	38	much	much	ADJ
easat-3999	44	39	of	of	ADP
easat-3999	44	40	the	the	DET
easat-3999	44	41	behavior	behavior	NOUN
easat-3999	44	42	of	of	ADP
easat-3999	44	43	waves	wave	NOUN
easat-3999	44	44	in	in	ADP
easat-3999	44	45	the	the	DET
easat-3999	44	46	sea	sea	NOUN
easat-3999	44	47	and	and	CCONJ
easat-3999	44	48	air	air	NOUN
easat-3999	44	49	,	,	PUNCT
easat-3999	44	50	and	and	CCONJ
easat-3999	44	51	multiple	multiple	ADJ
easat-3999	44	52	properties	property	NOUN
easat-3999	44	53	of	of	ADP
easat-3999	44	54	space	space	NOUN
easat-3999	44	55	-	-	PUNCT
easat-3999	44	56	time	time	NOUN
easat-3999	44	57	straddling	straddle	VERB
easat-3999	44	58	astronomy	astronomy	NOUN
easat-3999	44	59	,	,	PUNCT
easat-3999	44	60	theoretical	theoretical	ADJ
easat-3999	44	61	physics	physics	NOUN
easat-3999	44	62	,	,	PUNCT
easat-3999	44	63	and	and	CCONJ
easat-3999	44	64	general	general	ADJ
easat-3999	44	65	relativity	relativity	NOUN
easat-3999	44	66	.	.	PUNCT
easat-3999	45	1	the	the	DET
easat-3999	45	2	miletians	miletian	NOUN
easat-3999	45	3	,	,	PUNCT
easat-3999	45	4	thales	thales	PROPN
easat-3999	45	5	,	,	PUNCT
easat-3999	45	6	anaximander	anaximander	NOUN
easat-3999	45	7	,	,	PUNCT
easat-3999	45	8	and	and	CCONJ
easat-3999	45	9	anaximenes	anaximene	NOUN
easat-3999	45	10	assigned	assign	VERB
easat-3999	45	11	elemental	elemental	ADJ
easat-3999	45	12	roles	role	NOUN
easat-3999	45	13	of	of	ADP
easat-3999	45	14	reality	reality	NOUN
easat-3999	45	15	,	,	PUNCT
easat-3999	45	16	respectively	respectively	ADV
easat-3999	45	17	,	,	PUNCT
easat-3999	45	18	to	to	ADP
easat-3999	45	19	water	water	NOUN
easat-3999	45	20	,	,	PUNCT
easat-3999	45	21	an	an	DET
easat-3999	45	22	undefined	undefined	ADJ
easat-3999	45	23	substance	substance	NOUN
easat-3999	45	24	,	,	PUNCT
easat-3999	45	25	and	and	CCONJ
easat-3999	45	26	air	air	NOUN
easat-3999	45	27	.	.	PUNCT
easat-3999	46	1	they	they	PRON
easat-3999	46	2	studied	study	VERB
easat-3999	46	3	the	the	DET
easat-3999	46	4	transformations	transformation	NOUN
easat-3999	46	5	of	of	ADP
easat-3999	46	6	the	the	DET
easat-3999	46	7	elements	element	NOUN
easat-3999	46	8	between	between	ADP
easat-3999	46	9	the	the	DET
easat-3999	46	10	gaseous	gaseous	ADJ
easat-3999	46	11	,	,	PUNCT
easat-3999	46	12	liquid	liquid	NOUN
easat-3999	46	13	,	,	PUNCT
easat-3999	46	14	and	and	CCONJ
easat-3999	46	15	solid	solid	ADJ
easat-3999	46	16	states	state	NOUN
easat-3999	46	17	,	,	PUNCT
easat-3999	46	18	and	and	CCONJ
easat-3999	46	19	assigned	assign	VERB
easat-3999	46	20	cosmic	cosmic	ADJ
easat-3999	46	21	,	,	PUNCT
easat-3999	46	22	unifying	unify	VERB
easat-3999	46	23	sway	sway	NOUN
easat-3999	46	24	to	to	ADP
easat-3999	46	25	them	they	PRON
easat-3999	46	26	.	.	PUNCT
easat-3999	47	1	thales	thales	PROPN
easat-3999	47	2	postulated	postulate	VERB
easat-3999	47	3	liquid	liquid	NOUN
easat-3999	47	4	as	as	ADP
easat-3999	47	5	the	the	DET
easat-3999	47	6	essence	essence	NOUN
easat-3999	47	7	,	,	PUNCT
easat-3999	47	8	with	with	ADP
easat-3999	47	9	metal	metal	NOUN
easat-3999	47	10	,	,	PUNCT
easat-3999	47	11	stone	stone	NOUN
easat-3999	47	12	,	,	PUNCT
easat-3999	47	13	earth	earth	NOUN
easat-3999	47	14	,	,	PUNCT
easat-3999	47	15	and	and	CCONJ
easat-3999	47	16	the	the	DET
easat-3999	47	17	starry	starry	ADJ
easat-3999	47	18	abyss	abyss	NOUN
easat-3999	47	19	being	be	AUX
easat-3999	47	20	its	its	PRON
easat-3999	47	21	frozen	frozen	ADJ
easat-3999	47	22	,	,	PUNCT
easat-3999	47	23	liquid	liquid	ADJ
easat-3999	47	24	reflections	reflection	NOUN
easat-3999	47	25	.	.	PUNCT
easat-3999	48	1	upon	upon	SCONJ
easat-3999	48	2	a	a	DET
easat-3999	48	3	circle	circle	NOUN
easat-3999	48	4	,	,	PUNCT
easat-3999	48	5	a	a	DET
easat-3999	48	6	triangle	triangle	NOUN
easat-3999	48	7	can	can	AUX
easat-3999	48	8	be	be	AUX
easat-3999	48	9	built	build	VERB
easat-3999	48	10	whose	whose	DET
easat-3999	48	11	angles	angle	NOUN
easat-3999	48	12	are	be	AUX
easat-3999	48	13	all	all	ADV
easat-3999	48	14	right	right	ADJ
easat-3999	48	15	angles	angle	NOUN
easat-3999	48	16	.	.	PUNCT
easat-3999	49	1	these	these	DET
easat-3999	49	2	attributes	attribute	NOUN
easat-3999	49	3	can	can	AUX
easat-3999	49	4	not	not	PART
easat-3999	49	5	hold	hold	VERB
easat-3999	49	6	together	together	ADV
easat-3999	49	7	in	in	ADP
easat-3999	49	8	finite	finite	ADJ
easat-3999	49	9	,	,	PUNCT
easat-3999	49	10	flat	flat	ADJ
easat-3999	49	11	space	space	NOUN
easat-3999	49	12	.	.	PUNCT
easat-3999	50	1	realizable	realizable	ADJ
easat-3999	50	2	space	space	NOUN
easat-3999	50	3	-	-	PUNCT
easat-3999	50	4	time	time	NOUN
easat-3999	50	5	must	must	AUX
easat-3999	50	6	be	be	AUX
easat-3999	50	7	curved	curve	VERB
easat-3999	50	8	or	or	CCONJ
easat-3999	50	9	extend	extend	VERB
easat-3999	50	10	infinitely	infinitely	ADV
easat-3999	50	11	far	far	ADV
easat-3999	50	12	in	in	ADP
easat-3999	50	13	any	any	DET
easat-3999	50	14	direction	direction	NOUN
easat-3999	50	15	.	.	PUNCT
easat-3999	51	1	each	each	PRON
easat-3999	51	2	of	of	ADP
easat-3999	51	3	these	these	DET
easat-3999	51	4	proposals	proposal	NOUN
easat-3999	51	5	has	have	VERB
easat-3999	51	6	its	its	PRON
easat-3999	51	7	characteristic	characteristic	ADJ
easat-3999	51	8	set	set	NOUN
easat-3999	51	9	of	of	ADP
easat-3999	51	10	limitations	limitation	NOUN
easat-3999	51	11	and	and	CCONJ
easat-3999	51	12	strengths	strength	NOUN
easat-3999	51	13	in	in	ADP
easat-3999	51	14	terms	term	NOUN
easat-3999	51	15	of	of	ADP
easat-3999	51	16	testability	testability	NOUN
easat-3999	51	17	and	and	CCONJ
easat-3999	51	18	overall	overall	ADJ
easat-3999	51	19	coherence	coherence	NOUN
easat-3999	51	20	.	.	PUNCT
easat-3999	52	1	common	common	ADJ
easat-3999	52	2	to	to	ADP
easat-3999	52	3	all	all	PRON
easat-3999	52	4	is	be	AUX
easat-3999	52	5	the	the	DET
easat-3999	52	6	vital	vital	ADJ
easat-3999	52	7	step	step	NOUN
easat-3999	52	8	of	of	ADP
easat-3999	52	9	using	use	VERB
easat-3999	52	10	ancient	ancient	ADJ
easat-3999	52	11	geometries	geometry	NOUN
easat-3999	52	12	for	for	ADP
easat-3999	52	13	the	the	DET
easat-3999	52	14	preliminary	preliminary	ADJ
easat-3999	52	15	construction	construction	NOUN
easat-3999	52	16	of	of	ADP
easat-3999	52	17	validation	validation	NOUN
easat-3999	52	18	models	model	NOUN
easat-3999	52	19	,	,	PUNCT
easat-3999	52	20	capable	capable	ADJ
easat-3999	52	21	of	of	ADP
easat-3999	52	22	predicting	predict	VERB
easat-3999	52	23	events	event	NOUN
easat-3999	52	24	beyond	beyond	ADP
easat-3999	52	25	the	the	DET
easat-3999	52	26	usually	usually	ADV
easat-3999	52	27	examined	examine	VERB
easat-3999	52	28	smallness	smallness	NOUN
easat-3999	52	29	of	of	ADP
easat-3999	52	30	the	the	DET
easat-3999	52	31	nearby	nearby	ADJ
easat-3999	52	32	(	(	PUNCT
easat-3999	52	33	bennett	bennett	PROPN
easat-3999	52	34	,	,	PUNCT
easat-3999	52	35	2017	2017	NUM
easat-3999	52	36	;	;	PUNCT
easat-3999	52	37	cerri	cerri	NOUN
easat-3999	52	38	,	,	PUNCT
easat-3999	52	39	2017	2017	NUM
easat-3999	52	40	;	;	PUNCT
easat-3999	52	41	kandic	kandic	ADJ
easat-3999	52	42	,	,	PUNCT
easat-3999	52	43	2023	2023	NUM
easat-3999	52	44	)	)	PUNCT
easat-3999	52	45	.	.	PUNCT
easat-3999	53	1	3	3	X
easat-3999	53	2	.	.	X
easat-3999	53	3	methodology	methodology	NOUN
easat-3999	53	4	the	the	DET
easat-3999	53	5	current	current	ADJ
easat-3999	53	6	methodology	methodology	NOUN
easat-3999	53	7	is	be	AUX
easat-3999	53	8	based	base	VERB
easat-3999	53	9	on	on	ADP
easat-3999	53	10	mathematical	mathematical	ADJ
easat-3999	53	11	axiomatic	axiomatic	ADJ
easat-3999	53	12	physics	physics	NOUN
easat-3999	53	13	,	,	PUNCT
easat-3999	53	14	then	then	ADV
easat-3999	53	15	on	on	ADP
easat-3999	53	16	philosophy	philosophy	NOUN
easat-3999	53	17	,	,	PUNCT
easat-3999	53	18	mathematics	mathematic	NOUN
easat-3999	53	19	,	,	PUNCT
easat-3999	53	20	physics	physics	NOUN
easat-3999	53	21	and	and	CCONJ
easat-3999	53	22	logic	logic	NOUN
easat-3999	53	23	.	.	PUNCT
easat-3999	54	1	for	for	SCONJ
easat-3999	54	2	the	the	DET
easat-3999	54	3	data	datum	NOUN
easat-3999	54	4	is	be	AUX
easat-3999	54	5	used	use	VERB
easat-3999	54	6	the	the	DET
easat-3999	54	7	well	well	ADV
easat-3999	54	8	-	-	PUNCT
easat-3999	54	9	known	know	VERB
easat-3999	54	10	literature	literature	NOUN
easat-3999	54	11	review	review	NOUN
easat-3999	54	12	(	(	PUNCT
easat-3999	54	13	challoumis	challoumis	PROPN
easat-3999	54	14	,	,	PUNCT
easat-3999	54	15	2024b	2024b	NUM
easat-3999	54	16	,	,	PUNCT
easat-3999	54	17	2024a	2024a	NUM
easat-3999	54	18	,	,	PUNCT
easat-3999	54	19	2024c	2024c	NUM
easat-3999	54	20	)	)	PUNCT
easat-3999	54	21	.	.	PUNCT
easat-3999	55	1	in	in	ADP
easat-3999	55	2	their	their	PRON
easat-3999	55	3	approach	approach	NOUN
easat-3999	55	4	,	,	PUNCT
easat-3999	55	5	the	the	DET
easat-3999	55	6	methodology	methodology	NOUN
easat-3999	55	7	will	will	AUX
easat-3999	55	8	be	be	AUX
easat-3999	55	9	based	base	VERB
easat-3999	55	10	on	on	ADP
easat-3999	55	11	the	the	DET
easat-3999	55	12	most	most	ADV
easat-3999	55	13	fundamental	fundamental	ADJ
easat-3999	55	14	concepts	concept	NOUN
easat-3999	55	15	of	of	ADP
easat-3999	55	16	mathematical	mathematical	ADJ
easat-3999	55	17	axiomatic	axiomatic	ADJ
easat-3999	55	18	physics	physic	NOUN
easat-3999	55	19	,	,	PUNCT
easat-3999	55	20	considering	consider	VERB
easat-3999	55	21	that	that	SCONJ
easat-3999	55	22	this	this	DET
easat-3999	55	23	framework	framework	NOUN
easat-3999	55	24	puts	put	VERB
easat-3999	55	25	heavy	heavy	ADJ
easat-3999	55	26	emphasis	emphasis	NOUN
easat-3999	55	27	on	on	ADP
easat-3999	55	28	rigorous	rigorous	ADJ
easat-3999	55	29	axiomatic	axiomatic	ADJ
easat-3999	55	30	structures	structure	NOUN
easat-3999	55	31	in	in	ADP
easat-3999	55	32	describing	describe	VERB
easat-3999	55	33	and	and	CCONJ
easat-3999	55	34	analyzing	analyze	VERB
easat-3999	55	35	the	the	DET
easat-3999	55	36	physical	physical	ADJ
easat-3999	55	37	universe	universe	NOUN
easat-3999	55	38	.	.	PUNCT
easat-3999	56	1	this	this	DET
easat-3999	56	2	approach	approach	NOUN
easat-3999	56	3	is	be	AUX
easat-3999	56	4	embedded	embed	VERB
easat-3999	56	5	in	in	ADP
easat-3999	56	6	the	the	DET
easat-3999	56	7	formalization	formalization	NOUN
easat-3999	56	8	of	of	ADP
easat-3999	56	9	the	the	DET
easat-3999	56	10	laws	law	NOUN
easat-3999	56	11	of	of	ADP
easat-3999	56	12	nature	nature	NOUN
easat-3999	56	13	in	in	ADP
easat-3999	56	14	mathematical	mathematical	ADJ
easat-3999	56	15	terms	term	NOUN
easat-3999	56	16	,	,	PUNCT
easat-3999	56	17	ensuring	ensure	VERB
easat-3999	56	18	consistency	consistency	NOUN
easat-3999	56	19	,	,	PUNCT
easat-3999	56	20	generality	generality	NOUN
easat-3999	56	21	,	,	PUNCT
easat-3999	56	22	and	and	CCONJ
easat-3999	56	23	logical	logical	ADJ
easat-3999	56	24	soundness	soundness	NOUN
easat-3999	56	25	at	at	ADP
easat-3999	56	26	all	all	DET
easat-3999	56	27	instances	instance	NOUN
easat-3999	56	28	of	of	ADP
easat-3999	56	29	theory	theory	NOUN
easat-3999	56	30	formulation	formulation	NOUN
easat-3999	56	31	.	.	PUNCT
easat-3999	57	1	aiming	aim	VERB
easat-3999	57	2	from	from	ADP
easat-3999	57	3	well	well	ADV
easat-3999	57	4	-	-	PUNCT
easat-3999	57	5	defined	define	VERB
easat-3999	57	6	axioms	axiom	NOUN
easat-3999	57	7	,	,	PUNCT
easat-3999	57	8	this	this	DET
easat-3999	57	9	approach	approach	NOUN
easat-3999	57	10	should	should	AUX
easat-3999	57	11	enable	enable	VERB
easat-3999	57	12	the	the	DET
easat-3999	57	13	derivation	derivation	NOUN
easat-3999	57	14	of	of	ADP
easat-3999	57	15	some	some	DET
easat-3999	57	16	universal	universal	ADJ
easat-3999	57	17	truths	truth	NOUN
easat-3999	57	18	,	,	PUNCT
easat-3999	57	19	therefore	therefore	ADV
easat-3999	57	20	creating	create	VERB
easat-3999	57	21	insight	insight	NOUN
easat-3999	57	22	into	into	ADP
easat-3999	57	23	both	both	CCONJ
easat-3999	57	24	theoretical	theoretical	ADJ
easat-3999	57	25	and	and	CCONJ
easat-3999	57	26	applied	applied	ADJ
easat-3999	57	27	physics	physic	NOUN
easat-3999	57	28	.	.	PUNCT
easat-3999	58	1	building	build	VERB
easat-3999	58	2	on	on	ADP
easat-3999	58	3	this	this	PRON
easat-3999	58	4	,	,	PUNCT
easat-3999	58	5	the	the	DET
easat-3999	58	6	methodological	methodological	ADJ
easat-3999	58	7	aspect	aspect	NOUN
easat-3999	58	8	also	also	ADV
easat-3999	58	9	involves	involve	VERB
easat-3999	58	10	a	a	DET
easat-3999	58	11	philosophical	philosophical	ADJ
easat-3999	58	12	dimension	dimension	NOUN
easat-3999	58	13	in	in	ADP
easat-3999	58	14	its	its	PRON
easat-3999	58	15	conceptual	conceptual	ADJ
easat-3999	58	16	underpinning	underpinning	NOUN
easat-3999	58	17	of	of	ADP
easat-3999	58	18	physical	physical	ADJ
easat-3999	58	19	phenomena	phenomenon	NOUN
easat-3999	58	20	.	.	PUNCT
easat-3999	59	1	philosophy	philosophy	NOUN
easat-3999	59	2	serves	serve	VERB
easat-3999	59	3	as	as	ADP
easat-3999	59	4	a	a	DET
easat-3999	59	5	guide	guide	NOUN
easat-3999	59	6	for	for	ADP
easat-3999	59	7	surmising	surmise	VERB
easat-3999	59	8	the	the	DET
easat-3999	59	9	underpinning	underpinning	ADJ
easat-3999	59	10	assumptions	assumption	NOUN
easat-3999	59	11	,	,	PUNCT
easat-3999	59	12	implications	implication	NOUN
easat-3999	59	13	,	,	PUNCT
easat-3999	59	14	and	and	CCONJ
easat-3999	59	15	limits	limit	NOUN
easat-3999	59	16	of	of	ADP
easat-3999	59	17	mathematical	mathematical	ADJ
easat-3999	59	18	and	and	CCONJ
easat-3999	59	19	physical	physical	ADJ
easat-3999	59	20	modeling	modeling	NOUN
easat-3999	59	21	,	,	PUNCT
easat-3999	59	22	and	and	CCONJ
easat-3999	59	23	it	it	PRON
easat-3999	59	24	bridges	bridge	VERB
easat-3999	59	25	between	between	ADP
easat-3999	59	26	9358	9358	NUM
easat-3999	59	27	edelweiss	edelweiss	PROPN
easat-3999	59	28	applied	apply	VERB
easat-3999	59	29	science	science	NOUN
easat-3999	59	30	and	and	CCONJ
easat-3999	59	31	technology	technology	NOUN
easat-3999	59	32	issn	issn	PROPN
easat-3999	59	33	:	:	PUNCT
easat-3999	59	34	2576	2576	NUM
easat-3999	59	35	-	-	SYM
easat-3999	59	36	8484	8484	NUM
easat-3999	59	37	vol	vol	NOUN
easat-3999	59	38	.	.	PROPN
easat-3999	60	1	8	8	NUM
easat-3999	60	2	,	,	PUNCT
easat-3999	60	3	no	no	INTJ
easat-3999	60	4	.	.	NOUN
easat-3999	61	1	6	6	NUM
easat-3999	61	2	:	:	SYM
easat-3999	61	3	9356	9356	NUM
easat-3999	61	4	-	-	SYM
easat-3999	61	5	9375	9375	NUM
easat-3999	61	6	,	,	PUNCT
easat-3999	61	7	2024	2024	NUM
easat-3999	61	8	doi	doi	NOUN
easat-3999	61	9	:	:	PUNCT
easat-3999	61	10	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	61	11	©	©	PROPN
easat-3999	61	12	2024	2024	NUM
easat-3999	61	13	by	by	ADP
easat-3999	61	14	the	the	DET
easat-3999	61	15	author	author	NOUN
easat-3999	61	16	;	;	PUNCT
easat-3999	61	17	licensee	licensee	PROPN
easat-3999	61	18	learning	learning	NOUN
easat-3999	61	19	gate	gate	VERB
easat-3999	61	20	high	high	ADJ
easat-3999	61	21	-	-	PUNCT
easat-3999	61	22	level	level	NOUN
easat-3999	61	23	theory	theory	NOUN
easat-3999	61	24	and	and	CCONJ
easat-3999	61	25	concrete	concrete	ADJ
easat-3999	61	26	reality	reality	NOUN
easat-3999	61	27	.	.	PUNCT
easat-3999	62	1	in	in	ADP
easat-3999	62	2	this	this	DET
easat-3999	62	3	respect	respect	NOUN
easat-3999	62	4	,	,	PUNCT
easat-3999	62	5	questions	question	NOUN
easat-3999	62	6	regarding	regard	VERB
easat-3999	62	7	the	the	DET
easat-3999	62	8	nature	nature	NOUN
easat-3999	62	9	of	of	ADP
easat-3999	62	10	being	be	AUX
easat-3999	62	11	,	,	PUNCT
easat-3999	62	12	causation	causation	NOUN
easat-3999	62	13	,	,	PUNCT
easat-3999	62	14	and	and	CCONJ
easat-3999	62	15	epistemology	epistemology	NOUN
easat-3999	62	16	of	of	ADP
easat-3999	62	17	science	science	NOUN
easat-3999	62	18	are	be	AUX
easat-3999	62	19	tacked	tack	VERB
easat-3999	62	20	.	.	PUNCT
easat-3999	63	1	in	in	ADP
easat-3999	63	2	other	other	ADJ
easat-3999	63	3	words	word	NOUN
easat-3999	63	4	,	,	PUNCT
easat-3999	63	5	integration	integration	NOUN
easat-3999	63	6	of	of	ADP
easat-3999	63	7	mathematics	mathematic	NOUN
easat-3999	63	8	assures	assure	VERB
easat-3999	63	9	the	the	DET
easat-3999	63	10	methodology	methodology	NOUN
easat-3999	63	11	of	of	ADP
easat-3999	63	12	keeping	keep	VERB
easat-3999	63	13	the	the	DET
easat-3999	63	14	accuracy	accuracy	NOUN
easat-3999	63	15	and	and	CCONJ
easat-3999	63	16	strength	strength	NOUN
easat-3999	63	17	.	.	PUNCT
easat-3999	64	1	mathematics	mathematic	NOUN
easat-3999	64	2	acts	act	VERB
easat-3999	64	3	as	as	ADP
easat-3999	64	4	the	the	DET
easat-3999	64	5	lingua	lingua	PROPN
easat-3999	64	6	franca	franca	NOUN
easat-3999	64	7	for	for	ADP
easat-3999	64	8	describing	describe	VERB
easat-3999	64	9	any	any	DET
easat-3999	64	10	physical	physical	ADJ
easat-3999	64	11	phenomena	phenomenon	NOUN
easat-3999	64	12	;	;	PUNCT
easat-3999	64	13	thus	thus	ADV
easat-3999	64	14	,	,	PUNCT
easat-3999	64	15	it	it	PRON
easat-3999	64	16	allows	allow	VERB
easat-3999	64	17	formulating	formulate	VERB
easat-3999	64	18	equations	equation	NOUN
easat-3999	64	19	,	,	PUNCT
easat-3999	64	20	proof	proof	NOUN
easat-3999	64	21	,	,	PUNCT
easat-3999	64	22	and	and	CCONJ
easat-3999	64	23	prediction	prediction	NOUN
easat-3999	64	24	.	.	PUNCT
easat-3999	65	1	advanced	advanced	ADJ
easat-3999	65	2	mathematical	mathematical	ADJ
easat-3999	65	3	techniques	technique	NOUN
easat-3999	65	4	applied	apply	VERB
easat-3999	65	5	within	within	ADP
easat-3999	65	6	calculus	calculus	NOUN
easat-3999	65	7	,	,	PUNCT
easat-3999	65	8	differential	differential	NOUN
easat-3999	65	9	geometry	geometry	NOUN
easat-3999	65	10	,	,	PUNCT
easat-3999	65	11	and	and	CCONJ
easat-3999	65	12	algebra	algebra	NOUN
easat-3999	65	13	let	let	VERB
easat-3999	65	14	methodology	methodology	NOUN
easat-3999	65	15	fit	fit	VERB
easat-3999	65	16	all	all	DET
easat-3999	65	17	the	the	DET
easat-3999	65	18	complexity	complexity	NOUN
easat-3999	65	19	required	require	VERB
easat-3999	65	20	by	by	ADP
easat-3999	65	21	most	most	ADJ
easat-3999	65	22	of	of	ADP
easat-3999	65	23	the	the	DET
easat-3999	65	24	current	current	ADJ
easat-3999	65	25	scientific	scientific	ADJ
easat-3999	65	26	fields	field	NOUN
easat-3999	65	27	,	,	PUNCT
easat-3999	65	28	from	from	ADP
easat-3999	65	29	quantum	quantum	ADJ
easat-3999	65	30	mechanics	mechanic	NOUN
easat-3999	65	31	to	to	ADP
easat-3999	65	32	cosmology	cosmology	PROPN
easat-3999	65	33	.	.	PUNCT
easat-3999	66	1	physics	physics	NOUN
easat-3999	66	2	remains	remain	VERB
easat-3999	66	3	central	central	ADJ
easat-3999	66	4	and	and	CCONJ
easat-3999	66	5	forms	form	VERB
easat-3999	66	6	the	the	DET
easat-3999	66	7	empirical	empirical	ADJ
easat-3999	66	8	backbone	backbone	NOUN
easat-3999	66	9	of	of	ADP
easat-3999	66	10	all	all	DET
easat-3999	66	11	theoretical	theoretical	ADJ
easat-3999	66	12	constructs	construct	NOUN
easat-3999	66	13	.	.	PUNCT
easat-3999	67	1	the	the	DET
easat-3999	67	2	experimental	experimental	ADJ
easat-3999	67	3	data	datum	NOUN
easat-3999	67	4	and	and	CCONJ
easat-3999	67	5	observations	observation	NOUN
easat-3999	67	6	become	become	VERB
easat-3999	67	7	extremely	extremely	ADV
easat-3999	67	8	important	important	ADJ
easat-3999	67	9	in	in	ADP
easat-3999	67	10	testing	test	VERB
easat-3999	67	11	the	the	DET
easat-3999	67	12	hypotheses	hypothesis	NOUN
easat-3999	67	13	and	and	CCONJ
easat-3999	67	14	improving	improve	VERB
easat-3999	67	15	the	the	DET
easat-3999	67	16	models	model	NOUN
easat-3999	67	17	.	.	PUNCT
easat-3999	68	1	this	this	DET
easat-3999	68	2	approach	approach	NOUN
easat-3999	68	3	has	have	VERB
easat-3999	68	4	deep	deep	ADJ
easat-3999	68	5	grounds	ground	NOUN
easat-3999	68	6	in	in	ADP
easat-3999	68	7	understanding	understand	VERB
easat-3999	68	8	the	the	DET
easat-3999	68	9	underlying	underlying	ADJ
easat-3999	68	10	principles	principle	NOUN
easat-3999	68	11	of	of	ADP
easat-3999	68	12	classical	classical	ADJ
easat-3999	68	13	mechanics	mechanic	NOUN
easat-3999	68	14	,	,	PUNCT
easat-3999	68	15	electromagnetism	electromagnetism	NOUN
easat-3999	68	16	,	,	PUNCT
easat-3999	68	17	thermodynamics	thermodynamic	NOUN
easat-3999	68	18	,	,	PUNCT
easat-3999	68	19	and	and	CCONJ
easat-3999	68	20	quantum	quantum	NOUN
easat-3999	68	21	theory	theory	NOUN
easat-3999	68	22	for	for	ADP
easat-3999	68	23	tackling	tackle	VERB
easat-3999	68	24	traditional	traditional	ADJ
easat-3999	68	25	problems	problem	NOUN
easat-3999	68	26	and	and	CCONJ
easat-3999	68	27	new	new	ADJ
easat-3999	68	28	challenges	challenge	NOUN
easat-3999	68	29	facing	face	VERB
easat-3999	68	30	science	science	NOUN
easat-3999	68	31	.	.	PUNCT
easat-3999	69	1	coherence	coherence	NOUN
easat-3999	69	2	and	and	CCONJ
easat-3999	69	3	validity	validity	NOUN
easat-3999	69	4	are	be	AUX
easat-3999	69	5	achieved	achieve	VERB
easat-3999	69	6	through	through	ADP
easat-3999	69	7	the	the	DET
easat-3999	69	8	use	use	NOUN
easat-3999	69	9	of	of	ADP
easat-3999	69	10	logic	logic	NOUN
easat-3999	69	11	as	as	ADP
easat-3999	69	12	the	the	DET
easat-3999	69	13	guiding	guide	VERB
easat-3999	69	14	structure	structure	NOUN
easat-3999	69	15	for	for	ADP
easat-3999	69	16	reasoning	reasoning	NOUN
easat-3999	69	17	and	and	CCONJ
easat-3999	69	18	inference	inference	NOUN
easat-3999	69	19	.	.	PUNCT
easat-3999	70	1	logical	logical	ADJ
easat-3999	70	2	structures	structure	NOUN
easat-3999	70	3	are	be	AUX
easat-3999	70	4	employed	employ	VERB
easat-3999	70	5	to	to	PART
easat-3999	70	6	connect	connect	VERB
easat-3999	70	7	axioms	axiom	NOUN
easat-3999	70	8	,	,	PUNCT
easat-3999	70	9	definitions	definition	NOUN
easat-3999	70	10	,	,	PUNCT
easat-3999	70	11	and	and	CCONJ
easat-3999	70	12	theorems	theorem	NOUN
easat-3999	70	13	in	in	ADP
easat-3999	70	14	such	such	DET
easat-3999	70	15	a	a	DET
easat-3999	70	16	way	way	NOUN
easat-3999	70	17	that	that	PRON
easat-3999	70	18	the	the	DET
easat-3999	70	19	conclusions	conclusion	NOUN
easat-3999	70	20	follow	follow	VERB
easat-3999	70	21	systematically	systematically	ADV
easat-3999	70	22	from	from	ADP
easat-3999	70	23	premises	premise	NOUN
easat-3999	70	24	.	.	PUNCT
easat-3999	71	1	this	this	PRON
easat-3999	71	2	is	be	AUX
easat-3999	71	3	the	the	DET
easat-3999	71	4	logical	logical	ADJ
easat-3999	71	5	rigor	rigor	NOUN
easat-3999	71	6	that	that	PRON
easat-3999	71	7	inhibits	inhibit	VERB
easat-3999	71	8	inconsistency	inconsistency	NOUN
easat-3999	71	9	and	and	CCONJ
easat-3999	71	10	helps	help	VERB
easat-3999	71	11	in	in	ADP
easat-3999	71	12	formulating	formulate	VERB
easat-3999	71	13	predictive	predictive	ADJ
easat-3999	71	14	models	model	NOUN
easat-3999	71	15	that	that	PRON
easat-3999	71	16	correspond	correspond	VERB
easat-3999	71	17	to	to	ADP
easat-3999	71	18	the	the	DET
easat-3999	71	19	reality	reality	NOUN
easat-3999	71	20	observed	observe	VERB
easat-3999	71	21	.	.	PUNCT
easat-3999	72	1	based	base	VERB
easat-3999	72	2	on	on	ADP
easat-3999	72	3	data	datum	NOUN
easat-3999	72	4	and	and	CCONJ
easat-3999	72	5	analysis	analysis	NOUN
easat-3999	72	6	,	,	PUNCT
easat-3999	72	7	the	the	DET
easat-3999	72	8	methodology	methodology	NOUN
easat-3999	72	9	draws	draw	VERB
easat-3999	72	10	on	on	ADP
easat-3999	72	11	a	a	DET
easat-3999	72	12	wellestablished	wellestablished	ADJ
easat-3999	72	13	literature	literature	NOUN
easat-3999	72	14	review	review	NOUN
easat-3999	72	15	encompassing	encompass	VERB
easat-3999	72	16	both	both	CCONJ
easat-3999	72	17	historical	historical	ADJ
easat-3999	72	18	and	and	CCONJ
easat-3999	72	19	current	current	ADJ
easat-3999	72	20	works	work	NOUN
easat-3999	72	21	.	.	PUNCT
easat-3999	73	1	the	the	DET
easat-3999	73	2	holistic	holistic	ADJ
easat-3999	73	3	review	review	NOUN
easat-3999	73	4	not	not	PART
easat-3999	73	5	only	only	ADV
easat-3999	73	6	recognizes	recognize	VERB
easat-3999	73	7	the	the	DET
easat-3999	73	8	seminal	seminal	ADJ
easat-3999	73	9	contributions	contribution	NOUN
easat-3999	73	10	of	of	ADP
easat-3999	73	11	several	several	ADJ
easat-3999	73	12	key	key	ADJ
easat-3999	73	13	figures	figure	NOUN
easat-3999	73	14	but	but	CCONJ
easat-3999	73	15	also	also	ADV
easat-3999	73	16	integrates	integrate	VERB
easat-3999	73	17	recent	recent	ADJ
easat-3999	73	18	contributions	contribution	NOUN
easat-3999	73	19	for	for	ADP
easat-3999	73	20	the	the	DET
easat-3999	73	21	holistic	holistic	ADJ
easat-3999	73	22	view	view	NOUN
easat-3999	73	23	of	of	ADP
easat-3999	73	24	the	the	DET
easat-3999	73	25	subject	subject	NOUN
easat-3999	73	26	matter	matter	NOUN
easat-3999	73	27	.	.	PUNCT
easat-3999	74	1	the	the	DET
easat-3999	74	2	methodology	methodology	NOUN
easat-3999	74	3	at	at	ADP
easat-3999	74	4	least	least	ADJ
easat-3999	74	5	ensures	ensure	VERB
easat-3999	74	6	that	that	SCONJ
easat-3999	74	7	the	the	DET
easat-3999	74	8	findings	finding	NOUN
easat-3999	74	9	obtained	obtain	VERB
easat-3999	74	10	in	in	ADP
easat-3999	74	11	engaging	engage	VERB
easat-3999	74	12	a	a	DET
easat-3999	74	13	body	body	NOUN
easat-3999	74	14	of	of	ADP
easat-3999	74	15	knowledge	knowledge	NOUN
easat-3999	74	16	are	be	AUX
easat-3999	74	17	informed	inform	VERB
easat-3999	74	18	by	by	ADP
easat-3999	74	19	the	the	DET
easat-3999	74	20	cumulative	cumulative	ADJ
easat-3999	74	21	insights	insight	NOUN
easat-3999	74	22	of	of	ADP
easat-3999	74	23	the	the	DET
easat-3999	74	24	scientific	scientific	ADJ
easat-3999	74	25	community	community	NOUN
easat-3999	74	26	.	.	PUNCT
easat-3999	75	1	besides	besides	SCONJ
easat-3999	75	2	,	,	PUNCT
easat-3999	75	3	this	this	DET
easat-3999	75	4	multidisciplinarity	multidisciplinarity	NOUN
easat-3999	75	5	of	of	ADP
easat-3999	75	6	approach	approach	NOUN
easat-3999	75	7	and	and	CCONJ
easat-3999	75	8	synthesis	synthesis	NOUN
easat-3999	75	9	across	across	ADP
easat-3999	75	10	domains	domain	NOUN
easat-3999	75	11	come	come	VERB
easat-3999	75	12	together	together	ADV
easat-3999	75	13	in	in	ADP
easat-3999	75	14	an	an	DET
easat-3999	75	15	interesting	interesting	ADJ
easat-3999	75	16	mix	mix	NOUN
easat-3999	75	17	.	.	PUNCT
easat-3999	76	1	by	by	ADP
easat-3999	76	2	putting	put	VERB
easat-3999	76	3	together	together	ADP
easat-3999	76	4	philosophy	philosophy	NOUN
easat-3999	76	5	,	,	PUNCT
easat-3999	76	6	mathematics	mathematic	NOUN
easat-3999	76	7	,	,	PUNCT
easat-3999	76	8	physics	physics	NOUN
easat-3999	76	9	,	,	PUNCT
easat-3999	76	10	and	and	CCONJ
easat-3999	76	11	logic	logic	NOUN
easat-3999	76	12	,	,	PUNCT
easat-3999	76	13	the	the	DET
easat-3999	76	14	method	method	NOUN
easat-3999	76	15	goes	go	VERB
easat-3999	76	16	beyond	beyond	ADP
easat-3999	76	17	all	all	DET
easat-3999	76	18	boundaries	boundary	NOUN
easat-3999	76	19	to	to	PART
easat-3999	76	20	make	make	VERB
easat-3999	76	21	a	a	DET
easat-3999	76	22	versatile	versatile	ADJ
easat-3999	76	23	frame	frame	NOUN
easat-3999	76	24	capable	capable	ADJ
easat-3999	76	25	of	of	ADP
easat-3999	76	26	answering	answer	VERB
easat-3999	76	27	various	various	ADJ
easat-3999	76	28	scientific	scientific	ADJ
easat-3999	76	29	and	and	CCONJ
easat-3999	76	30	philosophical	philosophical	ADJ
easat-3999	76	31	questions	question	NOUN
easat-3999	76	32	.	.	PUNCT
easat-3999	77	1	the	the	DET
easat-3999	77	2	integrated	integrated	ADJ
easat-3999	77	3	perspective	perspective	NOUN
easat-3999	77	4	inspires	inspire	VERB
easat-3999	77	5	creativity	creativity	NOUN
easat-3999	77	6	,	,	PUNCT
easat-3999	77	7	which	which	PRON
easat-3999	77	8	aids	aid	VERB
easat-3999	77	9	cross	cross	NOUN
easat-3999	77	10	-	-	NOUN
easat-3999	77	11	pollination	pollination	NOUN
easat-3999	77	12	from	from	ADP
easat-3999	77	13	other	other	ADJ
easat-3999	77	14	disciplines	discipline	NOUN
easat-3999	77	15	in	in	ADP
easat-3999	77	16	terms	term	NOUN
easat-3999	77	17	of	of	ADP
easat-3999	77	18	concepts	concept	NOUN
easat-3999	77	19	and	and	CCONJ
easat-3999	77	20	approach	approach	NOUN
easat-3999	77	21	.	.	PUNCT
easat-3999	78	1	this	this	DET
easat-3999	78	2	current	current	ADJ
easat-3999	78	3	approach	approach	NOUN
easat-3999	78	4	is	be	AUX
easat-3999	78	5	sound	sound	ADJ
easat-3999	78	6	and	and	CCONJ
easat-3999	78	7	thorough	thorough	ADJ
easat-3999	78	8	for	for	ADP
easat-3999	78	9	the	the	DET
easat-3999	78	10	research	research	NOUN
easat-3999	78	11	and	and	CCONJ
easat-3999	78	12	understanding	understanding	NOUN
easat-3999	78	13	of	of	ADP
easat-3999	78	14	the	the	DET
easat-3999	78	15	physical	physical	ADJ
easat-3999	78	16	world	world	NOUN
easat-3999	78	17	.	.	PUNCT
easat-3999	79	1	it	it	PRON
easat-3999	79	2	relies	rely	VERB
easat-3999	79	3	on	on	ADP
easat-3999	79	4	mathematics	mathematic	NOUN
easat-3999	79	5	for	for	ADP
easat-3999	79	6	accuracy	accuracy	NOUN
easat-3999	79	7	,	,	PUNCT
easat-3999	79	8	physics	physics	NOUN
easat-3999	79	9	for	for	ADP
easat-3999	79	10	its	its	PRON
easat-3999	79	11	practical	practical	ADJ
easat-3999	79	12	awareness	awareness	NOUN
easat-3999	79	13	,	,	PUNCT
easat-3999	79	14	philosophy	philosophy	NOUN
easat-3999	79	15	for	for	ADP
easat-3999	79	16	analytical	analytical	ADJ
easat-3999	79	17	reasoning	reasoning	NOUN
easat-3999	79	18	,	,	PUNCT
easat-3999	79	19	and	and	CCONJ
easat-3999	79	20	logic	logic	NOUN
easat-3999	79	21	for	for	ADP
easat-3999	79	22	the	the	DET
easat-3999	79	23	framework	framework	NOUN
easat-3999	79	24	,	,	PUNCT
easat-3999	79	25	but	but	CCONJ
easat-3999	79	26	always	always	ADV
easat-3999	79	27	based	base	VERB
easat-3999	79	28	on	on	ADP
easat-3999	79	29	extensive	extensive	ADJ
easat-3999	79	30	research	research	NOUN
easat-3999	79	31	of	of	ADP
easat-3999	79	32	the	the	DET
easat-3999	79	33	available	available	ADJ
easat-3999	79	34	literature	literature	NOUN
easat-3999	79	35	.	.	PUNCT
easat-3999	80	1	this	this	DET
easat-3999	80	2	blend	blend	NOUN
easat-3999	80	3	of	of	ADP
easat-3999	80	4	disciplines	discipline	NOUN
easat-3999	80	5	will	will	AUX
easat-3999	80	6	ensure	ensure	VERB
easat-3999	80	7	that	that	SCONJ
easat-3999	80	8	the	the	DET
easat-3999	80	9	methodology	methodology	NOUN
easat-3999	80	10	is	be	AUX
easat-3999	80	11	both	both	PRON
easat-3999	80	12	scientifically	scientifically	ADV
easat-3999	80	13	rigorous	rigorous	ADJ
easat-3999	80	14	and	and	CCONJ
easat-3999	80	15	philosophically	philosophically	ADV
easat-3999	80	16	meaningful	meaningful	ADJ
easat-3999	80	17	,	,	PUNCT
easat-3999	80	18	capable	capable	ADJ
easat-3999	80	19	of	of	ADP
easat-3999	80	20	addressing	address	VERB
easat-3999	80	21	the	the	DET
easat-3999	80	22	complexities	complexity	NOUN
easat-3999	80	23	of	of	ADP
easat-3999	80	24	modern	modern	ADJ
easat-3999	80	25	scientific	scientific	ADJ
easat-3999	80	26	inquiry	inquiry	NOUN
easat-3999	80	27	.	.	PUNCT
easat-3999	81	1	(	(	PUNCT
easat-3999	81	2	bennett	bennett	PROPN
easat-3999	81	3	,	,	PUNCT
easat-3999	81	4	2017	2017	NUM
easat-3999	81	5	;	;	PUNCT
easat-3999	81	6	cerri	cerri	NOUN
easat-3999	81	7	,	,	PUNCT
easat-3999	81	8	2017	2017	NUM
easat-3999	81	9	;	;	PUNCT
easat-3999	81	10	disalle	disalle	NOUN
easat-3999	81	11	,	,	PUNCT
easat-3999	81	12	2006	2006	NUM
easat-3999	81	13	;	;	PUNCT
easat-3999	81	14	friedman	friedman	PROPN
easat-3999	81	15	,	,	PUNCT
easat-3999	81	16	2007	2007	NUM
easat-3999	81	17	;	;	PUNCT
easat-3999	81	18	kandic	kandic	ADJ
easat-3999	81	19	,	,	PUNCT
easat-3999	81	20	2023	2023	NUM
easat-3999	81	21	)	)	PUNCT
easat-3999	81	22	.	.	PUNCT
easat-3999	82	1	3.1	3.1	NUM
easat-3999	82	2	.	.	X
easat-3999	82	3	desmos	desmos	NOUN
easat-3999	82	4	the	the	DET
easat-3999	82	5	key	key	ADJ
easat-3999	82	6	role	role	NOUN
easat-3999	82	7	of	of	ADP
easat-3999	82	8	the	the	DET
easat-3999	82	9	𝜑𝑖	𝜑𝑖	NOUN
easat-3999	82	10	of	of	ADP
easat-3999	82	11	desmos	desmos	NOUN
easat-3999	82	12	(	(	PUNCT
easat-3999	82	13	or	or	CCONJ
easat-3999	82	14	bond	bond	NOUN
easat-3999	82	15	)	)	PUNCT
easat-3999	82	16	is	be	AUX
easat-3999	82	17	determined	determine	VERB
easat-3999	82	18	according	accord	VERB
easat-3999	82	19	to	to	ADP
easat-3999	82	20	the	the	DET
easat-3999	82	21	following	following	ADJ
easat-3999	82	22	way	way	NOUN
easat-3999	82	23	:	:	PUNCT
easat-3999	82	24	𝐸𝑖	𝐸𝑖	PROPN
easat-3999	82	25	=	=	PUNCT
easat-3999	82	26	𝑚𝑖	𝑚𝑖	ADP
easat-3999	82	27	⋅	⋅	PROPN
easat-3999	82	28	𝜑𝑖	𝜑𝑖	ADV
easat-3999	82	29	where	where	SCONJ
easat-3999	82	30	,	,	PUNCT
easat-3999	82	31	𝐸𝑖	𝐸𝑖	PROPN
easat-3999	82	32	is	be	AUX
easat-3999	82	33	the	the	DET
easat-3999	82	34	energy	energy	NOUN
easat-3999	82	35	of	of	ADP
easat-3999	82	36	a	a	DET
easat-3999	82	37	mass	mass	NOUN
easat-3999	82	38	𝑚𝑖.	𝑚𝑖.	PRON
easat-3999	82	39	𝑚𝑖	𝑚𝑖	NOUN
easat-3999	82	40	is	be	AUX
easat-3999	82	41	the	the	DET
easat-3999	82	42	mass	mass	NOUN
easat-3999	82	43	,	,	PUNCT
easat-3999	82	44	with	with	ADP
easat-3999	82	45	si	si	PROPN
easat-3999	82	46	units	unit	NOUN
easat-3999	82	47	of	of	ADP
easat-3999	82	48	kilograms	kilogram	NOUN
easat-3999	82	49	(	(	PUNCT
easat-3999	82	50	kg	kg	NOUN
easat-3999	82	51	)	)	PUNCT
easat-3999	82	52	.	.	PUNCT
easat-3999	83	1	𝜑𝑖	𝜑𝑖	ADV
easat-3999	83	2	is	be	AUX
easat-3999	83	3	some	some	DET
easat-3999	83	4	potential	potential	ADJ
easat-3999	83	5	or	or	CCONJ
easat-3999	83	6	other	other	ADJ
easat-3999	83	7	physical	physical	ADJ
easat-3999	83	8	parameter	parameter	NOUN
easat-3999	83	9	.	.	PUNCT
easat-3999	84	1	energy	energy	NOUN
easat-3999	84	2	𝐸𝑖	𝐸𝑖	PROPN
easat-3999	84	3	in	in	ADP
easat-3999	84	4	si	si	PROPN
easat-3999	84	5	units	unit	NOUN
easat-3999	84	6	is	be	AUX
easat-3999	84	7	measured	measure	VERB
easat-3999	84	8	in	in	ADP
easat-3999	84	9	joules	joules	PROPN
easat-3999	84	10	(	(	PUNCT
easat-3999	84	11	j	j	PROPN
easat-3999	84	12	)	)	PUNCT
easat-3999	84	13	.	.	PUNCT
easat-3999	85	1	since	since	SCONJ
easat-3999	85	2	:	:	PUNCT
easat-3999	85	3	𝐸𝑖	𝐸𝑖	PROPN
easat-3999	85	4	=	=	PUNCT
easat-3999	85	5	𝑚𝑖	𝑚𝑖	ADP
easat-3999	85	6	⋅	⋅	NUM
easat-3999	85	7	𝜑𝑖	𝜑𝑖	NOUN
easat-3999	85	8	[	[	X
easat-3999	85	9	𝐸𝑖	𝐸𝑖	NOUN
easat-3999	85	10	]	]	X
easat-3999	85	11	=	=	PUNCT
easat-3999	85	12	[	[	X
easat-3999	85	13	𝑚𝑖	𝑚𝑖	X
easat-3999	85	14	]	]	X
easat-3999	85	15	⋅	⋅	PROPN
easat-3999	86	1	[	[	X
easat-3999	86	2	𝜑𝑖	𝜑𝑖	NOUN
easat-3999	86	3	]	]	X
easat-3999	86	4	,	,	PUNCT
easat-3999	86	5	𝐽	𝐽	PROPN
easat-3999	86	6	=	=	PUNCT
easat-3999	87	1	𝑘𝑔	𝑘𝑔	ADJ
easat-3999	87	2	⋅	⋅	PROPN
easat-3999	88	1	[	[	X
easat-3999	88	2	𝜑𝑖	𝜑𝑖	X
easat-3999	88	3	]	]	X
easat-3999	88	4	𝑇ℎ𝑒	𝑇ℎ𝑒	PROPN
easat-3999	88	5	𝑗𝑜𝑢𝑙𝑒	𝑗𝑜𝑢𝑙𝑒	NOUN
easat-3999	88	6	(	(	PUNCT
easat-3999	88	7	𝐽)𝑖𝑠	𝐽)𝑖𝑠	PROPN
easat-3999	88	8	𝑎𝑙𝑠𝑜	𝑎𝑙𝑠𝑜	NOUN
easat-3999	88	9	𝑑𝑒𝑓𝑖𝑛𝑒𝑑	𝑑𝑒𝑓𝑖𝑛𝑒𝑑	NOUN
easat-3999	88	10	𝑎𝑠	𝑎𝑠	PROPN
easat-3999	88	11	:	:	PUNCT
easat-3999	88	12	1	1	NUM
easat-3999	88	13	𝐽	𝐽	NOUN
easat-3999	88	14	=	=	NOUN
easat-3999	88	15	1	1	NUM
easat-3999	88	16	𝑘𝑔	𝑘𝑔	ADJ
easat-3999	88	17	⋅	⋅	PROPN
easat-3999	88	18	𝑚2	𝑚2	NOUN
easat-3999	88	19	𝑠2	𝑠2	NOUN
easat-3999	88	20	so	so	ADV
easat-3999	88	21	,	,	PUNCT
easat-3999	88	22	𝑘𝑔	𝑘𝑔	ADP
easat-3999	88	23	⋅	⋅	PROPN
easat-3999	88	24	𝑚2	𝑚2	NOUN
easat-3999	88	25	𝑠2	𝑠2	NOUN
easat-3999	88	26	=	=	SYM
easat-3999	88	27	𝑘𝑔	𝑘𝑔	ADJ
easat-3999	88	28	⋅	⋅	PROPN
easat-3999	89	1	[	[	X
easat-3999	89	2	𝜑𝑖	𝜑𝑖	NOUN
easat-3999	89	3	]	]	PUNCT
easat-3999	89	4	thus	thus	ADV
easat-3999	89	5	,	,	PUNCT
easat-3999	89	6	[	[	X
easat-3999	89	7	φi	φi	ADP
easat-3999	89	8	]=	]=	NUM
easat-3999	89	9	m2	m2	PROPN
easat-3999	89	10	s2	s2	NOUN
easat-3999	89	11	so	so	ADV
easat-3999	89	12	,	,	PUNCT
easat-3999	89	13	the	the	DET
easat-3999	89	14	si	si	PROPN
easat-3999	89	15	unit	unit	NOUN
easat-3999	89	16	of	of	ADP
easat-3999	89	17	𝜑𝑖	𝜑𝑖	ADV
easat-3999	89	18	is	be	AUX
easat-3999	89	19	𝑚2	𝑚2	NOUN
easat-3999	89	20	𝑠2	𝑠2	NOUN
easat-3999	89	21	.	.	PUNCT
easat-3999	90	1	then	then	ADV
easat-3999	90	2	,	,	PUNCT
easat-3999	90	3	𝜑𝑖	𝜑𝑖	NOUN
easat-3999	90	4	=	=	PRON
easat-3999	90	5	√𝐺	√𝐺	NOUN
easat-3999	90	6	∙	∙	PROPN
easat-3999	90	7	𝑐	𝑐	PROPN
easat-3999	91	1	[	[	X
easat-3999	91	2	m	m	NOUN
easat-3999	91	3	/	/	SYM
easat-3999	91	4	s	s	X
easat-3999	91	5	]	]	PUNCT
easat-3999	91	6	9359	9359	NUM
easat-3999	91	7	edelweiss	edelweiss	PROPN
easat-3999	91	8	applied	apply	VERB
easat-3999	91	9	science	science	NOUN
easat-3999	91	10	and	and	CCONJ
easat-3999	91	11	technology	technology	NOUN
easat-3999	91	12	issn	issn	PROPN
easat-3999	91	13	:	:	PUNCT
easat-3999	91	14	2576	2576	NUM
easat-3999	91	15	-	-	SYM
easat-3999	91	16	8484	8484	NUM
easat-3999	91	17	vol	vol	NOUN
easat-3999	91	18	.	.	PROPN
easat-3999	91	19	8	8	NUM
easat-3999	91	20	,	,	PUNCT
easat-3999	91	21	no	no	INTJ
easat-3999	91	22	.	.	NOUN
easat-3999	92	1	6	6	NUM
easat-3999	92	2	:	:	SYM
easat-3999	92	3	9356	9356	NUM
easat-3999	92	4	-	-	SYM
easat-3999	92	5	9375	9375	NUM
easat-3999	92	6	,	,	PUNCT
easat-3999	92	7	2024	2024	NUM
easat-3999	92	8	doi	doi	NOUN
easat-3999	92	9	:	:	PUNCT
easat-3999	92	10	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	92	11	©	©	PROPN
easat-3999	92	12	2024	2024	NUM
easat-3999	92	13	by	by	ADP
easat-3999	92	14	the	the	DET
easat-3999	92	15	author	author	NOUN
easat-3999	92	16	;	;	PUNCT
easat-3999	92	17	licensee	licensee	NOUN
easat-3999	92	18	learning	learning	NOUN
easat-3999	92	19	gate	gate	NOUN
easat-3999	92	20	𝐹𝑔	𝐹𝑔	PROPN
easat-3999	92	21	=	=	PUNCT
easat-3999	92	22	𝑮	𝑮	PROPN
easat-3999	92	23	∙	∙	PROPN
easat-3999	92	24	𝑚1∙𝑚2	𝑚1∙𝑚2	NUM
easat-3999	92	25	𝒓2	𝒓2	NOUN
easat-3999	92	26	the	the	DET
easat-3999	92	27	parameter	parameter	NOUN
easat-3999	92	28	of	of	ADP
easat-3999	92	29	𝑓	𝑓	PRON
easat-3999	93	1	i	i	PRON
easat-3999	93	2	s	s	AUX
easat-3999	93	3	defined	define	VERB
easat-3999	93	4	as	as	SCONJ
easat-3999	93	5	follows	follow	VERB
easat-3999	93	6	,	,	PUNCT
easat-3999	93	7	in	in	ADP
easat-3999	93	8	the	the	DET
easat-3999	93	9	provided	provide	VERB
easat-3999	93	10	equation	equation	NOUN
easat-3999	93	11	:	:	PUNCT
easat-3999	93	12	∑𝛷(𝑠.	∑𝛷(𝑠.	PROPN
easat-3999	93	13	𝑑.	𝑑.	NOUN
easat-3999	93	14	,	,	PUNCT
easat-3999	93	15	𝐸1	𝐸1	PROPN
easat-3999	93	16	,	,	PUNCT
easat-3999	93	17	𝐸2	𝐸2	ADJ
easat-3999	93	18	)	)	PUNCT
easat-3999	94	1	=	=	SYM
easat-3999	94	2	𝛥	𝛥	PROPN
easat-3999	94	3	=	=	PUNCT
easat-3999	95	1	∑𝑓	∑𝑓	PRON
easat-3999	95	2	⋅	⋅	PROPN
easat-3999	95	3	(	(	PUNCT
easat-3999	95	4	∏	∏	X
easat-3999	95	5	𝑚i⋅𝜙i	𝑚i⋅𝜙i	NOUN
easat-3999	95	6	𝑚	𝑚	PROPN
easat-3999	95	7	𝑖=0	𝑖=0	PROPN
easat-3999	95	8	(	(	PUNCT
easat-3999	95	9	𝐴1⋅𝑒	𝐴1⋅𝑒	NOUN
easat-3999	95	10	−	−	PROPN
easat-3999	95	11	𝑝	𝑝	PROPN
easat-3999	95	12	𝑡1	𝑡1	PROPN
easat-3999	95	13	+	+	X
easat-3999	95	14	𝑠.𝑑.0)𝑛	𝑠.𝑑.0)𝑛	PROPN
easat-3999	95	15	)	)	PUNCT
easat-3999	95	16	assuming	assume	VERB
easat-3999	95	17	that	that	SCONJ
easat-3999	95	18	𝑓	𝑓	PRON
easat-3999	95	19	is	be	AUX
easat-3999	95	20	a	a	DET
easat-3999	95	21	dimensionless	dimensionless	NOUN
easat-3999	95	22	scaling	scale	VERB
easat-3999	95	23	factor	factor	NOUN
easat-3999	95	24	,	,	PUNCT
easat-3999	95	25	or	or	CCONJ
easat-3999	95	26	considering	consider	VERB
easat-3999	95	27	the	the	DET
easat-3999	95	28	structure	structure	NOUN
easat-3999	95	29	,	,	PUNCT
easat-3999	95	30	if	if	SCONJ
easat-3999	95	31	𝑓	𝑓	DET
easat-3999	95	32	multiplies	multiplie	NOUN
easat-3999	95	33	a	a	DET
easat-3999	95	34	term	term	NOUN
easat-3999	95	35	with	with	ADP
easat-3999	95	36	the	the	DET
easat-3999	95	37	same	same	ADJ
easat-3999	95	38	dimensions	dimension	NOUN
easat-3999	95	39	as	as	ADP
easat-3999	95	40	energy	energy	NOUN
easat-3999	95	41	,	,	PUNCT
easat-3999	95	42	𝑓	𝑓	PRON
easat-3999	95	43	itself	itself	PRON
easat-3999	95	44	is	be	AUX
easat-3999	95	45	dimensionless	dimensionless	NOUN
easat-3999	95	46	.	.	PUNCT
easat-3999	96	1	this	this	PRON
easat-3999	96	2	is	be	AUX
easat-3999	96	3	under	under	ADP
easat-3999	96	4	the	the	DET
easat-3999	96	5	concept	concept	NOUN
easat-3999	96	6	that	that	SCONJ
easat-3999	96	7	the	the	DET
easat-3999	96	8	summation	summation	NOUN
easat-3999	96	9	leads	lead	VERB
easat-3999	96	10	to	to	ADP
easat-3999	96	11	something	something	PRON
easat-3999	96	12	with	with	ADP
easat-3999	96	13	the	the	DET
easat-3999	96	14	dimension	dimension	NOUN
easat-3999	96	15	of	of	ADP
easat-3999	96	16	energy	energy	NOUN
easat-3999	96	17	,	,	PUNCT
easat-3999	96	18	and	and	CCONJ
easat-3999	96	19	𝑓	𝑓	PRON
easat-3999	96	20	adjusts	adjust	VERB
easat-3999	96	21	the	the	DET
easat-3999	96	22	magnitude	magnitude	NOUN
easat-3999	96	23	without	without	ADP
easat-3999	96	24	altering	alter	VERB
easat-3999	96	25	the	the	DET
easat-3999	96	26	physical	physical	ADJ
easat-3999	96	27	dimensions	dimension	NOUN
easat-3999	96	28	,	,	PUNCT
easat-3999	96	29	but	but	CCONJ
easat-3999	96	30	keeps	keep	VERB
easat-3999	96	31	each	each	DET
easat-3999	96	32	desmos	desmos	NOUN
easat-3999	96	33	connections	connection	NOUN
easat-3999	96	34	between	between	ADP
easat-3999	96	35	each	each	DET
easat-3999	96	36	system	system	NOUN
easat-3999	96	37	as	as	ADP
easat-3999	96	38	a	a	DET
easat-3999	96	39	fragment	fragment	NOUN
easat-3999	96	40	,	,	PUNCT
easat-3999	96	41	e.g	e.g	PROPN
easat-3999	96	42	the	the	DET
easat-3999	96	43	solar	solar	ADJ
easat-3999	96	44	system	system	NOUN
easat-3999	96	45	has	have	VERB
easat-3999	96	46	one	one	NUM
easat-3999	96	47	distinct	distinct	ADJ
easat-3999	96	48	fragment	fragment	NOUN
easat-3999	96	49	and	and	CCONJ
easat-3999	96	50	belongs	belong	VERB
easat-3999	96	51	to	to	ADP
easat-3999	96	52	another	another	DET
easat-3999	96	53	fragment	fragment	NOUN
easat-3999	96	54	of	of	ADP
easat-3999	96	55	our	our	PRON
easat-3999	96	56	galaxy	galaxy	NOUN
easat-3999	96	57	,	,	PUNCT
easat-3999	96	58	and	and	CCONJ
easat-3999	96	59	this	this	DET
easat-3999	96	60	galaxy	galaxy	NOUN
easat-3999	96	61	belongs	belong	VERB
easat-3999	96	62	to	to	ADP
easat-3999	96	63	another	another	DET
easat-3999	96	64	fragment	fragment	NOUN
easat-3999	96	65	,	,	PUNCT
easat-3999	96	66	and	and	CCONJ
easat-3999	96	67	according	accord	VERB
easat-3999	96	68	to	to	ADP
easat-3999	96	69	the	the	DET
easat-3999	96	70	that	that	DET
easat-3999	96	71	way	way	NOUN
easat-3999	96	72	everything	everything	PRON
easat-3999	96	73	are	be	AUX
easat-3999	96	74	connected	connect	VERB
easat-3999	96	75	and	and	CCONJ
easat-3999	96	76	the	the	DET
easat-3999	96	77	same	same	ADJ
easat-3999	96	78	time	time	NOUN
easat-3999	96	79	distinct	distinct	ADJ
easat-3999	96	80	forms	form	NOUN
easat-3999	96	81	.	.	PUNCT
easat-3999	97	1	thus,[𝑓	thus,[𝑓	VERB
easat-3999	97	2	]	]	PUNCT
easat-3999	97	3	=	=	SYM
easat-3999	97	4	1	1	NUM
easat-3999	97	5	,	,	PUNCT
easat-3999	97	6	it	it	PRON
easat-3999	97	7	is	be	AUX
easat-3999	97	8	dimensionless	dimensionless	NOUN
easat-3999	97	9	.	.	PUNCT
easat-3999	98	1	the	the	DET
easat-3999	98	2	parameter	parameter	NOUN
easat-3999	98	3	of	of	ADP
easat-3999	98	4	𝑘𝐵is	𝑘𝐵is	PROPN
easat-3999	98	5	determined	determine	VERB
easat-3999	98	6	as	as	SCONJ
easat-3999	98	7	follows	follow	VERB
easat-3999	98	8	:	:	PUNCT
easat-3999	98	9	n	n	CCONJ
easat-3999	98	10	the	the	DET
easat-3999	98	11	gravitational	gravitational	ADJ
easat-3999	98	12	force	force	NOUN
easat-3999	98	13	relationship	relationship	NOUN
easat-3999	98	14	:	:	PUNCT
easat-3999	98	15	𝐹𝑔	𝐹𝑔	NOUN
easat-3999	98	16	=	=	PUNCT
easat-3999	98	17	𝛥	𝛥	PROPN
easat-3999	98	18	=	=	PUNCT
easat-3999	98	19	𝑘𝐵	𝑘𝐵	ADJ
easat-3999	98	20	⋅	⋅	X
easat-3999	98	21	(	(	PUNCT
easat-3999	98	22	𝐸1⋅𝐸2	𝐸1⋅𝐸2	PROPN
easat-3999	98	23	𝑟𝑛	𝑟𝑛	NUM
easat-3999	98	24	)	)	PUNCT
easat-3999	98	25	where	where	SCONJ
easat-3999	98	26	,	,	PUNCT
easat-3999	98	27	𝐸1and	𝐸1and	PROPN
easat-3999	98	28	𝐸2are	𝐸2are	PROPN
easat-3999	98	29	the	the	DET
easat-3999	98	30	energy	energy	NOUN
easat-3999	98	31	states	state	NOUN
easat-3999	98	32	of	of	ADP
easat-3999	98	33	the	the	DET
easat-3999	98	34	two	two	NUM
easat-3999	98	35	bodies	body	NOUN
easat-3999	98	36	.	.	PUNCT
easat-3999	99	1	𝑟	𝑟	X
easat-3999	99	2	is	be	AUX
easat-3999	99	3	the	the	DET
easat-3999	99	4	distance	distance	NOUN
easat-3999	99	5	between	between	ADP
easat-3999	99	6	the	the	DET
easat-3999	99	7	two	two	NUM
easat-3999	99	8	bodies	body	NOUN
easat-3999	99	9	.	.	PUNCT
easat-3999	100	1	𝑘𝐵is	𝑘𝐵is	NOUN
easat-3999	100	2	a	a	DET
easat-3999	100	3	coefficient	coefficient	NOUN
easat-3999	100	4	describing	describe	VERB
easat-3999	100	5	the	the	DET
easat-3999	100	6	bond	bond	NOUN
easat-3999	100	7	.	.	PUNCT
easat-3999	101	1	𝑛	𝑛	PROPN
easat-3999	101	2	is	be	AUX
easat-3999	101	3	a	a	DET
easat-3999	101	4	parameter	parameter	NOUN
easat-3999	101	5	describing	describe	VERB
easat-3999	101	6	how	how	SCONJ
easat-3999	101	7	the	the	DET
easat-3999	101	8	force	force	NOUN
easat-3999	101	9	depends	depend	VERB
easat-3999	101	10	on	on	ADP
easat-3999	101	11	distance	distance	NOUN
easat-3999	101	12	,	,	PUNCT
easat-3999	101	13	which	which	PRON
easat-3999	101	14	may	may	AUX
easat-3999	101	15	differ	differ	VERB
easat-3999	101	16	from	from	ADP
easat-3999	101	17	the	the	DET
easat-3999	101	18	classical	classical	ADJ
easat-3999	101	19	relationship	relationship	NOUN
easat-3999	101	20	(	(	PUNCT
easat-3999	101	21	for	for	ADP
easat-3999	101	22	example	example	NOUN
easat-3999	101	23	,	,	PUNCT
easat-3999	101	24	𝑛	𝑛	DET
easat-3999	101	25	≠	≠	PROPN
easat-3999	101	26	2	2	NUM
easat-3999	101	27	)	)	PUNCT
easat-3999	102	1	[	[	X
easat-3999	102	2	𝐹𝑔	𝐹𝑔	NOUN
easat-3999	102	3	]	]	X
easat-3999	102	4	=	=	PUNCT
easat-3999	103	1	[	[	X
easat-3999	103	2	𝛥	𝛥	X
easat-3999	103	3	]	]	X
easat-3999	103	4	=	=	PUNCT
easat-3999	104	1	[	[	X
easat-3999	104	2	𝑘𝐵	𝑘𝐵	X
easat-3999	104	3	]	]	X
easat-3999	104	4	⋅	⋅	X
easat-3999	104	5	(	(	PUNCT
easat-3999	104	6	[	[	X
easat-3999	104	7	𝐸1]⋅[𝐸2	𝐸1]⋅[𝐸2	NOUN
easat-3999	104	8	]	]	X
easat-3999	105	1	[	[	X
easat-3999	105	2	𝑟𝑛	𝑟𝑛	X
easat-3999	105	3	]	]	PUNCT
easat-3999	105	4	)	)	PUNCT
easat-3999	105	5	clarifying	clarify	VERB
easat-3999	105	6	the	the	DET
easat-3999	105	7	units	unit	NOUN
easat-3999	105	8	:	:	PUNCT
easat-3999	105	9	𝑁	𝑁	PROPN
easat-3999	105	10	=	=	SYM
easat-3999	105	11	[	[	X
easat-3999	105	12	𝑘𝐵	𝑘𝐵	X
easat-3999	105	13	]	]	X
easat-3999	105	14	⋅	⋅	X
easat-3999	105	15	𝐽⋅𝐽	𝐽⋅𝐽	X
easat-3999	105	16	𝑚𝑛	𝑚𝑛	NOUN
easat-3999	105	17	the	the	DET
easat-3999	105	18	newton	newton	PROPN
easat-3999	105	19	(	(	PUNCT
easat-3999	105	20	n	n	CCONJ
easat-3999	105	21	)	)	PUNCT
easat-3999	105	22	is	be	AUX
easat-3999	105	23	defined	define	VERB
easat-3999	105	24	as	as	ADP
easat-3999	105	25	,	,	PUNCT
easat-3999	105	26	1	1	NUM
easat-3999	105	27	𝑁	𝑁	PROPN
easat-3999	105	28	=	=	SYM
easat-3999	105	29	1	1	NUM
easat-3999	105	30	𝑘𝑔	𝑘𝑔	ADJ
easat-3999	105	31	⋅	⋅	PROPN
easat-3999	105	32	𝑚	𝑚	ADP
easat-3999	105	33	𝑠2	𝑠2	NOUN
easat-3999	105	34	the	the	DET
easat-3999	105	35	joule	joule	NOUN
easat-3999	105	36	(	(	PUNCT
easat-3999	105	37	j	j	NOUN
easat-3999	105	38	)	)	PUNCT
easat-3999	105	39	is	be	AUX
easat-3999	105	40	,	,	PUNCT
easat-3999	105	41	1	1	NUM
easat-3999	105	42	𝐽	𝐽	NOUN
easat-3999	105	43	=	=	NOUN
easat-3999	105	44	1	1	NUM
easat-3999	105	45	𝑘𝑔	𝑘𝑔	ADJ
easat-3999	105	46	⋅	⋅	PROPN
easat-3999	105	47	𝑚2	𝑚2	NOUN
easat-3999	105	48	𝑠2	𝑠2	NOUN
easat-3999	105	49	so	so	ADV
easat-3999	105	50	,	,	PUNCT
easat-3999	105	51	𝑘𝑔	𝑘𝑔	ADP
easat-3999	105	52	⋅	⋅	PROPN
easat-3999	105	53	𝑚	𝑚	ADP
easat-3999	105	54	𝑠2	𝑠2	NOUN
easat-3999	105	55	=	=	PUNCT
easat-3999	106	1	[	[	X
easat-3999	106	2	𝑘𝐵	𝑘𝐵	X
easat-3999	106	3	]	]	X
easat-3999	106	4	⋅	⋅	X
easat-3999	106	5	(	(	PUNCT
easat-3999	106	6	𝑘𝑔⋅	𝑘𝑔⋅	NOUN
easat-3999	106	7	𝑚2	𝑚2	NOUN
easat-3999	106	8	𝑠2	𝑠2	NOUN
easat-3999	106	9	⋅𝑘𝑔⋅	⋅𝑘𝑔⋅	NOUN
easat-3999	106	10	𝑚2	𝑚2	NOUN
easat-3999	106	11	𝑠2	𝑠2	NOUN
easat-3999	106	12	𝑚𝑛	𝑚𝑛	NOUN
easat-3999	106	13	)	)	PUNCT
easat-3999	106	14	⇒	⇒	NOUN
easat-3999	106	15	𝑘𝑔	𝑘𝑔	VERB
easat-3999	106	16	⋅	⋅	PROPN
easat-3999	106	17	𝑚	𝑚	ADP
easat-3999	106	18	𝑠2	𝑠2	NOUN
easat-3999	106	19	=	=	SYM
easat-3999	106	20	〖[𝑘〗𝐵](𝑘𝑔2⋅	〖[𝑘〗𝐵](𝑘𝑔2⋅	NOUN
easat-3999	106	21	𝑚4	𝑚4	PROPN
easat-3999	106	22	𝑠4	𝑠4	PROPN
easat-3999	106	23	)	)	PUNCT
easat-3999	106	24	𝑚𝑛	𝑚𝑛	PRON
easat-3999	106	25	⇒	⇒	VERB
easat-3999	106	26	[	[	X
easat-3999	106	27	𝑘𝐵	𝑘𝐵	X
easat-3999	106	28	]	]	X
easat-3999	106	29	=	=	PUNCT
easat-3999	106	30	𝑘𝑔⋅	𝑘𝑔⋅	NOUN
easat-3999	106	31	𝑚	𝑚	ADP
easat-3999	106	32	𝑠2	𝑠2	NOUN
easat-3999	106	33	𝑘𝑔2⋅	𝑘𝑔2⋅	PROPN
easat-3999	107	1	𝑚4−𝑛	𝑚4−𝑛	PROPN
easat-3999	107	2	𝑠4	𝑠4	PROPN
easat-3999	107	3	⇒	⇒	VERB
easat-3999	107	4	[	[	X
easat-3999	107	5	𝑘𝐵	𝑘𝐵	X
easat-3999	107	6	]	]	X
easat-3999	107	7	=	=	SYM
easat-3999	107	8	1	1	NUM
easat-3999	107	9	𝑘𝑔⋅𝑚3−𝑛∙𝑠2	𝑘𝑔⋅𝑚3−𝑛∙𝑠2	PROPN
easat-3999	107	10	therefore	therefore	ADV
easat-3999	107	11	,	,	PUNCT
easat-3999	107	12	𝜙1	𝜙1	NOUN
easat-3999	107	13	,	,	PUNCT
easat-3999	107	14	𝜙2	𝜙2	PROPN
easat-3999	107	15	[	[	PUNCT
easat-3999	107	16	𝑚2	𝑚2	NOUN
easat-3999	107	17	𝑠2	𝑠2	NOUN
easat-3999	107	18	]	]	PUNCT
easat-3999	107	19	𝑓	𝑓	PRON
easat-3999	108	1	[	[	X
easat-3999	108	2	𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠	𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠	X
easat-3999	108	3	]	]	X
easat-3999	108	4	𝑘𝐵	𝑘𝐵	NOUN
easat-3999	109	1	[	[	X
easat-3999	109	2	𝑘𝑔−1	𝑘𝑔−1	X
easat-3999	109	3	∙	∙	PROPN
easat-3999	109	4	𝑚𝑛−3∙𝑠2	𝑚𝑛−3∙𝑠2	PROPN
easat-3999	109	5	]	]	PUNCT
easat-3999	109	6	connection	connection	NOUN
easat-3999	109	7	between	between	ADP
easat-3999	109	8	the	the	DET
easat-3999	109	9	desmos	desmos	NOUN
easat-3999	109	10	to	to	PART
easat-3999	109	11	form	form	NOUN
easat-3999	109	12	of	of	ADP
easat-3999	109	13	a	a	DET
easat-3999	109	14	special	special	ADJ
easat-3999	109	15	case	case	NOUN
easat-3999	109	16	like	like	ADP
easat-3999	109	17	classical	classical	ADJ
easat-3999	109	18	form	form	NOUN
easat-3999	109	19	of	of	ADP
easat-3999	109	20	gravity	gravity	NOUN
easat-3999	109	21	:	:	PUNCT
easat-3999	109	22	𝑘𝐵	𝑘𝐵	PROPN
easat-3999	109	23	=	=	PUNCT
easat-3999	109	24	𝐺	𝐺	PROPN
easat-3999	109	25	⋅	⋅	PROPN
easat-3999	109	26	𝑐𝑐ℎ	𝑐𝑐ℎ	PROPN
easat-3999	110	1	=	=	PROPN
easat-3999	110	2	𝐺	𝐺	PROPN
easat-3999	111	1	∙	∙	PROPN
easat-3999	111	2	𝑚𝑛	𝑚𝑛	PUNCT
easat-3999	112	1	∙	∙	PROPN
easat-3999	112	2	𝑘𝑔	𝑘𝑔	ADP
easat-3999	112	3	∙	∙	PROPN
easat-3999	112	4	𝑠4	𝑠4	PROPN
easat-3999	112	5	,	,	PUNCT
easat-3999	112	6	𝑛	𝑛	NOUN
easat-3999	112	7	=	=	SYM
easat-3999	112	8	2	2	NUM
easat-3999	112	9	,	,	PUNCT
easat-3999	112	10	𝜙1	𝜙1	NOUN
easat-3999	112	11	,	,	PUNCT
easat-3999	112	12	𝜙2	𝜙2	NOUN
easat-3999	112	13	=	=	SYM
easat-3999	112	14	1	1	NUM
easat-3999	112	15	estimations	estimation	NOUN
easat-3999	112	16	of	of	ADP
easat-3999	112	17	desmos	desmo	NOUN
easat-3999	112	18	are	be	AUX
easat-3999	112	19	based	base	VERB
easat-3999	112	20	on	on	ADP
easat-3999	112	21	the	the	DET
easat-3999	112	22	following	follow	VERB
easat-3999	112	23	concept	concept	NOUN
easat-3999	112	24	.	.	PUNCT
easat-3999	113	1	the	the	DET
easat-3999	113	2	distances	distance	NOUN
easat-3999	113	3	and	and	CCONJ
easat-3999	113	4	the	the	DET
easat-3999	113	5	masses	masse	NOUN
easat-3999	113	6	of	of	ADP
easat-3999	113	7	moon	moon	NOUN
easat-3999	113	8	,	,	PUNCT
easat-3999	113	9	sun	sun	NOUN
easat-3999	113	10	and	and	CCONJ
easat-3999	113	11	earth	earth	NOUN
easat-3999	113	12	are	be	AUX
easat-3999	113	13	the	the	DET
easat-3999	113	14	following	follow	VERB
easat-3999	113	15	:	:	PUNCT
easat-3999	114	1	𝑀𝐸𝑎𝑟𝑡ℎ	𝑀𝐸𝑎𝑟𝑡ℎ	PROPN
easat-3999	114	2	=	=	PUNCT
easat-3999	114	3	5.972	5.972	NUM
easat-3999	114	4	∗	∗	NOUN
easat-3999	114	5	1024𝐾𝑔	1024𝐾𝑔	NUM
easat-3999	114	6	𝑟𝐸𝑎𝑟𝑡ℎ−𝑀𝑜𝑜𝑛	𝑟𝐸𝑎𝑟𝑡ℎ−𝑀𝑜𝑜𝑛	NOUN
easat-3999	114	7	=	=	SYM
easat-3999	114	8	3.844	3.844	NUM
easat-3999	114	9	∗	∗	NOUN
easat-3999	114	10	108𝑚	108𝑚	NOUN
easat-3999	114	11	𝑀𝑀𝑜𝑜𝑛	𝑀𝑀𝑜𝑜𝑛	PUNCT
easat-3999	114	12	=	=	PUNCT
easat-3999	114	13	7.342	7.342	NUM
easat-3999	114	14	∗	∗	NOUN
easat-3999	114	15	1022𝐾𝑔	1022𝐾𝑔	NUM
easat-3999	114	16	𝑀𝑆𝑢𝑛	𝑀𝑆𝑢𝑛	NOUN
easat-3999	114	17	=	=	SYM
easat-3999	114	18	1.989	1.989	NUM
easat-3999	114	19	∗	∗	NOUN
easat-3999	114	20	1030𝐾𝑔	1030𝐾𝑔	NUM
easat-3999	114	21	9360	9360	NUM
easat-3999	114	22	edelweiss	edelweiss	PROPN
easat-3999	114	23	applied	apply	VERB
easat-3999	114	24	science	science	NOUN
easat-3999	114	25	and	and	CCONJ
easat-3999	114	26	technology	technology	NOUN
easat-3999	114	27	issn	issn	PROPN
easat-3999	114	28	:	:	PUNCT
easat-3999	114	29	2576	2576	NUM
easat-3999	114	30	-	-	SYM
easat-3999	114	31	8484	8484	NUM
easat-3999	114	32	vol	vol	NOUN
easat-3999	114	33	.	.	PROPN
easat-3999	114	34	8	8	NUM
easat-3999	114	35	,	,	PUNCT
easat-3999	114	36	no	no	INTJ
easat-3999	114	37	.	.	NOUN
easat-3999	115	1	6	6	NUM
easat-3999	115	2	:	:	SYM
easat-3999	115	3	9356	9356	NUM
easat-3999	115	4	-	-	SYM
easat-3999	115	5	9375	9375	NUM
easat-3999	115	6	,	,	PUNCT
easat-3999	115	7	2024	2024	NUM
easat-3999	115	8	doi	doi	NOUN
easat-3999	115	9	:	:	PUNCT
easat-3999	115	10	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	115	11	©	©	PROPN
easat-3999	115	12	2024	2024	NUM
easat-3999	115	13	by	by	ADP
easat-3999	115	14	the	the	DET
easat-3999	115	15	author	author	NOUN
easat-3999	115	16	;	;	PUNCT
easat-3999	115	17	licensee	licensee	NOUN
easat-3999	115	18	learning	learning	NOUN
easat-3999	115	19	gate	gate	NOUN
easat-3999	115	20	𝑟𝑀𝑜𝑜𝑛−𝑆𝑢𝑛	𝑟𝑀𝑜𝑜𝑛−𝑆𝑢𝑛	X
easat-3999	115	21	≈	≈	PROPN
easat-3999	115	22	𝑟𝐸𝑎𝑟𝑡ℎ−𝑆𝑢𝑛	𝑟𝐸𝑎𝑟𝑡ℎ−𝑆𝑢𝑛	ADP
easat-3999	115	23	=	=	NOUN
easat-3999	115	24	1.496	1.496	NUM
easat-3999	115	25	∗	∗	NOUN
easat-3999	115	26	1011𝑚	1011𝑚	NOUN
easat-3999	115	27	defining	define	VERB
easat-3999	115	28	𝜙𝑖	𝜙𝑖	ADP
easat-3999	115	29	,	,	PUNCT
easat-3999	115	30	for	for	ADP
easat-3999	115	31	the	the	DET
easat-3999	115	32	case	case	NOUN
easat-3999	115	33	of	of	ADP
easat-3999	115	34	earth	earth	NOUN
easat-3999	115	35	-	-	PUNCT
easat-3999	115	36	moon	moon	NOUN
easat-3999	115	37	:	:	PUNCT
easat-3999	115	38	𝜑𝐸𝑎𝑟𝑡ℎ	𝜑𝐸𝑎𝑟𝑡ℎ	PROPN
easat-3999	115	39	=	=	SYM
easat-3999	116	1	𝐺∙𝑀𝐸𝑎𝑟𝑡ℎ	𝐺∙𝑀𝐸𝑎𝑟𝑡ℎ	PROPN
easat-3999	116	2	𝑟𝐸𝑎𝑟𝑡ℎ−𝑀𝑜𝑜𝑛	𝑟𝐸𝑎𝑟𝑡ℎ−𝑀𝑜𝑜𝑛	NUM
easat-3999	116	3	=	=	SYM
easat-3999	116	4	6.674∗10−11∗5.972∗1024	6.674∗10−11∗5.972∗1024	NOUN
easat-3999	116	5	3.884∗108	3.884∗108	NUM
easat-3999	116	6	≈	≈	PROPN
easat-3999	116	7	1.036	1.036	NUM
easat-3999	116	8	∗	∗	NOUN
easat-3999	116	9	106	106	NUM
easat-3999	116	10	𝑚2	𝑚2	NOUN
easat-3999	116	11	𝑠2	𝑠2	NOUN
easat-3999	116	12	𝜑𝑀𝑜𝑜𝑛	𝜑𝑀𝑜𝑜𝑛	PROPN
easat-3999	116	13	=	=	SYM
easat-3999	116	14	𝐺∙𝑀𝐸𝑎𝑟𝑡ℎ	𝐺∙𝑀𝐸𝑎𝑟𝑡ℎ	PROPN
easat-3999	116	15	𝑟𝐸𝑎𝑟𝑡ℎ−𝑀𝑜𝑜𝑛	𝑟𝐸𝑎𝑟𝑡ℎ−𝑀𝑜𝑜𝑛	NUM
easat-3999	116	16	=	=	SYM
easat-3999	116	17	6.674∗10−11∗7.342∗1022	6.674∗10−11∗7.342∗1022	PROPN
easat-3999	116	18	3.884∗108	3.884∗108	NUM
easat-3999	116	19	≈	≈	PROPN
easat-3999	116	20	1.27	1.27	NUM
easat-3999	116	21	∗	∗	NOUN
easat-3999	116	22	104	104	NUM
easat-3999	116	23	𝑚2	𝑚2	NOUN
easat-3999	116	24	𝑠2	𝑠2	NOUN
easat-3999	116	25	defining	define	VERB
easat-3999	116	26	𝜙𝑖	𝜙𝑖	ADP
easat-3999	116	27	,	,	PUNCT
easat-3999	116	28	for	for	ADP
easat-3999	116	29	the	the	DET
easat-3999	116	30	case	case	NOUN
easat-3999	116	31	of	of	ADP
easat-3999	116	32	moon	moon	NOUN
easat-3999	116	33	-	-	PUNCT
easat-3999	116	34	sun	sun	NOUN
easat-3999	116	35	:	:	PUNCT
easat-3999	116	36	𝜑𝐸𝑎𝑟𝑡ℎ	𝜑𝐸𝑎𝑟𝑡ℎ	PROPN
easat-3999	116	37	=	=	PUNCT
easat-3999	117	1	𝐺∙𝑀𝑀𝑜𝑜𝑛	𝐺∙𝑀𝑀𝑜𝑜𝑛	NOUN
easat-3999	117	2	𝑟𝐸𝑎𝑟𝑡ℎ−𝑀𝑜𝑜𝑛	𝑟𝐸𝑎𝑟𝑡ℎ−𝑀𝑜𝑜𝑛	X
easat-3999	117	3	=	=	SYM
easat-3999	117	4	6.674∗10−11∗7.342∗1022	6.674∗10−11∗7.342∗1022	NOUN
easat-3999	117	5	1.496∗1011	1.496∗1011	NUM
easat-3999	118	1	≈	≈	PROPN
easat-3999	118	2	3.27	3.27	NUM
easat-3999	118	3	∗	∗	NOUN
easat-3999	118	4	10−7	10−7	NUM
easat-3999	118	5	𝑚2	𝑚2	NOUN
easat-3999	118	6	𝑠2	𝑠2	NOUN
easat-3999	119	1	𝜑𝑆𝑢𝑛	𝜑𝑆𝑢𝑛	NOUN
easat-3999	119	2	=	=	NOUN
easat-3999	119	3	𝐺∙𝑀𝑆𝑢𝑛	𝐺∙𝑀𝑆𝑢𝑛	NOUN
easat-3999	119	4	𝑟𝑀𝑜𝑜𝑛−𝑆𝑢𝑛	𝑟𝑀𝑜𝑜𝑛−𝑆𝑢𝑛	X
easat-3999	119	5	=	=	SYM
easat-3999	119	6	6.674∗10−11∗1.989∗1030	6.674∗10−11∗1.989∗1030	PROPN
easat-3999	119	7	1.496∗1011	1.496∗1011	NUM
easat-3999	120	1	≈	≈	PROPN
easat-3999	120	2	8.86	8.86	NUM
easat-3999	120	3	∗	∗	NOUN
easat-3999	120	4	108	108	NUM
easat-3999	120	5	𝑚2	𝑚2	NOUN
easat-3999	120	6	𝑠2	𝑠2	NOUN
easat-3999	120	7	calculating	calculate	VERB
easat-3999	120	8	∏	∏	PROPN
easat-3999	120	9	𝑚i	𝑚i	PROPN
easat-3999	120	10	⋅	⋅	PROPN
easat-3999	120	11	𝜙i	𝜙i	ADP
easat-3999	120	12	𝑚	𝑚	NOUN
easat-3999	120	13	𝑖=0	𝑖=0	PROPN
easat-3999	120	14	as	as	SCONJ
easat-3999	120	15	follows	follow	VERB
easat-3999	120	16	,	,	PUNCT
easat-3999	120	17	for	for	ADP
easat-3999	120	18	the	the	DET
easat-3999	120	19	case	case	NOUN
easat-3999	120	20	of	of	ADP
easat-3999	120	21	earth	earth	NOUN
easat-3999	120	22	-	-	PUNCT
easat-3999	120	23	moon	moon	NOUN
easat-3999	120	24	:	:	PUNCT
easat-3999	120	25	∏	∏	PROPN
easat-3999	120	26	𝑚i	𝑚i	PROPN
easat-3999	120	27	⋅	⋅	PROPN
easat-3999	120	28	𝜙i	𝜙i	NOUN
easat-3999	120	29	𝑚	𝑚	NOUN
easat-3999	120	30	𝑖=0	𝑖=0	PROPN
easat-3999	120	31	=	=	SYM
easat-3999	121	1	𝑀𝐸𝑎𝑟𝑡ℎ	𝑀𝐸𝑎𝑟𝑡ℎ	PROPN
easat-3999	121	2	∙	∙	PUNCT
easat-3999	121	3	𝜑𝐸𝑎𝑟𝑡ℎ	𝜑𝐸𝑎𝑟𝑡ℎ	PROPN
easat-3999	122	1	∙	∙	NOUN
easat-3999	122	2	𝑀𝑀𝑜𝑜𝑛	𝑀𝑀𝑜𝑜𝑛	PROPN
easat-3999	123	1	∙	∙	PROPN
easat-3999	123	2	𝜑𝑀𝑜𝑜𝑛	𝜑𝑀𝑜𝑜𝑛	PROPN
easat-3999	123	3	=	=	PUNCT
easat-3999	123	4	(	(	PUNCT
easat-3999	123	5	5.972	5.972	NUM
easat-3999	123	6	*	*	SYM
easat-3999	123	7	1024	1024	NUM
easat-3999	123	8	*	*	NUM
easat-3999	123	9	1.036	1.036	NUM
easat-3999	123	10	*	*	NUM
easat-3999	123	11	106	106	NUM
easat-3999	123	12	)	)	PUNCT
easat-3999	123	13	*	*	PUNCT
easat-3999	123	14	(	(	PUNCT
easat-3999	123	15	7.342	7.342	NUM
easat-3999	123	16	*	*	SYM
easat-3999	123	17	1022	1022	NUM
easat-3999	123	18	*	*	SYM
easat-3999	123	19	1.27	1.27	NUM
easat-3999	123	20	*	*	NUM
easat-3999	123	21	104	104	NUM
easat-3999	123	22	)	)	PUNCT
easat-3999	123	23	⇒	⇒	VERB
easat-3999	123	24	∏	∏	PROPN
easat-3999	123	25	𝑚i	𝑚i	PROPN
easat-3999	123	26	⋅	⋅	PROPN
easat-3999	123	27	𝜙i	𝜙i	NOUN
easat-3999	123	28	𝑚	𝑚	PROPN
easat-3999	123	29	𝑖=0	𝑖=0	PROPN
easat-3999	124	1	≈	≈	PROPN
easat-3999	124	2	5.831	5.831	NUM
easat-3999	124	3	∗	∗	NOUN
easat-3999	124	4	1057𝑘𝑔2𝑚4	1057𝑘𝑔2𝑚4	NUM
easat-3999	124	5	𝑠4	𝑠4	PROPN
easat-3999	124	6	calculating	calculate	VERB
easat-3999	124	7	∏	∏	PROPN
easat-3999	124	8	𝑚i	𝑚i	PROPN
easat-3999	124	9	⋅	⋅	PROPN
easat-3999	124	10	𝜙i	𝜙i	ADP
easat-3999	124	11	𝑚	𝑚	NOUN
easat-3999	124	12	𝑖=0	𝑖=0	PROPN
easat-3999	124	13	as	as	SCONJ
easat-3999	124	14	follows	follow	VERB
easat-3999	124	15	,	,	PUNCT
easat-3999	124	16	for	for	ADP
easat-3999	124	17	the	the	DET
easat-3999	124	18	case	case	NOUN
easat-3999	124	19	of	of	ADP
easat-3999	124	20	moon	moon	NOUN
easat-3999	124	21	-	-	PUNCT
easat-3999	124	22	sun	sun	NOUN
easat-3999	124	23	:	:	PUNCT
easat-3999	124	24	∏	∏	PROPN
easat-3999	124	25	𝑚i	𝑚i	PROPN
easat-3999	124	26	⋅	⋅	PROPN
easat-3999	124	27	𝜙i	𝜙i	NOUN
easat-3999	124	28	𝑚	𝑚	PROPN
easat-3999	125	1	𝑖=0	𝑖=0	PROPN
easat-3999	125	2	=	=	SYM
easat-3999	125	3	𝑀𝑀𝑜𝑜	𝑀𝑀𝑜𝑜	PROPN
easat-3999	126	1	∙	∙	PROPN
easat-3999	126	2	𝜑𝑀𝑜𝑜𝑛	𝜑𝑀𝑜𝑜𝑛	PROPN
easat-3999	126	3	∙	∙	PROPN
easat-3999	126	4	𝑀𝑆𝑢𝑛	𝑀𝑆𝑢𝑛	PUNCT
easat-3999	127	1	∙	∙	PROPN
easat-3999	127	2	𝜑𝑆𝑢𝑛	𝜑𝑆𝑢𝑛	PROPN
easat-3999	127	3	=	=	SYM
easat-3999	127	4	(	(	PUNCT
easat-3999	127	5	7.342	7.342	NUM
easat-3999	127	6	*	*	SYM
easat-3999	127	7	1022	1022	NUM
easat-3999	127	8	*	*	NUM
easat-3999	127	9	3.27	3.27	NUM
easat-3999	127	10	*	*	SYM
easat-3999	127	11	10−7	10−7	NUM
easat-3999	127	12	)	)	PUNCT
easat-3999	127	13	*	*	NOUN
easat-3999	127	14	(	(	PUNCT
easat-3999	127	15	1.989	1.989	NUM
easat-3999	127	16	*	*	NOUN
easat-3999	127	17	1030	1030	NUM
easat-3999	127	18	*	*	SYM
easat-3999	127	19	8.86	8.86	NUM
easat-3999	127	20	*	*	NUM
easat-3999	127	21	108	108	NUM
easat-3999	127	22	)	)	PUNCT
easat-3999	127	23	⇒	⇒	VERB
easat-3999	127	24	∏	∏	PROPN
easat-3999	127	25	𝑚i	𝑚i	PROPN
easat-3999	127	26	⋅	⋅	PROPN
easat-3999	127	27	𝜙i	𝜙i	NOUN
easat-3999	127	28	𝑚	𝑚	NOUN
easat-3999	127	29	𝑖=0	𝑖=0	PROPN
easat-3999	128	1	≈	≈	PROPN
easat-3999	128	2	4.263	4.263	NUM
easat-3999	128	3	∗	∗	NOUN
easat-3999	128	4	1054𝑘𝑔2𝑚4	1054𝑘𝑔2𝑚4	NUM
easat-3999	128	5	𝑠4	𝑠4	AUX
easat-3999	128	6	considering	consider	VERB
easat-3999	128	7	𝐴1	𝐴1	PROPN
easat-3999	128	8	=	=	SYM
easat-3999	128	9	1	1	NUM
easat-3999	128	10	,	,	PUNCT
easat-3999	128	11	𝑝	𝑝	NOUN
easat-3999	128	12	=	=	SYM
easat-3999	128	13	0	0	NUM
easat-3999	128	14	,	,	PUNCT
easat-3999	128	15	𝑠.	𝑠.	NOUN
easat-3999	128	16	𝑑.0	𝑑.0	NOUN
easat-3999	128	17	=	=	SYM
easat-3999	128	18	1𝑚	1𝑚	X
easat-3999	128	19	and	and	CCONJ
easat-3999	128	20	𝑛	𝑛	NOUN
easat-3999	128	21	=	=	SYM
easat-3999	128	22	2	2	X
easat-3999	128	23	.	.	X
easat-3999	128	24	𝛥	𝛥	PROPN
easat-3999	128	25	=	=	PUNCT
easat-3999	128	26	∑𝛷(𝑠.	∑𝛷(𝑠.	PROPN
easat-3999	128	27	𝑑.	𝑑.	NOUN
easat-3999	128	28	,	,	PUNCT
easat-3999	128	29	𝐸1	𝐸1	NOUN
easat-3999	128	30	,	,	PUNCT
easat-3999	128	31	𝐸2)𝐸𝑎𝑟𝑡ℎ−𝑀𝑜𝑜𝑛	𝐸2)𝐸𝑎𝑟𝑡ℎ−𝑀𝑜𝑜𝑛	PROPN
easat-3999	128	32	≈	≈	PROPN
easat-3999	129	1	𝑓	𝑓	DET
easat-3999	129	2	⋅	⋅	X
easat-3999	129	3	(	(	PUNCT
easat-3999	129	4	5.831∗1057	5.831∗1057	NUM
easat-3999	129	5	4	4	NUM
easat-3999	129	6	)	)	PUNCT
easat-3999	129	7	≈	≈	PROPN
easat-3999	129	8	1.458	1.458	NUM
easat-3999	129	9	∗	∗	NOUN
easat-3999	129	10	1057	1057	NUM
easat-3999	129	11	𝑘𝑔2𝑚4	𝑘𝑔2𝑚4	PUNCT
easat-3999	129	12	𝑠4	𝑠4	PROPN
easat-3999	129	13	𝛥	𝛥	PROPN
easat-3999	129	14	=	=	PUNCT
easat-3999	129	15	∑𝛷(𝑠.	∑𝛷(𝑠.	PROPN
easat-3999	129	16	𝑑.	𝑑.	NOUN
easat-3999	129	17	,	,	PUNCT
easat-3999	129	18	𝐸1	𝐸1	NOUN
easat-3999	129	19	,	,	PUNCT
easat-3999	129	20	𝐸2)𝑀𝑜𝑜𝑛−𝑆𝑢𝑛	𝐸2)𝑀𝑜𝑜𝑛−𝑆𝑢𝑛	PUNCT
easat-3999	130	1	≈	≈	PROPN
easat-3999	130	2	𝑓	𝑓	PROPN
easat-3999	130	3	⋅	⋅	PROPN
easat-3999	130	4	(	(	PUNCT
easat-3999	130	5	4.263∗1054	4.263∗1054	NUM
easat-3999	130	6	4	4	NUM
easat-3999	130	7	)	)	PUNCT
easat-3999	130	8	≈	≈	PROPN
easat-3999	130	9	1.066	1.066	NUM
easat-3999	130	10	∗	∗	NOUN
easat-3999	130	11	1054	1054	NUM
easat-3999	131	1	𝑘𝑔2𝑚4	𝑘𝑔2𝑚4	PROPN
easat-3999	131	2	𝑠4	𝑠4	PROPN
easat-3999	131	3	then	then	ADV
easat-3999	131	4	,	,	PUNCT
easat-3999	131	5	according	accord	VERB
easat-3999	131	6	to	to	ADP
easat-3999	131	7	classical	classical	ADJ
easat-3999	131	8	physics	physic	NOUN
easat-3999	131	9	,	,	PUNCT
easat-3999	131	10	to	to	ADP
easat-3999	131	11	the	the	DET
easat-3999	131	12	earth	earth	NOUN
easat-3999	131	13	-	-	PUNCT
easat-3999	131	14	moon	moon	NOUN
easat-3999	131	15	system	system	NOUN
easat-3999	131	16	:	:	PUNCT
easat-3999	131	17	𝐹𝑔	𝐹𝑔	NOUN
easat-3999	131	18	=	=	PUNCT
easat-3999	131	19	𝐺⋅𝑀1⋅𝑀2	𝐺⋅𝑀1⋅𝑀2	NUM
easat-3999	131	20	𝑟2	𝑟2	NOUN
easat-3999	131	21	𝐹𝐸𝑎𝑟𝑡ℎ−𝑀𝑜𝑜𝑛	𝐹𝐸𝑎𝑟𝑡ℎ−𝑀𝑜𝑜𝑛	NOUN
easat-3999	131	22	=	=	SYM
easat-3999	131	23	6.674∗10−11∗5.972∗1024∗7.342∗1022	6.674∗10−11∗5.972∗1024∗7.342∗1022	PROPN
easat-3999	131	24	(	(	PUNCT
easat-3999	131	25	〖3.884∗108)〗2	〖3.884∗108)〗2	PROPN
easat-3999	132	1	≈	≈	PROPN
easat-3999	132	2	1.982	1.982	NUM
easat-3999	132	3	∗	∗	NOUN
easat-3999	132	4	1020𝑁	1020𝑁	PROPN
easat-3999	132	5	and	and	CCONJ
easat-3999	132	6	to	to	ADP
easat-3999	132	7	the	the	DET
easat-3999	132	8	system	system	NOUN
easat-3999	132	9	of	of	ADP
easat-3999	132	10	moon	moon	NOUN
easat-3999	132	11	-	-	PUNCT
easat-3999	132	12	sun	sun	NOUN
easat-3999	132	13	:	:	PUNCT
easat-3999	132	14	𝐹𝑀𝑜𝑜𝑛−𝑆𝑢𝑛	𝐹𝑀𝑜𝑜𝑛−𝑆𝑢𝑛	X
easat-3999	132	15	=	=	SYM
easat-3999	132	16	6.674∗10−11∗7.342∗1022∗1.989∗1030	6.674∗10−11∗7.342∗1022∗1.989∗1030	NUM
easat-3999	132	17	(	(	PUNCT
easat-3999	132	18	〖1.496∗1011)〗2	〖1.496∗1011)〗2	VERB
easat-3999	133	1	≈	≈	PROPN
easat-3999	133	2	4.363	4.363	NUM
easat-3999	133	3	∗	∗	NOUN
easat-3999	133	4	1020𝑁	1020𝑁	NOUN
easat-3999	133	5	to	to	ADP
easat-3999	133	6	the	the	DET
easat-3999	133	7	system	system	NOUN
easat-3999	133	8	of	of	ADP
easat-3999	133	9	earth	earth	NOUN
easat-3999	133	10	-	-	PUNCT
easat-3999	133	11	moon	moon	NOUN
easat-3999	133	12	,	,	PUNCT
easat-3999	133	13	the	the	DET
easat-3999	133	14	energy	energy	NOUN
easat-3999	133	15	is	be	AUX
easat-3999	133	16	:	:	PUNCT
easat-3999	133	17	𝑈	𝑈	PROPN
easat-3999	133	18	=	=	SYM
easat-3999	133	19	−	−	PROPN
easat-3999	133	20	𝐺⋅𝑀1⋅𝑀2	𝐺⋅𝑀1⋅𝑀2	NUM
easat-3999	133	21	𝑟	𝑟	NOUN
easat-3999	134	1	𝑈𝐸𝑎𝑟𝑡ℎ−𝑀𝑜𝑜𝑛	𝑈𝐸𝑎𝑟𝑡ℎ−𝑀𝑜𝑜𝑛	PROPN
easat-3999	134	2	=	=	SYM
easat-3999	134	3	6.674∗10−11∗5.972∗1024∗7.342∗1022	6.674∗10−11∗5.972∗1024∗7.342∗1022	NUM
easat-3999	134	4	3.884∗108	3.884∗108	NUM
easat-3999	135	1	≈	≈	PROPN
easat-3999	135	2	−7.63	−7.63	PROPN
easat-3999	135	3	∗	∗	X
easat-3999	135	4	1028𝐽	1028𝐽	NOUN
easat-3999	135	5	to	to	ADP
easat-3999	135	6	the	the	DET
easat-3999	135	7	system	system	NOUN
easat-3999	135	8	of	of	ADP
easat-3999	135	9	moon	moon	NOUN
easat-3999	135	10	-	-	PUNCT
easat-3999	135	11	sun	sun	NOUN
easat-3999	135	12	,	,	PUNCT
easat-3999	135	13	the	the	DET
easat-3999	135	14	energy	energy	NOUN
easat-3999	135	15	is	be	AUX
easat-3999	135	16	:	:	PUNCT
easat-3999	135	17	𝑈𝑀𝑜𝑜𝑛−𝑆𝑢𝑛	𝑈𝑀𝑜𝑜𝑛−𝑆𝑢𝑛	X
easat-3999	135	18	=	=	SYM
easat-3999	135	19	6.674∗10−11∗7.342∗1022∗1.989∗1030	6.674∗10−11∗7.342∗1022∗1.989∗1030	NUM
easat-3999	135	20	1.496∗1011	1.496∗1011	NUM
easat-3999	136	1	≈	≈	PROPN
easat-3999	136	2	−6.51	−6.51	PROPN
easat-3999	136	3	∗	∗	PROPN
easat-3999	136	4	1029𝐽	1029𝐽	PROPN
easat-3999	136	5	9361	9361	NUM
easat-3999	136	6	edelweiss	edelweiss	PROPN
easat-3999	136	7	applied	apply	VERB
easat-3999	136	8	science	science	NOUN
easat-3999	136	9	and	and	CCONJ
easat-3999	136	10	technology	technology	NOUN
easat-3999	136	11	issn	issn	PROPN
easat-3999	136	12	:	:	PUNCT
easat-3999	136	13	2576	2576	NUM
easat-3999	136	14	-	-	SYM
easat-3999	136	15	8484	8484	NUM
easat-3999	136	16	vol	vol	NOUN
easat-3999	136	17	.	.	PROPN
easat-3999	136	18	8	8	NUM
easat-3999	136	19	,	,	PUNCT
easat-3999	136	20	no	no	INTJ
easat-3999	136	21	.	.	NOUN
easat-3999	137	1	6	6	NUM
easat-3999	137	2	:	:	SYM
easat-3999	137	3	9356	9356	NUM
easat-3999	137	4	-	-	SYM
easat-3999	137	5	9375	9375	NUM
easat-3999	137	6	,	,	PUNCT
easat-3999	137	7	2024	2024	NUM
easat-3999	137	8	doi	doi	NOUN
easat-3999	137	9	:	:	PUNCT
easat-3999	137	10	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	137	11	©	©	PROPN
easat-3999	137	12	2024	2024	NUM
easat-3999	137	13	by	by	ADP
easat-3999	137	14	the	the	DET
easat-3999	137	15	author	author	NOUN
easat-3999	137	16	;	;	PUNCT
easat-3999	137	17	licensee	licensee	PROPN
easat-3999	137	18	learning	learn	VERB
easat-3999	137	19	gate	gate	PROPN
easat-3999	137	20	figure	figure	NOUN
easat-3999	137	21	1	1	NUM
easat-3999	137	22	.	.	PUNCT
easat-3999	137	23	desmos	desmo	NOUN
easat-3999	137	24	(	(	PUNCT
easat-3999	137	25	author	author	NOUN
easat-3999	137	26	’s	’s	PART
easat-3999	137	27	scheme	scheme	NOUN
easat-3999	137	28	,	,	PUNCT
easat-3999	137	29	see	see	VERB
easat-3999	137	30	appendix	appendix	NOUN
easat-3999	137	31	)	)	PUNCT
easat-3999	137	32	.	.	PUNCT
easat-3999	138	1	the	the	DET
easat-3999	138	2	binding	binding	ADJ
easat-3999	138	3	or	or	CCONJ
easat-3999	138	4	interaction	interaction	NOUN
easat-3999	138	5	energy	energy	NOUN
easat-3999	138	6	between	between	ADP
easat-3999	138	7	the	the	DET
easat-3999	138	8	earth	earth	NOUN
easat-3999	138	9	and	and	CCONJ
easat-3999	138	10	moon	moon	NOUN
easat-3999	138	11	is	be	AUX
easat-3999	138	12	significantly	significantly	ADV
easat-3999	138	13	higher	high	ADJ
easat-3999	138	14	than	than	ADP
easat-3999	138	15	that	that	PRON
easat-3999	138	16	between	between	ADP
easat-3999	138	17	the	the	DET
easat-3999	138	18	moon	moon	NOUN
easat-3999	138	19	and	and	CCONJ
easat-3999	138	20	sun	sun	NOUN
easat-3999	138	21	.	.	PUNCT
easat-3999	139	1	this	this	PRON
easat-3999	139	2	is	be	AUX
easat-3999	139	3	interesting	interesting	ADJ
easat-3999	139	4	because	because	SCONJ
easat-3999	139	5	,	,	PUNCT
easat-3999	139	6	while	while	SCONJ
easat-3999	139	7	classical	classical	ADJ
easat-3999	139	8	gravitational	gravitational	ADJ
easat-3999	139	9	force	force	NOUN
easat-3999	139	10	between	between	ADP
easat-3999	139	11	the	the	DET
easat-3999	139	12	earth	earth	NOUN
easat-3999	139	13	and	and	CCONJ
easat-3999	139	14	moon	moon	NOUN
easat-3999	139	15	is	be	AUX
easat-3999	139	16	indeed	indeed	ADV
easat-3999	139	17	lower	low	ADJ
easat-3999	139	18	than	than	ADP
easat-3999	139	19	that	that	PRON
easat-3999	139	20	between	between	ADP
easat-3999	139	21	the	the	DET
easat-3999	139	22	moon	moon	NOUN
easat-3999	139	23	and	and	CCONJ
easat-3999	139	24	sun	sun	PROPN
easat-3999	139	25	.	.	PROPN
easat-3999	139	26	desmos	desmos	PROPN
easat-3999	139	27	fixes	fix	VERB
easat-3999	139	28	the	the	DET
easat-3999	139	29	problem	problem	NOUN
easat-3999	139	30	that	that	SCONJ
easat-3999	139	31	according	accord	VERB
easat-3999	139	32	to	to	ADP
easat-3999	139	33	classical	classical	ADJ
easat-3999	139	34	equation	equation	NOUN
easat-3999	139	35	or	or	CCONJ
easat-3999	139	36	the	the	DET
easat-3999	139	37	more	more	ADV
easat-3999	139	38	specialized	specialized	ADJ
easat-3999	139	39	equation	equation	NOUN
easat-3999	139	40	the	the	DET
easat-3999	139	41	force	force	NOUN
easat-3999	139	42	is	be	AUX
easat-3999	139	43	higher	high	ADJ
easat-3999	139	44	between	between	ADP
easat-3999	139	45	the	the	DET
easat-3999	139	46	sun	sun	NOUN
easat-3999	139	47	and	and	CCONJ
easat-3999	139	48	the	the	DET
easat-3999	139	49	moon	moon	NOUN
easat-3999	139	50	.	.	PUNCT
easat-3999	140	1	then	then	ADV
easat-3999	140	2	the	the	DET
easat-3999	140	3	moon	moon	NOUN
easat-3999	140	4	should	should	AUX
easat-3999	140	5	be	be	AUX
easat-3999	140	6	planet	planet	NOUN
easat-3999	140	7	not	not	PART
easat-3999	140	8	satellite	satellite	NOUN
easat-3999	140	9	.	.	PUNCT
easat-3999	141	1	but	but	CCONJ
easat-3999	141	2	bond	bond	NOUN
easat-3999	141	3	includes	include	VERB
easat-3999	141	4	and	and	CCONJ
easat-3999	141	5	the	the	DET
easat-3999	141	6	space	space	NOUN
easat-3999	141	7	-	-	PUNCT
easat-3999	141	8	time	time	NOUN
easat-3999	141	9	curve	curve	NOUN
easat-3999	141	10	through	through	ADP
easat-3999	141	11	𝜙i	𝜙i	NOUN
easat-3999	142	1	and	and	CCONJ
easat-3999	142	2	it	it	PRON
easat-3999	142	3	is	be	AUX
easat-3999	142	4	in	in	ADP
easat-3999	142	5	the	the	DET
easat-3999	142	6	same	same	ADJ
easat-3999	142	7	line	line	NOUN
easat-3999	142	8	to	to	ADP
easat-3999	142	9	cosmos	cosmos	PROPN
easat-3999	142	10	rules	rule	NOUN
easat-3999	142	11	.	.	PUNCT
easat-3999	143	1	3.2	3.2	NUM
easat-3999	143	2	.	.	PUNCT
easat-3999	144	1	mercury	mercury	PROPN
easat-3999	144	2	’s	’s	PART
easat-3999	144	3	precession	precession	NOUN
easat-3999	144	4	δ	δ	PROPN
easat-3999	144	5	between	between	ADP
easat-3999	144	6	mercury	mercury	NOUN
easat-3999	144	7	and	and	CCONJ
easat-3999	144	8	the	the	DET
easat-3999	144	9	sun	sun	NOUN
easat-3999	144	10	:	:	PUNCT
easat-3999	144	11	𝛥𝑀𝑒𝑟𝑐𝑢𝑟𝑦−𝑆𝑢𝑛	𝛥𝑀𝑒𝑟𝑐𝑢𝑟𝑦−𝑆𝑢𝑛	X
easat-3999	144	12	=	=	PUNCT
easat-3999	144	13	𝑓	𝑓	DET
easat-3999	144	14	⋅	⋅	PROPN
easat-3999	144	15	𝑀𝑆𝑢𝑛⋅𝜙1⋅𝑀𝑀𝑒𝑟𝑐𝑢𝑟𝑦⋅𝜙2	𝑀𝑆𝑢𝑛⋅𝜙1⋅𝑀𝑀𝑒𝑟𝑐𝑢𝑟𝑦⋅𝜙2	X
easat-3999	144	16	(	(	PUNCT
easat-3999	144	17	𝐴1⋅𝑒	𝐴1⋅𝑒	NOUN
easat-3999	144	18	−	−	PROPN
easat-3999	144	19	𝑝	𝑝	PROPN
easat-3999	144	20	𝑡1	𝑡1	PROPN
easat-3999	144	21	+	+	CCONJ
easat-3999	144	22	𝑠.𝑑.0)𝑛	𝑠.𝑑.0)𝑛	PROPN
easat-3999	144	23	⇒	⇒	NOUN
easat-3999	144	24	𝛥𝑀𝑒𝑟𝑐𝑢𝑟𝑦−𝑆𝑢𝑛	𝛥𝑀𝑒𝑟𝑐𝑢𝑟𝑦−𝑆𝑢𝑛	NOUN
easat-3999	144	25	=	=	PUNCT
easat-3999	144	26	𝑓	𝑓	DET
easat-3999	144	27	⋅	⋅	PROPN
easat-3999	144	28	𝐺2∙𝑀𝑆𝑢𝑛	𝐺2∙𝑀𝑆𝑢𝑛	PUNCT
easat-3999	144	29	2	2	NUM
easat-3999	144	30	∙𝑀𝑀𝑒𝑟𝑐𝑢𝑟𝑦	∙𝑀𝑀𝑒𝑟𝑐𝑢𝑟𝑦	NUM
easat-3999	144	31	2	2	NUM
easat-3999	144	32	𝑟2∙(𝐴1⋅𝑒	𝑟2∙(𝐴1⋅𝑒	NUM
easat-3999	144	33	−	−	PROPN
easat-3999	144	34	𝑝	𝑝	PROPN
easat-3999	144	35	𝑡1	𝑡1	PROPN
easat-3999	144	36	+	+	CCONJ
easat-3999	144	37	𝑠.𝑑.0)𝑛	𝑠.𝑑.0)𝑛	PROPN
easat-3999	144	38	𝛥𝐸	𝛥𝐸	PROPN
easat-3999	144	39	=	=	SYM
easat-3999	144	40	𝛥𝑚𝑖𝑛	𝛥𝑚𝑖𝑛	PROPN
easat-3999	144	41	−	−	PROPN
easat-3999	144	42	𝛥𝑚𝑎𝑥	𝛥𝑚𝑎𝑥	NOUN
easat-3999	144	43	,	,	PUNCT
easat-3999	144	44	𝛥𝑚𝑖𝑛	𝛥𝑚𝑖𝑛	PROPN
easat-3999	144	45	=	=	PUNCT
easat-3999	144	46	𝑓	𝑓	DET
easat-3999	144	47	⋅	⋅	PROPN
easat-3999	144	48	𝐺2∙𝑀𝑆𝑢𝑛	𝐺2∙𝑀𝑆𝑢𝑛	PUNCT
easat-3999	144	49	2	2	NUM
easat-3999	144	50	∙𝑀𝑀𝑒𝑟𝑐𝑢𝑟𝑦	∙𝑀𝑀𝑒𝑟𝑐𝑢𝑟𝑦	NUM
easat-3999	144	51	2	2	NUM
easat-3999	144	52	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
easat-3999	144	53	𝑚	𝑚	NOUN
easat-3999	144	54	and	and	CCONJ
easat-3999	144	55	𝛥𝑚𝑎𝑥	𝛥𝑚𝑎𝑥	PROPN
easat-3999	144	56	=	=	PUNCT
easat-3999	144	57	𝑓	𝑓	DET
easat-3999	144	58	⋅	⋅	PROPN
easat-3999	144	59	𝐺2∙𝑀𝑆𝑢𝑛	𝐺2∙𝑀𝑆𝑢𝑛	PUNCT
easat-3999	144	60	2	2	NUM
easat-3999	144	61	∙𝑀𝑀𝑒𝑟𝑐𝑢𝑟𝑦	∙𝑀𝑀𝑒𝑟𝑐𝑢𝑟𝑦	NUM
easat-3999	144	62	2	2	NUM
easat-3999	144	63	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
easat-3999	144	64	𝑚	𝑚	ADP
easat-3999	144	65	difference	difference	NOUN
easat-3999	144	66	in	in	ADP
easat-3999	144	67	energy	energy	NOUN
easat-3999	144	68	𝛥𝐸	𝛥𝐸	PROPN
easat-3999	144	69	leads	lead	VERB
easat-3999	144	70	to	to	ADP
easat-3999	144	71	precession	precession	NOUN
easat-3999	144	72	,	,	PUNCT
easat-3999	144	73	and	and	CCONJ
easat-3999	144	74	for	for	ADP
easat-3999	144	75	small	small	ADJ
easat-3999	144	76	precession	precession	NOUN
easat-3999	144	77	angles	angle	VERB
easat-3999	144	78	𝛿𝜃	𝛿𝜃	ADP
easat-3999	144	79	:	:	PUNCT
easat-3999	144	80	𝛿𝜃	𝛿𝜃	SCONJ
easat-3999	144	81	≈	≈	PROPN
easat-3999	144	82	𝛥𝛦	𝛥𝛦	NOUN
easat-3999	144	83	𝛥m	𝛥m	NOUN
easat-3999	144	84	τhe	τhe	VERB
easat-3999	144	85	precession	precession	NOUN
easat-3999	144	86	per	per	ADP
easat-3999	144	87	orbit	orbit	NOUN
easat-3999	144	88	for	for	ADP
easat-3999	144	89	a	a	DET
easat-3999	144	90	small	small	ADJ
easat-3999	144	91	angle	angle	NOUN
easat-3999	144	92	is	be	AUX
easat-3999	144	93	related	relate	VERB
easat-3999	144	94	to	to	ADP
easat-3999	144	95	the	the	DET
easat-3999	144	96	fractional	fractional	ADJ
easat-3999	144	97	change	change	NOUN
easat-3999	144	98	in	in	ADP
easat-3999	144	99	energy	energy	NOUN
easat-3999	144	100	:	:	PUNCT
easat-3999	144	101	9362	9362	NUM
easat-3999	144	102	edelweiss	edelweiss	PROPN
easat-3999	144	103	applied	apply	VERB
easat-3999	144	104	science	science	NOUN
easat-3999	144	105	and	and	CCONJ
easat-3999	144	106	technology	technology	NOUN
easat-3999	144	107	issn	issn	PROPN
easat-3999	144	108	:	:	PUNCT
easat-3999	144	109	2576	2576	NUM
easat-3999	144	110	-	-	SYM
easat-3999	144	111	8484	8484	NUM
easat-3999	144	112	vol	vol	NOUN
easat-3999	144	113	.	.	PROPN
easat-3999	145	1	8	8	NUM
easat-3999	145	2	,	,	PUNCT
easat-3999	145	3	no	no	INTJ
easat-3999	145	4	.	.	NOUN
easat-3999	146	1	6	6	NUM
easat-3999	146	2	:	:	SYM
easat-3999	146	3	9356	9356	NUM
easat-3999	146	4	-	-	SYM
easat-3999	146	5	9375	9375	NUM
easat-3999	146	6	,	,	PUNCT
easat-3999	146	7	2024	2024	NUM
easat-3999	146	8	doi	doi	NOUN
easat-3999	146	9	:	:	PUNCT
easat-3999	146	10	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	146	11	©	©	PROPN
easat-3999	146	12	2024	2024	NUM
easat-3999	146	13	by	by	ADP
easat-3999	146	14	the	the	DET
easat-3999	146	15	author	author	NOUN
easat-3999	146	16	;	;	PUNCT
easat-3999	146	17	licensee	licensee	PROPN
easat-3999	146	18	learning	learning	NOUN
easat-3999	146	19	gate	gate	NOUN
easat-3999	146	20	𝛿𝜃	𝛿𝜃	ADP
easat-3999	146	21	≈	≈	PROPN
easat-3999	146	22	𝛥𝛦	𝛥𝛦	PROPN
easat-3999	146	23	𝐸0	𝐸0	NOUN
easat-3999	146	24	per	per	ADP
easat-3999	146	25	orbit	orbit	NOUN
easat-3999	146	26	where	where	SCONJ
easat-3999	146	27	𝐸0	𝐸0	PROPN
easat-3999	146	28	is	be	AUX
easat-3999	146	29	the	the	DET
easat-3999	146	30	binding	bind	VERB
easat-3999	146	31	energy	energy	NOUN
easat-3999	146	32	.	.	PUNCT
easat-3999	147	1	𝛿𝜃	𝛿𝜃	ADP
easat-3999	147	2	≈	≈	PROPN
easat-3999	147	3	43	43	NUM
easat-3999	147	4	arcseconds	arcsecond	NOUN
easat-3999	147	5	per	per	ADP
easat-3999	147	6	century	century	NOUN
easat-3999	147	7	𝛿𝜃	𝛿𝜃	ADP
easat-3999	147	8	≈	≈	PROPN
easat-3999	147	9	43	43	NUM
easat-3999	147	10	∗	∗	NOUN
easat-3999	147	11	1	1	NUM
easat-3999	147	12	100∗365.25	100∗365.25	NUM
easat-3999	147	13	arcseconds	arcsecond	NOUN
easat-3999	147	14	per	per	ADP
easat-3999	147	15	orbit	orbit	NOUN
easat-3999	147	16	this	this	DET
easat-3999	147	17	angle	angle	NOUN
easat-3999	147	18	corresponds	correspond	VERB
easat-3999	147	19	to	to	ADP
easat-3999	147	20	a	a	DET
easat-3999	147	21	very	very	ADV
easat-3999	147	22	small	small	ADJ
easat-3999	147	23	fractional	fractional	ADJ
easat-3999	147	24	energy	energy	NOUN
easat-3999	147	25	shift	shift	NOUN
easat-3999	147	26	.	.	PUNCT
easat-3999	148	1	based	base	VERB
easat-3999	148	2	on	on	ADP
easat-3999	148	3	the	the	DET
easat-3999	148	4	energy	energy	NOUN
easat-3999	148	5	expression	expression	NOUN
easat-3999	148	6	:	:	PUNCT
easat-3999	148	7	𝛥𝛦	𝛥𝛦	PROPN
easat-3999	148	8	=	=	SYM
easat-3999	148	9	𝐸0	𝐸0	NOUN
easat-3999	148	10	∙	∙	PROPN
easat-3999	148	11	𝛿𝜃	𝛿𝜃	ADP
easat-3999	148	12	∝	∝	PROPN
easat-3999	148	13	1	1	NUM
easat-3999	148	14	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
easat-3999	148	15	𝑚	𝑚	NOUN
easat-3999	148	16	−	−	PROPN
easat-3999	148	17	1	1	NUM
easat-3999	148	18	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
easat-3999	148	19	𝑚	𝑚	ADP
easat-3999	148	20	a	a	DET
easat-3999	148	21	relationship	relationship	NOUN
easat-3999	148	22	for	for	SCONJ
easat-3999	148	23	𝑛	𝑛	PRON
easat-3999	148	24	to	to	PART
easat-3999	148	25	match	match	VERB
easat-3999	148	26	this	this	DET
easat-3999	148	27	energy	energy	NOUN
easat-3999	148	28	shift	shift	NOUN
easat-3999	148	29	:	:	PUNCT
easat-3999	148	30	𝛿𝜃	𝛿𝜃	ADP
easat-3999	148	31	∝	∝	PROPN
easat-3999	148	32	(	(	PUNCT
easat-3999	148	33	1	1	NUM
easat-3999	148	34	𝑟𝑚𝑖𝑛	𝑟𝑚𝑖𝑛	NOUN
easat-3999	148	35	𝑚	𝑚	NOUN
easat-3999	148	36	−	−	PROPN
easat-3999	148	37	1	1	NUM
easat-3999	148	38	𝑟𝑚𝑎𝑥	𝑟𝑚𝑎𝑥	NOUN
easat-3999	148	39	𝑚	𝑚	NOUN
easat-3999	148	40	)	)	PUNCT
easat-3999	149	1	∙	∙	PROPN
easat-3999	149	2	1	1	NUM
easat-3999	149	3	𝑟𝑛	𝑟𝑛	NUM
easat-3999	149	4	figure	figure	NOUN
easat-3999	149	5	2	2	NUM
easat-3999	149	6	.	.	PUNCT
easat-3999	149	7	mercury	mercury	PROPN
easat-3999	149	8	’s	’s	PART
easat-3999	149	9	precession	precession	NOUN
easat-3999	149	10	(	(	PUNCT
easat-3999	149	11	author	author	NOUN
easat-3999	149	12	’s	’s	PART
easat-3999	149	13	scheme	scheme	NOUN
easat-3999	149	14	,	,	PUNCT
easat-3999	149	15	see	see	VERB
easat-3999	149	16	appendix	appendix	NOUN
easat-3999	149	17	b	b	NOUN
easat-3999	149	18	)	)	PUNCT
easat-3999	149	19	.	.	PUNCT
easat-3999	150	1	then	then	ADV
easat-3999	150	2	,	,	PUNCT
easat-3999	150	3	n	n	PROPN
easat-3999	150	4	≈	≈	PROPN
easat-3999	150	5	2.1	2.1	NUM
easat-3999	150	6	,	,	PUNCT
easat-3999	150	7	value	value	NOUN
easat-3999	150	8	close	close	ADV
easat-3999	150	9	to	to	ADP
easat-3999	150	10	classical	classical	ADJ
easat-3999	150	11	𝑚	𝑚	NOUN
easat-3999	150	12	and	and	CCONJ
easat-3999	150	13	𝑛	𝑛	ADJ
easat-3999	150	14	,	,	PUNCT
easat-3999	150	15	slightly	slightly	ADV
easat-3999	150	16	above	above	ADP
easat-3999	150	17	2	2	NUM
easat-3999	150	18	,	,	PUNCT
easat-3999	150	19	showing	show	VERB
easat-3999	150	20	that	that	SCONJ
easat-3999	150	21	because	because	SCONJ
easat-3999	150	22	of	of	ADP
easat-3999	150	23	curve	curve	NOUN
easat-3999	150	24	of	of	ADP
easat-3999	150	25	space	space	NOUN
easat-3999	150	26	-	-	PUNCT
easat-3999	150	27	time	time	NOUN
easat-3999	150	28	,	,	PUNCT
easat-3999	150	29	something	something	PRON
easat-3999	150	30	that	that	PRON
easat-3999	150	31	is	be	AUX
easat-3999	150	32	regulated	regulate	VERB
easat-3999	150	33	between	between	ADP
easat-3999	150	34	the	the	DET
easat-3999	150	35	𝐴1	𝐴1	PROPN
easat-3999	150	36	⋅	⋅	PROPN
easat-3999	150	37	𝑒	𝑒	PROPN
easat-3999	150	38	−	−	PROPN
easat-3999	150	39	𝑝	𝑝	PROPN
easat-3999	150	40	𝑡1	𝑡1	NOUN
easat-3999	150	41	+	+	CCONJ
easat-3999	150	42	𝑠.	𝑠.	NOUN
easat-3999	150	43	𝑑.0and	𝑑.0and	NOUN
easat-3999	150	44	n	n	CCONJ
easat-3999	150	45	,	,	PUNCT
easat-3999	150	46	it	it	PRON
easat-3999	150	47	is	be	AUX
easat-3999	150	48	plausible	plausible	ADJ
easat-3999	150	49	to	to	PART
easat-3999	150	50	determine	determine	VERB
easat-3999	150	51	or	or	CCONJ
easat-3999	150	52	𝐴1	𝐴1	PROPN
easat-3999	150	53	⋅	⋅	PROPN
easat-3999	150	54	𝑒	𝑒	PROPN
easat-3999	150	55	−	−	PROPN
easat-3999	150	56	𝑝	𝑝	PROPN
easat-3999	150	57	𝑡1	𝑡1	NOUN
easat-3999	150	58	+	+	CCONJ
easat-3999	150	59	𝑠.	𝑠.	NOUN
easat-3999	150	60	𝑑.0using	𝑑.0use	VERB
easat-3999	150	61	𝑛	𝑛	PRON
easat-3999	150	62	at	at	ADP
easat-3999	150	63	a	a	DET
easat-3999	150	64	specific	specific	ADJ
easat-3999	150	65	value	value	NOUN
easat-3999	150	66	,	,	PUNCT
easat-3999	150	67	or	or	CCONJ
easat-3999	150	68	the	the	DET
easat-3999	150	69	𝑛	𝑛	ADJ
easat-3999	150	70	using	use	VERB
easat-3999	150	71	𝐴1	𝐴1	PROPN
easat-3999	150	72	⋅	⋅	PROPN
easat-3999	150	73	𝑒	𝑒	PROPN
easat-3999	150	74	−	−	PROPN
easat-3999	150	75	𝑝	𝑝	PROPN
easat-3999	150	76	𝑡1	𝑡1	NOUN
easat-3999	150	77	+	+	CCONJ
easat-3999	150	78	𝑠.	𝑠.	NOUN
easat-3999	150	79	𝑑.0	𝑑.0	PROPN
easat-3999	150	80	at	at	ADP
easat-3999	150	81	a	a	DET
easat-3999	150	82	specific	specific	ADJ
easat-3999	150	83	value	value	NOUN
easat-3999	150	84	(	(	PUNCT
easat-3999	150	85	also	also	ADV
easat-3999	150	86	,	,	PUNCT
easat-3999	150	87	there	there	PRON
easat-3999	150	88	are	be	VERB
easat-3999	150	89	and	and	CCONJ
easat-3999	150	90	more	more	ADV
easat-3999	150	91	complex	complex	ADJ
easat-3999	150	92	cases	case	NOUN
easat-3999	150	93	)	)	PUNCT
easat-3999	150	94	.	.	PUNCT
easat-3999	151	1	the	the	DET
easat-3999	151	2	higher	high	ADJ
easat-3999	151	3	value	value	NOUN
easat-3999	151	4	than	than	ADP
easat-3999	151	5	2.1	2.1	NUM
easat-3999	151	6	means	mean	VERB
easat-3999	151	7	contraction	contraction	NOUN
easat-3999	151	8	of	of	ADP
easat-3999	151	9	space	space	NOUN
easat-3999	151	10	-	-	PUNCT
easat-3999	151	11	time	time	NOUN
easat-3999	151	12	(	(	PUNCT
easat-3999	151	13	lower	low	ADJ
easat-3999	151	14	value	value	NOUN
easat-3999	151	15	would	would	AUX
easat-3999	151	16	mean	mean	VERB
easat-3999	151	17	expansion	expansion	NOUN
easat-3999	151	18	.	.	PUNCT
easat-3999	152	1	3.3	3.3	NUM
easat-3999	152	2	.	.	PUNCT
easat-3999	152	3	hubble	hubble	ADJ
easat-3999	152	4	calculation	calculation	NOUN
easat-3999	152	5	9363	9363	NUM
easat-3999	152	6	edelweiss	edelweiss	PROPN
easat-3999	152	7	applied	apply	VERB
easat-3999	152	8	science	science	NOUN
easat-3999	152	9	and	and	CCONJ
easat-3999	152	10	technology	technology	NOUN
easat-3999	152	11	issn	issn	PROPN
easat-3999	152	12	:	:	PUNCT
easat-3999	152	13	2576	2576	NUM
easat-3999	152	14	-	-	SYM
easat-3999	152	15	8484	8484	NUM
easat-3999	152	16	vol	vol	NOUN
easat-3999	152	17	.	.	PROPN
easat-3999	152	18	8	8	NUM
easat-3999	152	19	,	,	PUNCT
easat-3999	152	20	no	no	INTJ
easat-3999	152	21	.	.	NOUN
easat-3999	153	1	6	6	NUM
easat-3999	153	2	:	:	SYM
easat-3999	153	3	9356	9356	NUM
easat-3999	153	4	-	-	SYM
easat-3999	153	5	9375	9375	NUM
easat-3999	153	6	,	,	PUNCT
easat-3999	153	7	2024	2024	NUM
easat-3999	153	8	doi	doi	NOUN
easat-3999	153	9	:	:	PUNCT
easat-3999	153	10	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	153	11	©	©	PROPN
easat-3999	153	12	2024	2024	NUM
easat-3999	153	13	by	by	ADP
easat-3999	153	14	the	the	DET
easat-3999	153	15	author	author	NOUN
easat-3999	153	16	;	;	PUNCT
easat-3999	153	17	licensee	licensee	PROPN
easat-3999	153	18	learning	learning	NOUN
easat-3999	153	19	gate	gate	VERB
easat-3999	153	20	the	the	DET
easat-3999	153	21	value	value	NOUN
easat-3999	153	22	of	of	ADP
easat-3999	153	23	𝑛	𝑛	PRON
easat-3999	153	24	for	for	ADP
easat-3999	153	25	hubble	hubble	ADJ
easat-3999	153	26	phenomenon	phenomenon	NOUN
easat-3999	153	27	:	:	PUNCT
easat-3999	153	28	𝐷𝑒𝑠𝑚𝑜𝑠[𝐹𝑜𝑟𝑐𝑒	𝐷𝑒𝑠𝑚𝑜𝑠[𝐹𝑜𝑟𝑐𝑒	NOUN
easat-3999	153	29	𝑜𝑟	𝑜𝑟	ADP
easat-3999	153	30	𝐸𝑛𝑒𝑟𝑔𝑦	𝐸𝑛𝑒𝑟𝑔𝑦	PROPN
easat-3999	153	31	]	]	PUNCT
easat-3999	154	1	∝	∝	PROPN
easat-3999	154	2	1	1	NUM
easat-3999	154	3	𝑟𝑛	𝑟𝑛	ADP
easat-3999	154	4	𝑣	𝑣	PROPN
easat-3999	154	5	=	=	PUNCT
easat-3999	154	6	𝐻0	𝐻0	PROPN
easat-3999	154	7	∙	∙	PROPN
easat-3999	154	8	𝑑	𝑑	PROPN
easat-3999	154	9	≈	≈	PROPN
easat-3999	154	10	70	70	NUM
easat-3999	154	11	𝑘𝑚	𝑘𝑚	NOUN
easat-3999	154	12	𝑠	𝑠	PROPN
easat-3999	154	13	𝑀𝑝𝑐	𝑀𝑝𝑐	PROPN
easat-3999	154	14	𝑜𝑟	𝑜𝑟	ADP
easat-3999	154	15	2.3	2.3	NUM
easat-3999	154	16	∗	∗	NOUN
easat-3999	154	17	10−18𝑠−1	10−18𝑠−1	NUM
easat-3999	154	18	also	also	ADV
easat-3999	154	19	,	,	PUNCT
easat-3999	154	20	𝜙i=𝑣2	𝜙i=𝑣2	VERB
easat-3999	154	21	[	[	PUNCT
easat-3999	154	22	𝛥	𝛥	PROPN
easat-3999	154	23	=	=	SYM
easat-3999	154	24	∏	∏	PROPN
easat-3999	154	25	𝑚i⋅𝑚	𝑚i⋅𝑚	PUNCT
easat-3999	154	26	𝑖=0	𝑖=0	PROPN
easat-3999	154	27	𝑣2	𝑣2	PROPN
easat-3999	154	28	(	(	PUNCT
easat-3999	154	29	𝐴1⋅𝑒	𝐴1⋅𝑒	NOUN
easat-3999	154	30	−	−	PROPN
easat-3999	154	31	𝑝	𝑝	PROPN
easat-3999	154	32	𝑡1	𝑡1	PROPN
easat-3999	154	33	+	+	CCONJ
easat-3999	154	34	𝑠.𝑑.0)𝑛	𝑠.𝑑.0)𝑛	PROPN
easat-3999	154	35	⇒	⇒	NOUN
easat-3999	154	36	𝛥	𝛥	PROPN
easat-3999	154	37	=	=	SYM
easat-3999	154	38	∏	∏	PROPN
easat-3999	154	39	⋅𝑚i∙𝑚	⋅𝑚i∙𝑚	PRON
easat-3999	154	40	𝑖=0	𝑖=0	PROPN
easat-3999	154	41	(	(	PUNCT
easat-3999	154	42	𝐻0∙𝑑)2	𝐻0∙𝑑)2	X
easat-3999	154	43	(	(	PUNCT
easat-3999	154	44	𝐴1⋅𝑒	𝐴1⋅𝑒	NOUN
easat-3999	154	45	−	−	PROPN
easat-3999	154	46	𝑝	𝑝	PROPN
easat-3999	154	47	𝑡1	𝑡1	PROPN
easat-3999	154	48	+	+	CCONJ
easat-3999	154	49	𝑠.𝑑.0)𝑛	𝑠.𝑑.0)𝑛	PROPN
easat-3999	154	50	or	or	CCONJ
easat-3999	154	51	{	{	PUNCT
easat-3999	154	52	(	(	PUNCT
easat-3999	154	53	𝐴1	𝐴1	PROPN
easat-3999	154	54	⋅	⋅	PROPN
easat-3999	154	55	𝑒	𝑒	PROPN
easat-3999	154	56	−	−	PROPN
easat-3999	154	57	𝑝	𝑝	PROPN
easat-3999	154	58	𝑡1	𝑡1	NOUN
easat-3999	154	59	+	+	CCONJ
easat-3999	154	60	𝑠.	𝑠.	NOUN
easat-3999	154	61	𝑑.0	𝑑.0	X
easat-3999	154	62	)	)	PUNCT
easat-3999	154	63	𝑛	𝑛	PROPN
easat-3999	154	64	∝	∝	PROPN
easat-3999	154	65	∏	∏	PROPN
easat-3999	154	66	⋅	⋅	PROPN
easat-3999	154	67	𝑚i	𝑚i	PROPN
easat-3999	154	68	∙𝑚	∙𝑚	PROPN
easat-3999	154	69	𝑖=0	𝑖=0	PROPN
easat-3999	154	70	(	(	PUNCT
easat-3999	154	71	𝐻0	𝐻0	PROPN
easat-3999	154	72	∙	∙	PROPN
easat-3999	154	73	𝑑)2	𝑑)2	PROPN
easat-3999	154	74	or	or	CCONJ
easat-3999	154	75	𝑑2	𝑑2	AUX
easat-3999	154	76	∝	∝	PROPN
easat-3999	154	77	1	1	NUM
easat-3999	154	78	𝐻0	𝐻0	NOUN
easat-3999	154	79	2	2	NUM
easat-3999	154	80	or	or	CCONJ
easat-3999	154	81	𝑑	𝑑	PRON
easat-3999	154	82	∝	∝	PROPN
easat-3999	154	83	1	1	NUM
easat-3999	154	84	𝐻0	𝐻0	PROPN
easat-3999	154	85	}	}	PUNCT
easat-3999	154	86	⇒	⇒	VERB
easat-3999	154	87	𝑑2	𝑑2	NOUN
easat-3999	154	88	=	=	SYM
easat-3999	154	89	(	(	PUNCT
easat-3999	154	90	𝐴1⋅𝑒	𝐴1⋅𝑒	NOUN
easat-3999	154	91	−	−	PROPN
easat-3999	154	92	𝑝	𝑝	PROPN
easat-3999	154	93	𝑡1	𝑡1	PROPN
easat-3999	154	94	+	+	CCONJ
easat-3999	154	95	𝑠.𝑑.0)𝑛	𝑠.𝑑.0)𝑛	PROPN
easat-3999	154	96	∏	∏	PROPN
easat-3999	154	97	⋅𝑚i∙𝑚	⋅𝑚i∙𝑚	DET
easat-3999	154	98	𝑖=0	𝑖=0	PROPN
easat-3999	154	99	𝐻0	𝐻0	PROPN
easat-3999	154	100	2	2	NUM
easat-3999	154	101	or	or	CCONJ
easat-3999	154	102	𝑑2=	𝑑2=	NUM
easat-3999	154	103	𝛥∙𝑟𝑛	𝛥∙𝑟𝑛	NUM
easat-3999	154	104	𝑚galaxy1∗𝑚galaxy2∗𝐻0	𝑚galaxy1∗𝑚galaxy2∗𝐻0	PROPN
easat-3999	154	105	2	2	NUM
easat-3999	154	106	or	or	CCONJ
easat-3999	154	107	𝑣2=	𝑣2=	PROPN
easat-3999	154	108	𝛥∙𝑟𝑛	𝛥∙𝑟𝑛	NUM
easat-3999	154	109	𝑚galaxy1𝑚galaxy2	𝑚galaxy1𝑚galaxy2	NUM
easat-3999	154	110	⇒	⇒	NOUN
easat-3999	154	111	(	(	PUNCT
easat-3999	154	112	𝐻0	𝐻0	PROPN
easat-3999	154	113	∙	∙	PROPN
easat-3999	154	114	𝑟)2=	𝑟)2=	PROPN
easat-3999	154	115	𝛥∙𝑟𝑛	𝛥∙𝑟𝑛	NUM
easat-3999	154	116	𝑚galaxy1𝑚galaxy2	𝑚galaxy1𝑚galaxy2	NUM
easat-3999	154	117	⇒	⇒	NOUN
easat-3999	154	118	𝑟2−𝑛	𝑟2−𝑛	PROPN
easat-3999	155	1	=	=	SYM
easat-3999	155	2	𝛥	𝛥	PROPN
easat-3999	155	3	𝑚galaxy1∙𝑚galaxy2	𝑚galaxy1∙𝑚galaxy2	PUNCT
easat-3999	155	4	⇒	⇒	NOUN
easat-3999	155	5	𝑛	𝑛	X
easat-3999	155	6	=	=	SYM
easat-3999	155	7	2	2	NUM
easat-3999	155	8	−	−	NOUN
easat-3999	155	9	ln	ln	ADJ
easat-3999	155	10	(	(	PUNCT
easat-3999	155	11	𝛥	𝛥	PROPN
easat-3999	155	12	𝐻0	𝐻0	PROPN
easat-3999	155	13	2∙𝑚galaxy1∙𝑚galaxy2	2∙𝑚galaxy1∙𝑚galaxy2	NUM
easat-3999	155	14	)	)	PUNCT
easat-3999	155	15	𝑙𝑛𝑟	𝑙𝑛𝑟	NOUN
easat-3999	155	16	for	for	ADP
easat-3999	155	17	a	a	DET
easat-3999	155	18	galaxy	galaxy	NOUN
easat-3999	155	19	δ	δ	NOUN
easat-3999	155	20	using	use	VERB
easat-3999	155	21	the	the	DET
easat-3999	155	22	data	datum	NOUN
easat-3999	155	23	from	from	ADP
easat-3999	155	24	moon	moon	NOUN
easat-3999	155	25	,	,	PUNCT
easat-3999	155	26	earth	earth	NOUN
easat-3999	155	27	and	and	CCONJ
easat-3999	155	28	sun	sun	NOUN
easat-3999	155	29	:	:	PUNCT
easat-3999	155	30	∑𝛷(𝑠.	∑𝛷(𝑠.	NOUN
easat-3999	155	31	𝑑.	𝑑.	PROPN
easat-3999	155	32	,	,	PUNCT
easat-3999	155	33	𝐸1	𝐸1	PROPN
easat-3999	155	34	,	,	PUNCT
easat-3999	155	35	𝐸2	𝐸2	ADJ
easat-3999	155	36	)	)	PUNCT
easat-3999	155	37	∝	∝	PROPN
easat-3999	155	38	𝑀𝐺𝑎𝑙𝑎𝑥𝑦	𝑀𝐺𝑎𝑙𝑎𝑥𝑦	PROPN
easat-3999	155	39	2	2	NUM
easat-3999	155	40	𝑅𝐺𝑎𝑙𝑎𝑥𝑦	𝑅𝐺𝑎𝑙𝑎𝑥𝑦	PROPN
easat-3999	155	41	𝑛	𝑛	PRON
easat-3999	155	42	≈	≈	PROPN
easat-3999	155	43	(	(	PUNCT
easat-3999	155	44	1042	1042	NUM
easat-3999	155	45	)	)	PUNCT
easat-3999	155	46	2	2	NUM
easat-3999	155	47	(	(	PUNCT
easat-3999	155	48	1021	1021	NUM
easat-3999	155	49	)	)	PUNCT
easat-3999	155	50	𝑛	𝑛	PROPN
easat-3999	155	51	(	(	PUNCT
easat-3999	155	52	1024	1024	NUM
easat-3999	155	53	)	)	PUNCT
easat-3999	155	54	2	2	NUM
easat-3999	155	55	(	(	PUNCT
easat-3999	155	56	108	108	NUM
easat-3999	155	57	)	)	PUNCT
easat-3999	155	58	𝑛	𝑛	NOUN
easat-3999	155	59	,	,	PUNCT
easat-3999	155	60	for	for	ADP
easat-3999	155	61	𝑛	𝑛	PRON
easat-3999	155	62	=	=	SYM
easat-3999	155	63	2⇒	2⇒	PROPN
easat-3999	155	64	𝛥	𝛥	PROPN
easat-3999	155	65	=	=	PUNCT
easat-3999	155	66	∑𝛷(𝑠.	∑𝛷(𝑠.	PROPN
easat-3999	155	67	𝑑.	𝑑.	NOUN
easat-3999	155	68	,	,	PUNCT
easat-3999	155	69	𝐸1	𝐸1	PROPN
easat-3999	155	70	,	,	PUNCT
easat-3999	155	71	𝐸2	𝐸2	ADJ
easat-3999	155	72	)	)	PUNCT
easat-3999	155	73	∝	∝	PROPN
easat-3999	155	74	1010	1010	NUM
easat-3999	155	75	∗	∗	NOUN
easat-3999	155	76	1.458	1.458	NUM
easat-3999	155	77	∗	∗	NOUN
easat-3999	155	78	1067	1067	NUM
easat-3999	156	1	𝑘𝑔2𝑚2	𝑘𝑔2𝑚2	ADV
easat-3999	156	2	𝑠4	𝑠4	VERB
easat-3999	156	3	thus	thus	ADV
easat-3999	156	4	,	,	PUNCT
easat-3999	156	5	𝑛	𝑛	PROPN
easat-3999	156	6	≈	≈	PROPN
easat-3999	156	7	1.10	1.10	NUM
easat-3999	156	8	9364	9364	NUM
easat-3999	156	9	edelweiss	edelweiss	PROPN
easat-3999	156	10	applied	apply	VERB
easat-3999	156	11	science	science	NOUN
easat-3999	156	12	and	and	CCONJ
easat-3999	156	13	technology	technology	NOUN
easat-3999	156	14	issn	issn	PROPN
easat-3999	156	15	:	:	PUNCT
easat-3999	156	16	2576	2576	NUM
easat-3999	156	17	-	-	SYM
easat-3999	156	18	8484	8484	NUM
easat-3999	156	19	vol	vol	NOUN
easat-3999	156	20	.	.	PROPN
easat-3999	156	21	8	8	NUM
easat-3999	156	22	,	,	PUNCT
easat-3999	156	23	no	no	INTJ
easat-3999	156	24	.	.	NOUN
easat-3999	156	25	6	6	NUM
easat-3999	156	26	:	:	SYM
easat-3999	156	27	9356	9356	NUM
easat-3999	156	28	-	-	SYM
easat-3999	156	29	9375	9375	NUM
easat-3999	156	30	,	,	PUNCT
easat-3999	156	31	2024	2024	NUM
easat-3999	156	32	doi	doi	NOUN
easat-3999	156	33	:	:	PUNCT
easat-3999	156	34	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	156	35	©	©	PROPN
easat-3999	156	36	2024	2024	NUM
easat-3999	156	37	by	by	ADP
easat-3999	156	38	the	the	DET
easat-3999	156	39	author	author	NOUN
easat-3999	156	40	;	;	PUNCT
easat-3999	156	41	licensee	licensee	PROPN
easat-3999	156	42	learning	learn	VERB
easat-3999	156	43	gate	gate	PROPN
easat-3999	156	44	figure	figure	NOUN
easat-3999	156	45	3	3	NUM
easat-3999	156	46	.	.	PUNCT
easat-3999	156	47	expansion	expansion	NOUN
easat-3999	156	48	of	of	ADP
easat-3999	156	49	space	space	NOUN
easat-3999	156	50	-	-	PUNCT
easat-3999	156	51	time	time	NOUN
easat-3999	156	52	(	(	PUNCT
easat-3999	156	53	author	author	NOUN
easat-3999	156	54	’s	’s	PART
easat-3999	156	55	scheme	scheme	NOUN
easat-3999	156	56	,	,	PUNCT
easat-3999	156	57	see	see	VERB
easat-3999	156	58	appendix	appendix	NOUN
easat-3999	156	59	c	c	NOUN
easat-3999	156	60	)	)	PUNCT
easat-3999	156	61	.	.	PUNCT
easat-3999	157	1	in	in	ADP
easat-3999	157	2	cosmological	cosmological	ADJ
easat-3999	157	3	terms	term	NOUN
easat-3999	157	4	,	,	PUNCT
easat-3999	157	5	a	a	DET
easat-3999	157	6	value	value	NOUN
easat-3999	157	7	of	of	ADP
easat-3999	157	8	𝑛	𝑛	DET
easat-3999	157	9	around	around	ADP
easat-3999	157	10	1.10	1.10	NUM
easat-3999	157	11	suggests	suggest	VERB
easat-3999	157	12	that	that	SCONJ
easat-3999	157	13	as	as	SCONJ
easat-3999	157	14	galaxies	galaxy	NOUN
easat-3999	157	15	move	move	VERB
easat-3999	157	16	farther	far	ADV
easat-3999	157	17	apart	apart	ADV
easat-3999	157	18	,	,	PUNCT
easat-3999	157	19	the	the	DET
easat-3999	157	20	influence	influence	NOUN
easat-3999	157	21	or	or	CCONJ
easat-3999	157	22	effective	effective	ADJ
easat-3999	157	23	interaction	interaction	NOUN
easat-3999	157	24	(	(	PUNCT
easat-3999	157	25	related	relate	VERB
easat-3999	157	26	to	to	ADP
easat-3999	157	27	gravitational	gravitational	ADJ
easat-3999	157	28	or	or	CCONJ
easat-3999	157	29	other	other	ADJ
easat-3999	157	30	cosmic	cosmic	ADJ
easat-3999	157	31	dynamics	dynamic	NOUN
easat-3999	157	32	)	)	PUNCT
easat-3999	157	33	weakens	weaken	VERB
easat-3999	157	34	with	with	ADP
easat-3999	157	35	distance	distance	NOUN
easat-3999	157	36	but	but	CCONJ
easat-3999	157	37	not	not	PART
easat-3999	157	38	as	as	ADV
easat-3999	157	39	drastically	drastically	ADV
easat-3999	157	40	as	as	ADP
easat-3999	157	41	the	the	DET
easat-3999	157	42	classical	classical	ADJ
easat-3999	157	43	inverse	inverse	NOUN
easat-3999	157	44	-	-	PUNCT
easat-3999	157	45	square	square	NOUN
easat-3999	157	46	law	law	NOUN
easat-3999	157	47	.	.	PUNCT
easat-3999	158	1	3.4	3.4	NUM
easat-3999	158	2	.	.	PUNCT
easat-3999	158	3	gravity	gravity	NOUN
easat-3999	158	4	deflection	deflection	NOUN
easat-3999	158	5	the	the	DET
easat-3999	158	6	elliptical	elliptical	ADJ
easat-3999	158	7	forms	form	NOUN
easat-3999	158	8	on	on	ADP
easat-3999	158	9	cosmos	cosmo	NOUN
easat-3999	158	10	are	be	AUX
easat-3999	158	11	the	the	DET
easat-3999	158	12	prove	prove	NOUN
easat-3999	158	13	of	of	ADP
easat-3999	158	14	rotation	rotation	NOUN
easat-3999	158	15	of	of	ADP
easat-3999	158	16	gravity	gravity	NOUN
easat-3999	158	17	from	from	ADP
easat-3999	158	18	desmos	desmo	NOUN
easat-3999	158	19	impact	impact	NOUN
easat-3999	158	20	.	.	PUNCT
easat-3999	159	1	something	something	PRON
easat-3999	159	2	that	that	PRON
easat-3999	159	3	show	show	VERB
easat-3999	159	4	the	the	DET
easat-3999	159	5	way	way	NOUN
easat-3999	159	6	to	to	PART
easat-3999	159	7	control	control	VERB
easat-3999	159	8	and	and	CCONJ
easat-3999	159	9	create	create	VERB
easat-3999	159	10	gravity	gravity	NOUN
easat-3999	159	11	.	.	PUNCT
easat-3999	160	1	also	also	ADV
easat-3999	160	2	,	,	PUNCT
easat-3999	160	3	in	in	ADP
easat-3999	160	4	that	that	DET
easat-3999	160	5	way	way	NOUN
easat-3999	160	6	is	be	AUX
easat-3999	160	7	explained	explain	VERB
easat-3999	160	8	that	that	SCONJ
easat-3999	160	9	there	there	ADV
easat-3999	160	10	the	the	DET
easat-3999	160	11	dark	dark	ADJ
easat-3999	160	12	matter	matter	NOUN
easat-3999	160	13	is	be	AUX
easat-3999	160	14	a	a	DET
easat-3999	160	15	space	space	NOUN
easat-3999	160	16	-	-	PUNCT
easat-3999	160	17	time	time	NOUN
easat-3999	160	18	and	and	CCONJ
easat-3999	160	19	energy	energy	NOUN
easat-3999	160	20	effect	effect	NOUN
easat-3999	160	21	from	from	ADP
easat-3999	160	22	equations	equation	NOUN
easat-3999	160	23	of	of	ADP
easat-3999	160	24	desmos	desmos	NOUN
easat-3999	160	25	(	(	PUNCT
easat-3999	160	26	bond	bond	NOUN
easat-3999	160	27	)	)	PUNCT
easat-3999	160	28	.	.	PUNCT
easat-3999	161	1	it	it	PRON
easat-3999	161	2	follows	follow	VERB
easat-3999	161	3	the	the	DET
easat-3999	161	4	mathematical	mathematical	ADJ
easat-3999	161	5	framework	framework	NOUN
easat-3999	161	6	of	of	ADP
easat-3999	161	7	gravitational	gravitational	ADJ
easat-3999	161	8	potential	potential	NOUN
easat-3999	161	9	around	around	ADP
easat-3999	161	10	a	a	DET
easat-3999	161	11	rotating	rotate	VERB
easat-3999	161	12	body	body	NOUN
easat-3999	161	13	.	.	PUNCT
easat-3999	162	1	the	the	DET
easat-3999	162	2	gravitational	gravitational	ADJ
easat-3999	162	3	potential	potential	NOUN
easat-3999	162	4	at	at	ADP
easat-3999	162	5	a	a	DET
easat-3999	162	6	distance	distance	NOUN
easat-3999	162	7	𝒓	𝒓	NOUN
easat-3999	162	8	from	from	ADP
easat-3999	162	9	a	a	DET
easat-3999	162	10	rotating	rotate	VERB
easat-3999	162	11	celestial	celestial	ADJ
easat-3999	162	12	body	body	NOUN
easat-3999	162	13	is	be	AUX
easat-3999	162	14	given	give	VERB
easat-3999	162	15	by	by	ADP
easat-3999	162	16	:	:	PUNCT
easat-3999	162	17	φ(𝑟	φ(𝑟	PROPN
easat-3999	162	18	,	,	PUNCT
easat-3999	162	19	𝜃	𝜃	NOUN
easat-3999	162	20	)	)	PUNCT
easat-3999	162	21	=	=	PUNCT
easat-3999	163	1	−	−	PRON
easat-3999	163	2	𝐺𝑀	𝐺𝑀	PROPN
easat-3999	163	3	𝑟	𝑟	NOUN
easat-3999	163	4	+	+	NUM
easat-3999	163	5	𝜔2𝑟2sin2𝜃	𝜔2𝑟2sin2𝜃	NOUN
easat-3999	163	6	2	2	NUM
easat-3999	163	7	where	where	SCONJ
easat-3999	163	8	:	:	PUNCT
easat-3999	163	9	𝐺	𝐺	PROPN
easat-3999	163	10	is	be	AUX
easat-3999	163	11	the	the	DET
easat-3999	163	12	gravitational	gravitational	ADJ
easat-3999	163	13	constant	constant	NOUN
easat-3999	163	14	,	,	PUNCT
easat-3999	163	15	𝑀	𝑀	PROPN
easat-3999	163	16	is	be	AUX
easat-3999	163	17	the	the	DET
easat-3999	163	18	mass	mass	NOUN
easat-3999	163	19	of	of	ADP
easat-3999	163	20	the	the	DET
easat-3999	163	21	central	central	ADJ
easat-3999	163	22	body	body	NOUN
easat-3999	163	23	,	,	PUNCT
easat-3999	163	24	𝑟	𝑟	PRON
easat-3999	163	25	is	be	AUX
easat-3999	163	26	the	the	DET
easat-3999	163	27	distance	distance	NOUN
easat-3999	163	28	from	from	ADP
easat-3999	163	29	the	the	DET
easat-3999	163	30	center	center	NOUN
easat-3999	163	31	,	,	PUNCT
easat-3999	163	32	𝜃	𝜃	X
easat-3999	163	33	is	be	AUX
easat-3999	163	34	the	the	DET
easat-3999	163	35	angle	angle	NOUN
easat-3999	163	36	relative	relative	ADJ
easat-3999	163	37	to	to	ADP
easat-3999	163	38	the	the	DET
easat-3999	163	39	rotational	rotational	ADJ
easat-3999	163	40	axis	axis	NOUN
easat-3999	163	41	,	,	PUNCT
easat-3999	163	42	𝜔	𝜔	X
easat-3999	163	43	is	be	AUX
easat-3999	163	44	the	the	DET
easat-3999	163	45	angular	angular	ADJ
easat-3999	163	46	velocity	velocity	NOUN
easat-3999	163	47	of	of	ADP
easat-3999	163	48	the	the	DET
easat-3999	163	49	rotating	rotate	VERB
easat-3999	163	50	body	body	NOUN
easat-3999	163	51	.	.	PUNCT
easat-3999	164	1	the	the	DET
easat-3999	164	2	term	term	NOUN
easat-3999	164	3	𝜔2𝑟2sin2𝜃	𝜔2𝑟2sin2𝜃	NOUN
easat-3999	164	4	2	2	NUM
easat-3999	164	5	accounts	account	NOUN
easat-3999	164	6	for	for	ADP
easat-3999	164	7	centrifugal	centrifugal	ADJ
easat-3999	164	8	force	force	NOUN
easat-3999	164	9	,	,	PUNCT
easat-3999	164	10	which	which	PRON
easat-3999	164	11	is	be	AUX
easat-3999	164	12	strongest	strong	ADJ
easat-3999	164	13	at	at	ADP
easat-3999	164	14	the	the	DET
easat-3999	164	15	equator	equator	NOUN
easat-3999	164	16	(	(	PUNCT
easat-3999	164	17	𝜃	𝜃	NOUN
easat-3999	164	18	=	=	PUNCT
easat-3999	164	19	𝜋	𝜋	NOUN
easat-3999	164	20	2	2	NUM
easat-3999	164	21	)	)	PUNCT
easat-3999	164	22	and	and	CCONJ
easat-3999	164	23	zero	zero	NUM
easat-3999	164	24	at	at	ADP
easat-3999	164	25	the	the	DET
easat-3999	164	26	poles	pole	NOUN
easat-3999	164	27	(	(	PUNCT
easat-3999	164	28	𝜃	𝜃	NOUN
easat-3999	164	29	=	=	NOUN
easat-3999	164	30	0	0	NUM
easat-3999	164	31	)	)	PUNCT
easat-3999	164	32	.	.	PUNCT
easat-3999	165	1	9365	9365	NUM
easat-3999	165	2	edelweiss	edelweiss	PROPN
easat-3999	165	3	applied	apply	VERB
easat-3999	165	4	science	science	NOUN
easat-3999	165	5	and	and	CCONJ
easat-3999	165	6	technology	technology	NOUN
easat-3999	165	7	issn	issn	PROPN
easat-3999	165	8	:	:	PUNCT
easat-3999	165	9	2576	2576	NUM
easat-3999	165	10	-	-	SYM
easat-3999	165	11	8484	8484	NUM
easat-3999	165	12	vol	vol	NOUN
easat-3999	165	13	.	.	PROPN
easat-3999	165	14	8	8	NUM
easat-3999	165	15	,	,	PUNCT
easat-3999	165	16	no	no	INTJ
easat-3999	165	17	.	.	NOUN
easat-3999	165	18	6	6	NUM
easat-3999	165	19	:	:	SYM
easat-3999	165	20	9356	9356	NUM
easat-3999	165	21	-	-	SYM
easat-3999	165	22	9375	9375	NUM
easat-3999	165	23	,	,	PUNCT
easat-3999	165	24	2024	2024	NUM
easat-3999	165	25	doi	doi	NOUN
easat-3999	165	26	:	:	PUNCT
easat-3999	165	27	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	165	28	©	©	PROPN
easat-3999	165	29	2024	2024	NUM
easat-3999	165	30	by	by	ADP
easat-3999	165	31	the	the	DET
easat-3999	165	32	author	author	NOUN
easat-3999	165	33	;	;	PUNCT
easat-3999	165	34	licensee	licensee	PROPN
easat-3999	165	35	learning	learn	VERB
easat-3999	165	36	gate	gate	NOUN
easat-3999	165	37	geometry	geometry	NOUN
easat-3999	165	38	of	of	ADP
easat-3999	165	39	the	the	DET
easat-3999	165	40	equatorial	equatorial	PROPN
easat-3999	165	41	bulge	bulge	PROPN
easat-3999	165	42	:	:	PUNCT
easat-3999	165	43	the	the	DET
easat-3999	165	44	radius	radius	NOUN
easat-3999	165	45	difference	difference	NOUN
easat-3999	165	46	between	between	ADP
easat-3999	165	47	the	the	DET
easat-3999	165	48	equator	equator	NOUN
easat-3999	165	49	(	(	PUNCT
easat-3999	165	50	𝑹𝐞𝐪	𝑹𝐞𝐪	PROPN
easat-3999	165	51	)	)	PUNCT
easat-3999	165	52	and	and	CCONJ
easat-3999	165	53	the	the	DET
easat-3999	165	54	poles	pole	NOUN
easat-3999	165	55	(	(	PUNCT
easat-3999	165	56	𝑹𝐩𝐨𝐥𝐞	𝑹𝐩𝐨𝐥𝐞	PROPN
easat-3999	165	57	)	)	PUNCT
easat-3999	165	58	for	for	ADP
easat-3999	165	59	a	a	DET
easat-3999	165	60	rotating	rotate	VERB
easat-3999	165	61	sphere	sphere	NOUN
easat-3999	165	62	is	be	AUX
easat-3999	165	63	:	:	PUNCT
easat-3999	165	64	δ𝑅	δ𝑅	PROPN
easat-3999	165	65	=	=	PUNCT
easat-3999	165	66	𝑅eq	𝑅eq	PROPN
easat-3999	165	67	−	−	PROPN
easat-3999	165	68	𝑅pole	𝑅pole	PROPN
easat-3999	165	69	≈	≈	PROPN
easat-3999	165	70	𝜔2𝑅3	𝜔2𝑅3	PROPN
easat-3999	165	71	2𝐺𝑀	2𝐺𝑀	NUM
easat-3999	165	72	where	where	SCONJ
easat-3999	165	73	:	:	PUNCT
easat-3999	165	74	δ𝑅	δ𝑅	PROPN
easat-3999	165	75	is	be	AUX
easat-3999	165	76	the	the	DET
easat-3999	165	77	equatorial	equatorial	ADJ
easat-3999	165	78	bulge	bulge	NOUN
easat-3999	165	79	.	.	PUNCT
easat-3999	166	1	gravitational	gravitational	ADJ
easat-3999	166	2	force	force	NOUN
easat-3999	166	3	distribution	distribution	NOUN
easat-3999	166	4	the	the	DET
easat-3999	166	5	effective	effective	ADJ
easat-3999	166	6	gravitational	gravitational	ADJ
easat-3999	166	7	force	force	NOUN
easat-3999	166	8	depends	depend	VERB
easat-3999	166	9	on	on	ADP
easat-3999	166	10	the	the	DET
easat-3999	166	11	gradient	gradient	NOUN
easat-3999	166	12	of	of	ADP
easat-3999	166	13	the	the	DET
easat-3999	166	14	gravitational	gravitational	ADJ
easat-3999	166	15	potential	potential	NOUN
easat-3999	166	16	:	:	PUNCT
easat-3999	166	17	𝐹𝑟	𝐹𝑟	PROPN
easat-3999	166	18	=	=	PUNCT
easat-3999	166	19	−	−	PROPN
easat-3999	166	20	𝜕φ	𝜕φ	NOUN
easat-3999	166	21	𝜕𝑟	𝜕𝑟	ADV
easat-3999	166	22	,	,	PUNCT
easat-3999	167	1	𝐹𝜃	𝐹𝜃	PROPN
easat-3999	167	2	=	=	PUNCT
easat-3999	167	3	−	−	PROPN
easat-3999	167	4	1	1	NUM
easat-3999	168	1	𝑟	𝑟	NOUN
easat-3999	168	2	𝜕φ	𝜕φ	NOUN
easat-3999	168	3	𝜕𝜃	𝜕𝜃	VERB
easat-3999	168	4	𝐹𝑟	𝐹𝑟	NOUN
easat-3999	168	5	:	:	PUNCT
easat-3999	168	6	radial	radial	ADJ
easat-3999	168	7	force	force	NOUN
easat-3999	168	8	,	,	PUNCT
easat-3999	168	9	symmetric	symmetric	ADJ
easat-3999	168	10	in	in	ADP
easat-3999	168	11	all	all	DET
easat-3999	168	12	directions	direction	NOUN
easat-3999	168	13	.	.	PUNCT
easat-3999	169	1	𝐹𝜃	𝐹𝜃	ADP
easat-3999	169	2	:	:	PUNCT
easat-3999	169	3	angular	angular	ADJ
easat-3999	169	4	force	force	NOUN
easat-3999	169	5	,	,	PUNCT
easat-3999	169	6	strongest	strong	ADJ
easat-3999	169	7	at	at	ADP
easat-3999	169	8	the	the	DET
easat-3999	169	9	equatorial	equatorial	ADJ
easat-3999	169	10	plane	plane	NOUN
easat-3999	169	11	(	(	PUNCT
easat-3999	169	12	𝜃	𝜃	NOUN
easat-3999	169	13	=	=	PUNCT
easat-3999	169	14	𝜋	𝜋	NOUN
easat-3999	169	15	2	2	NUM
easat-3999	169	16	)	)	PUNCT
easat-3999	169	17	.	.	PUNCT
easat-3999	170	1	conservation	conservation	NOUN
easat-3999	170	2	of	of	ADP
easat-3999	170	3	angular	angular	ADJ
easat-3999	170	4	momentum	momentum	NOUN
easat-3999	170	5	:	:	PUNCT
easat-3999	170	6	the	the	DET
easat-3999	170	7	angular	angular	ADJ
easat-3999	170	8	momentum	momentum	NOUN
easat-3999	170	9	𝐿	𝐿	PROPN
easat-3999	170	10	of	of	ADP
easat-3999	170	11	a	a	DET
easat-3999	170	12	rotating	rotate	VERB
easat-3999	170	13	system	system	NOUN
easat-3999	170	14	is	be	AUX
easat-3999	170	15	:	:	PUNCT
easat-3999	170	16	𝐿	𝐿	NOUN
easat-3999	170	17	=	=	NOUN
easat-3999	170	18	𝑚𝑣𝑟	𝑚𝑣𝑟	NOUN
easat-3999	170	19	=	=	SYM
easat-3999	171	1	𝑚𝜔𝑟2	𝑚𝜔𝑟2	NOUN
easat-3999	171	2	orbiting	orbit	VERB
easat-3999	171	3	bodies	body	NOUN
easat-3999	171	4	align	align	VERB
easat-3999	171	5	their	their	PRON
easat-3999	171	6	motion	motion	NOUN
easat-3999	171	7	along	along	ADP
easat-3999	171	8	the	the	DET
easat-3999	171	9	equatorial	equatorial	ADJ
easat-3999	171	10	plane	plane	NOUN
easat-3999	171	11	to	to	PART
easat-3999	171	12	maximize	maximize	VERB
easat-3999	171	13	angular	angular	ADJ
easat-3999	171	14	momentum	momentum	NOUN
easat-3999	171	15	.	.	PUNCT
easat-3999	172	1	example	example	NOUN
easat-3999	172	2	calculation	calculation	NOUN
easat-3999	172	3	:	:	PUNCT
easat-3999	172	4	equatorial	equatorial	ADJ
easat-3999	172	5	bulge	bulge	NOUN
easat-3999	172	6	and	and	CCONJ
easat-3999	172	7	the	the	DET
easat-3999	172	8	angular	angular	ADJ
easat-3999	172	9	velocity	velocity	NOUN
easat-3999	172	10	of	of	ADP
easat-3999	172	11	the	the	DET
easat-3999	172	12	sun	sun	NOUN
easat-3999	172	13	is	be	AUX
easat-3999	172	14	:	:	PUNCT
easat-3999	172	15	𝜔	𝜔	PART
easat-3999	172	16	=	=	NUM
easat-3999	172	17	2𝜋	2𝜋	NUM
easat-3999	172	18	𝑇	𝑇	PROPN
easat-3999	172	19	=	=	SYM
easat-3999	172	20	2𝜋	2𝜋	PROPN
easat-3999	172	21	25×24×3600	25×24×3600	NUM
easat-3999	173	1	≈	≈	PROPN
easat-3999	173	2	2.91	2.91	NUM
easat-3999	173	3	×	×	NOUN
easat-3999	173	4	10−6	10−6	NUM
easat-3999	173	5	rad	rad	PROPN
easat-3999	173	6	/	/	SYM
easat-3999	173	7	s	s	VERB
easat-3999	173	8	the	the	DET
easat-3999	173	9	equatorial	equatorial	ADJ
easat-3999	173	10	bulge	bulge	NOUN
easat-3999	173	11	is	be	AUX
easat-3999	173	12	:	:	PUNCT
easat-3999	173	13	δ𝑅	δ𝑅	PROPN
easat-3999	173	14	≈	≈	PROPN
easat-3999	173	15	𝜔2𝑅3	𝜔2𝑅3	PROPN
easat-3999	173	16	2𝐺𝑀	2𝐺𝑀	NUM
easat-3999	173	17	=	=	SYM
easat-3999	173	18	(	(	PUNCT
easat-3999	173	19	2.91×10−6)2(6.96×108)3	2.91×10−6)2(6.96×108)3	NOUN
easat-3999	173	20	2(6.674×10−11)(1.989×1030	2(6.674×10−11)(1.989×1030	NUM
easat-3999	173	21	)	)	PUNCT
easat-3999	173	22	δ𝑅	δ𝑅	PROPN
easat-3999	173	23	≈	≈	PROPN
easat-3999	173	24	10.5	10.5	NUM
easat-3999	173	25	m	m	NOUN
easat-3999	173	26	gravitational	gravitational	ADJ
easat-3999	173	27	potential	potential	ADJ
easat-3999	173	28	distribution	distribution	NOUN
easat-3999	173	29	at	at	ADP
easat-3999	173	30	𝑟	𝑟	NOUN
easat-3999	173	31	=	=	SYM
easat-3999	173	32	1.5	1.5	NUM
easat-3999	173	33	×	×	NOUN
easat-3999	173	34	1011	1011	NUM
easat-3999	173	35	m	m	NOUN
easat-3999	173	36	(	(	PUNCT
easat-3999	173	37	distance	distance	NOUN
easat-3999	173	38	from	from	ADP
easat-3999	173	39	earth	earth	NOUN
easat-3999	173	40	to	to	ADP
easat-3999	173	41	sun	sun	NOUN
easat-3999	173	42	):	):	PUNCT
easat-3999	173	43	φ(𝑟	φ(𝑟	PROPN
easat-3999	173	44	,	,	PUNCT
easat-3999	173	45	𝜃	𝜃	NOUN
easat-3999	173	46	)	)	PUNCT
easat-3999	173	47	=	=	PUNCT
easat-3999	174	1	−	−	PRON
easat-3999	174	2	𝐺𝑀	𝐺𝑀	PROPN
easat-3999	174	3	𝑟	𝑟	NOUN
easat-3999	174	4	+	+	NUM
easat-3999	174	5	𝜔2𝑟2sin2𝜃	𝜔2𝑟2sin2𝜃	NOUN
easat-3999	174	6	2	2	NUM
easat-3999	174	7	at	at	ADP
easat-3999	174	8	the	the	DET
easat-3999	174	9	equator	equator	NOUN
easat-3999	174	10	(	(	PUNCT
easat-3999	174	11	𝜃	𝜃	NOUN
easat-3999	174	12	=	=	X
easat-3999	174	13	𝜋	𝜋	X
easat-3999	174	14	2	2	NUM
easat-3999	174	15	):	):	PUNCT
easat-3999	174	16	φeq	φeq	NOUN
easat-3999	175	1	≈	≈	PROPN
easat-3999	175	2	−	−	PROPN
easat-3999	175	3	(	(	PUNCT
easat-3999	175	4	6.674×10−11)(1.989×1030	6.674×10−11)(1.989×1030	PROPN
easat-3999	175	5	)	)	PUNCT
easat-3999	175	6	1.5×1011	1.5×1011	NUM
easat-3999	176	1	+	+	CCONJ
easat-3999	176	2	(	(	PUNCT
easat-3999	176	3	2.91×10−6)2(1.5×1011)2	2.91×10−6)2(1.5×1011)2	NUM
easat-3999	176	4	2	2	NUM
easat-3999	176	5	φeq	φeq	NOUN
easat-3999	176	6	≈	≈	PROPN
easat-3999	176	7	−8.85	−8.85	NOUN
easat-3999	177	1	×	×	NOUN
easat-3999	178	1	108	108	NUM
easat-3999	179	1	+	+	CCONJ
easat-3999	179	2	6.34	6.34	NUM
easat-3999	179	3	×	×	NOUN
easat-3999	179	4	108	108	NUM
easat-3999	180	1	≈	≈	PROPN
easat-3999	181	1	−2.51	−2.51	PROPN
easat-3999	181	2	×	×	NOUN
easat-3999	181	3	108	108	NUM
easat-3999	181	4	j	j	NOUN
easat-3999	181	5	/	/	SYM
easat-3999	181	6	kg	kg	PROPN
easat-3999	181	7	at	at	ADP
easat-3999	181	8	the	the	DET
easat-3999	181	9	pole	pole	NOUN
easat-3999	181	10	(	(	PUNCT
easat-3999	181	11	𝜃	𝜃	NOUN
easat-3999	181	12	=	=	SYM
easat-3999	181	13	0	0	NUM
easat-3999	181	14	):	):	PUNCT
easat-3999	181	15	φpole	φpole	NOUN
easat-3999	182	1	≈	≈	PROPN
easat-3999	182	2	−8.85	−8.85	PROPN
easat-3999	182	3	×	×	NOUN
easat-3999	182	4	108	108	NUM
easat-3999	182	5	j	j	NOUN
easat-3999	182	6	/	/	SYM
easat-3999	182	7	kg	kg	PROPN
easat-3999	182	8	this	this	PRON
easat-3999	182	9	demonstrates	demonstrate	VERB
easat-3999	182	10	that	that	SCONJ
easat-3999	182	11	the	the	DET
easat-3999	182	12	gravitational	gravitational	ADJ
easat-3999	182	13	potential	potential	NOUN
easat-3999	182	14	is	be	AUX
easat-3999	182	15	shallower	shallow	ADJ
easat-3999	182	16	at	at	ADP
easat-3999	182	17	the	the	DET
easat-3999	182	18	equator	equator	NOUN
easat-3999	182	19	,	,	PUNCT
easat-3999	182	20	favoring	favor	VERB
easat-3999	182	21	a	a	DET
easat-3999	182	22	diskshaped	diskshaped	NOUN
easat-3999	182	23	mass	mass	NOUN
easat-3999	182	24	distribution	distribution	NOUN
easat-3999	182	25	.	.	PUNCT
easat-3999	183	1	9366	9366	NUM
easat-3999	183	2	edelweiss	edelweiss	PROPN
easat-3999	183	3	applied	apply	VERB
easat-3999	183	4	science	science	NOUN
easat-3999	183	5	and	and	CCONJ
easat-3999	183	6	technology	technology	NOUN
easat-3999	183	7	issn	issn	PROPN
easat-3999	183	8	:	:	PUNCT
easat-3999	183	9	2576	2576	NUM
easat-3999	183	10	-	-	SYM
easat-3999	183	11	8484	8484	NUM
easat-3999	183	12	vol	vol	NOUN
easat-3999	183	13	.	.	PROPN
easat-3999	183	14	8	8	NUM
easat-3999	183	15	,	,	PUNCT
easat-3999	183	16	no	no	INTJ
easat-3999	183	17	.	.	NOUN
easat-3999	183	18	6	6	NUM
easat-3999	183	19	:	:	SYM
easat-3999	183	20	9356	9356	NUM
easat-3999	183	21	-	-	SYM
easat-3999	183	22	9375	9375	NUM
easat-3999	183	23	,	,	PUNCT
easat-3999	183	24	2024	2024	NUM
easat-3999	183	25	doi	doi	NOUN
easat-3999	183	26	:	:	PUNCT
easat-3999	183	27	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	183	28	©	©	PROPN
easat-3999	183	29	2024	2024	NUM
easat-3999	183	30	by	by	ADP
easat-3999	183	31	the	the	DET
easat-3999	183	32	author	author	NOUN
easat-3999	183	33	;	;	PUNCT
easat-3999	183	34	licensee	licensee	PROPN
easat-3999	183	35	learning	learn	VERB
easat-3999	183	36	gate	gate	NOUN
easat-3999	183	37	figure	figure	NOUN
easat-3999	183	38	4	4	NUM
easat-3999	183	39	.	.	PUNCT
easat-3999	183	40	gravity	gravity	NOUN
easat-3999	183	41	reflection	reflection	NOUN
easat-3999	183	42	(	(	PUNCT
easat-3999	183	43	author	author	NOUN
easat-3999	183	44	’s	’s	PART
easat-3999	183	45	scheme	scheme	NOUN
easat-3999	183	46	,	,	PUNCT
easat-3999	183	47	,	,	PUNCT
easat-3999	183	48	see	see	VERB
easat-3999	183	49	appendix	appendix	NOUN
easat-3999	183	50	d	d	NOUN
easat-3999	183	51	)	)	PUNCT
easat-3999	183	52	.	.	PUNCT
easat-3999	184	1	gravitational	gravitational	ADJ
easat-3999	184	2	deflection	deflection	NOUN
easat-3999	184	3	angle	angle	NOUN
easat-3999	184	4	and	and	CCONJ
easat-3999	184	5	potential	potential	NOUN
easat-3999	184	6	in	in	ADP
easat-3999	184	7	the	the	DET
easat-3999	184	8	desmos	desmos	PROPN
easat-3999	184	9	model	model	NOUN
easat-3999	184	10	.	.	PUNCT
easat-3999	185	1	deflection	deflection	NOUN
easat-3999	185	2	angle	angle	NOUN
easat-3999	185	3	in	in	ADP
easat-3999	185	4	desmos	desmos	NOUN
easat-3999	185	5	model	model	NOUN
easat-3999	185	6	.	.	PUNCT
easat-3999	186	1	the	the	DET
easat-3999	186	2	total	total	ADJ
easat-3999	186	3	deflection	deflection	NOUN
easat-3999	186	4	angle	angle	NOUN
easat-3999	186	5	𝚫𝜶𝐭𝐨𝐭𝐚𝐥	𝚫𝜶𝐭𝐨𝐭𝐚𝐥	PROPN
easat-3999	186	6	is	be	AUX
easat-3999	186	7	given	give	VERB
easat-3999	186	8	by	by	ADP
easat-3999	186	9	:	:	PUNCT
easat-3999	186	10	δ𝛼total	δ𝛼total	ADJ
easat-3999	186	11	=	=	SYM
easat-3999	186	12	4𝐺(𝑀+𝑀dark	4𝐺(𝑀+𝑀dark	NOUN
easat-3999	186	13	)	)	PUNCT
easat-3999	186	14	𝑐2⋅𝑏⋅𝑓(𝜃	𝑐2⋅𝑏⋅𝑓(𝜃	PROPN
easat-3999	186	15	)	)	PUNCT
easat-3999	186	16	⋅	⋅	PROPN
easat-3999	186	17	(	(	PUNCT
easat-3999	186	18	1	1	NUM
easat-3999	186	19	+	+	CCONJ
easat-3999	186	20	𝑣(𝑟	𝑣(𝑟	NOUN
easat-3999	186	21	)	)	PUNCT
easat-3999	186	22	𝑐	𝑐	NOUN
easat-3999	186	23	)	)	PUNCT
easat-3999	187	1	+	+	CCONJ
easat-3999	187	2	𝑘	𝑘	DET
easat-3999	187	3	⋅	⋅	PROPN
easat-3999	187	4	𝜌(𝑟	𝜌(𝑟	PROPN
easat-3999	187	5	,	,	PUNCT
easat-3999	187	6	𝜃	𝜃	NOUN
easat-3999	187	7	)	)	PUNCT
easat-3999	187	8	⋅	⋅	PROPN
easat-3999	187	9	cos(𝜃	cos(𝜃	PROPN
easat-3999	187	10	)	)	PUNCT
easat-3999	187	11	where	where	SCONJ
easat-3999	187	12	:	:	PUNCT
easat-3999	187	13	𝑀	𝑀	PROPN
easat-3999	187	14	+	+	CCONJ
easat-3999	187	15	𝑀dark	𝑀dark	PROPN
easat-3999	187	16	:	:	PUNCT
easat-3999	187	17	total	total	ADJ
easat-3999	187	18	effective	effective	ADJ
easat-3999	187	19	mass	mass	NOUN
easat-3999	187	20	,	,	PUNCT
easat-3999	187	21	including	include	VERB
easat-3999	187	22	observable	observable	ADJ
easat-3999	187	23	mass	mass	NOUN
easat-3999	187	24	𝑀	𝑀	PROPN
easat-3999	187	25	and	and	CCONJ
easat-3999	187	26	dark	dark	ADJ
easat-3999	187	27	matter	matter	NOUN
easat-3999	187	28	𝑀dark	𝑀dark	PROPN
easat-3999	187	29	.	.	PUNCT
easat-3999	188	1	𝑏	𝑏	DET
easat-3999	188	2	⋅	⋅	PROPN
easat-3999	188	3	𝑓(𝜃	𝑓(𝜃	PROPN
easat-3999	188	4	):	):	PUNCT
easat-3999	188	5	modified	modify	VERB
easat-3999	188	6	impact	impact	NOUN
easat-3999	188	7	parameter	parameter	NOUN
easat-3999	188	8	,	,	PUNCT
easat-3999	188	9	accounting	account	VERB
easat-3999	188	10	for	for	ADP
easat-3999	188	11	angular	angular	ADJ
easat-3999	188	12	dependencies	dependency	NOUN
easat-3999	188	13	.	.	PUNCT
easat-3999	189	1	𝑣(𝑟	𝑣(𝑟	VERB
easat-3999	189	2	)	)	PUNCT
easat-3999	189	3	𝑐	𝑐	NOUN
easat-3999	189	4	:	:	PUNCT
easat-3999	189	5	relativistic	relativistic	ADJ
easat-3999	189	6	velocity	velocity	NOUN
easat-3999	189	7	effects	effect	NOUN
easat-3999	189	8	.	.	PUNCT
easat-3999	190	1	𝜌(𝑟	𝜌(𝑟	NOUN
easat-3999	190	2	,	,	PUNCT
easat-3999	190	3	𝜃	𝜃	NOUN
easat-3999	190	4	)	)	PUNCT
easat-3999	190	5	⋅	⋅	PROPN
easat-3999	190	6	cos(𝜃	cos(𝜃	PROPN
easat-3999	190	7	):	):	PUNCT
easat-3999	190	8	density	density	NOUN
easat-3999	190	9	-	-	PUNCT
easat-3999	190	10	dependent	dependent	ADJ
easat-3999	190	11	modulation	modulation	NOUN
easat-3999	190	12	of	of	ADP
easat-3999	190	13	deflection	deflection	NOUN
easat-3999	190	14	.	.	PUNCT
easat-3999	191	1	gravitational	gravitational	ADJ
easat-3999	191	2	potential	potential	NOUN
easat-3999	191	3	in	in	ADP
easat-3999	191	4	desmos	desmos	NOUN
easat-3999	191	5	model	model	NOUN
easat-3999	191	6	the	the	DET
easat-3999	191	7	gravitational	gravitational	ADJ
easat-3999	191	8	potential	potential	ADJ
easat-3999	191	9	𝚽(𝒓	𝚽(𝒓	NUM
easat-3999	191	10	,	,	PUNCT
easat-3999	191	11	𝜽	𝜽	NOUN
easat-3999	191	12	)	)	PUNCT
easat-3999	191	13	in	in	ADP
easat-3999	191	14	the	the	DET
easat-3999	191	15	desmos	desmos	NOUN
easat-3999	191	16	model	model	NOUN
easat-3999	191	17	is	be	AUX
easat-3999	191	18	:	:	PUNCT
easat-3999	191	19	φ(𝑟	φ(𝑟	PROPN
easat-3999	191	20	,	,	PUNCT
easat-3999	191	21	𝜃	𝜃	NOUN
easat-3999	191	22	)	)	PUNCT
easat-3999	191	23	=	=	PUNCT
easat-3999	192	1	−	−	PRON
easat-3999	192	2	𝐺𝑀	𝐺𝑀	PROPN
easat-3999	192	3	𝑟	𝑟	NOUN
easat-3999	192	4	+	+	NUM
easat-3999	192	5	𝜔2𝑟2sin2𝜃	𝜔2𝑟2sin2𝜃	NOUN
easat-3999	192	6	2	2	NUM
easat-3999	192	7	where	where	SCONJ
easat-3999	192	8	:	:	PUNCT
easat-3999	192	9	−	−	PROPN
easat-3999	192	10	𝐺𝑀	𝐺𝑀	PROPN
easat-3999	192	11	𝑟	𝑟	NOUN
easat-3999	192	12	:	:	PUNCT
easat-3999	192	13	classical	classical	ADJ
easat-3999	192	14	gravitational	gravitational	ADJ
easat-3999	192	15	potential	potential	NOUN
easat-3999	192	16	.	.	PUNCT
easat-3999	193	1	𝜔2𝑟2sin2𝜃	𝜔2𝑟2sin2𝜃	NOUN
easat-3999	193	2	2	2	NUM
easat-3999	193	3	:	:	PUNCT
easat-3999	193	4	rotational	rotational	ADJ
easat-3999	193	5	effects	effect	NOUN
easat-3999	193	6	,	,	PUNCT
easat-3999	193	7	strongest	strong	ADJ
easat-3999	193	8	at	at	ADP
easat-3999	193	9	the	the	DET
easat-3999	193	10	equator	equator	NOUN
easat-3999	193	11	(	(	PUNCT
easat-3999	193	12	𝜃	𝜃	NOUN
easat-3999	193	13	=	=	PUNCT
easat-3999	193	14	𝜋	𝜋	NOUN
easat-3999	193	15	2	2	NUM
easat-3999	193	16	)	)	PUNCT
easat-3999	193	17	.	.	PUNCT
easat-3999	194	1	relating	relate	VERB
easat-3999	194	2	the	the	DET
easat-3999	194	3	deflection	deflection	NOUN
easat-3999	194	4	angle	angle	NOUN
easat-3999	194	5	to	to	ADP
easat-3999	194	6	the	the	DET
easat-3999	194	7	gravitational	gravitational	ADJ
easat-3999	194	8	potential	potential	NOUN
easat-3999	194	9	:	:	PUNCT
easat-3999	194	10	the	the	DET
easat-3999	194	11	deflection	deflection	NOUN
easat-3999	194	12	angle	angle	NOUN
easat-3999	194	13	δ𝛼total	δ𝛼total	NOUN
easat-3999	194	14	arises	arise	VERB
easat-3999	194	15	from	from	ADP
easat-3999	194	16	the	the	DET
easat-3999	194	17	gradient	gradient	NOUN
easat-3999	194	18	of	of	ADP
easat-3999	194	19	the	the	DET
easat-3999	194	20	gravitational	gravitational	ADJ
easat-3999	194	21	potential	potential	ADJ
easat-3999	194	22	φ(𝑟	φ(𝑟	PROPN
easat-3999	194	23	,	,	PUNCT
easat-3999	194	24	𝜃	𝜃	NOUN
easat-3999	194	25	):	):	PUNCT
easat-3999	194	26	δ𝛼total	δ𝛼total	ADJ
easat-3999	194	27	∝	∝	PROPN
easat-3999	194	28	∇φ(𝑟	∇φ(𝑟	NOUN
easat-3999	194	29	,	,	PUNCT
easat-3999	194	30	𝜃	𝜃	NOUN
easat-3999	194	31	)	)	PUNCT
easat-3999	194	32	decomposing	decompose	VERB
easat-3999	194	33	𝜵𝛷(𝑟	𝜵𝛷(𝑟	PROPN
easat-3999	194	34	,	,	PUNCT
easat-3999	194	35	𝜃	𝜃	NOUN
easat-3999	194	36	)	)	PUNCT
easat-3999	194	37	the	the	DET
easat-3999	194	38	gradient	gradient	NOUN
easat-3999	194	39	in	in	ADP
easat-3999	194	40	spherical	spherical	ADJ
easat-3999	194	41	coordinates	coordinate	NOUN
easat-3999	194	42	(	(	PUNCT
easat-3999	194	43	𝑟	𝑟	NOUN
easat-3999	194	44	,	,	PUNCT
easat-3999	194	45	𝜃	𝜃	NOUN
easat-3999	194	46	)	)	PUNCT
easat-3999	194	47	is	be	AUX
easat-3999	194	48	:	:	PUNCT
easat-3999	194	49	∇φ(𝑟	∇φ(𝑟	NOUN
easat-3999	194	50	,	,	PUNCT
easat-3999	194	51	𝜃	𝜃	NOUN
easat-3999	194	52	)	)	PUNCT
easat-3999	194	53	=	=	SYM
easat-3999	194	54	𝜕φ	𝜕φ	NOUN
easat-3999	194	55	𝜕𝑟	𝜕𝑟	NOUN
easat-3999	194	56	�	�	PROPN
easat-3999	194	57	̂	̂	VERB
easat-3999	194	58	�	�	NOUN
easat-3999	194	59	+	+	CCONJ
easat-3999	194	60	1	1	NUM
easat-3999	194	61	𝑟	𝑟	NOUN
easat-3999	194	62	𝜕φ	𝜕φ	NOUN
easat-3999	194	63	𝜕𝜃	𝜕𝜃	VERB
easat-3999	194	64	𝜃	𝜃	PRON
easat-3999	194	65	radial	radial	ADJ
easat-3999	194	66	component	component	NOUN
easat-3999	194	67	(	(	PUNCT
easat-3999	194	68	𝜕φ	𝜕φ	NOUN
easat-3999	194	69	𝜕𝑟	𝜕𝑟	NOUN
easat-3999	194	70	):	):	PUNCT
easat-3999	194	71	9367	9367	NUM
easat-3999	194	72	edelweiss	edelweiss	PROPN
easat-3999	194	73	applied	apply	VERB
easat-3999	194	74	science	science	NOUN
easat-3999	194	75	and	and	CCONJ
easat-3999	194	76	technology	technology	NOUN
easat-3999	194	77	issn	issn	PROPN
easat-3999	194	78	:	:	PUNCT
easat-3999	194	79	2576	2576	NUM
easat-3999	194	80	-	-	SYM
easat-3999	194	81	8484	8484	NUM
easat-3999	194	82	vol	vol	NOUN
easat-3999	194	83	.	.	PROPN
easat-3999	194	84	8	8	NUM
easat-3999	194	85	,	,	PUNCT
easat-3999	194	86	no	no	INTJ
easat-3999	194	87	.	.	NOUN
easat-3999	194	88	6	6	NUM
easat-3999	194	89	:	:	SYM
easat-3999	194	90	9356	9356	NUM
easat-3999	194	91	-	-	SYM
easat-3999	194	92	9375	9375	NUM
easat-3999	194	93	,	,	PUNCT
easat-3999	194	94	2024	2024	NUM
easat-3999	194	95	doi	doi	NOUN
easat-3999	194	96	:	:	PUNCT
easat-3999	194	97	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	194	98	©	©	PROPN
easat-3999	194	99	2024	2024	NUM
easat-3999	194	100	by	by	ADP
easat-3999	194	101	the	the	DET
easat-3999	194	102	author	author	NOUN
easat-3999	194	103	;	;	PUNCT
easat-3999	194	104	licensee	licensee	NOUN
easat-3999	194	105	learning	learning	NOUN
easat-3999	194	106	gate	gate	NOUN
easat-3999	194	107	𝜕φ	𝜕φ	PROPN
easat-3999	194	108	𝜕𝑟	𝜕𝑟	PROPN
easat-3999	194	109	=	=	SYM
easat-3999	194	110	𝐺𝑀	𝐺𝑀	PROPN
easat-3999	194	111	𝑟2	𝑟2	NOUN
easat-3999	194	112	+	+	CCONJ
easat-3999	194	113	𝜔2𝑟sin2𝜃	𝜔2𝑟sin2𝜃	DET
easat-3999	194	114	the	the	DET
easat-3999	194	115	classical	classical	ADJ
easat-3999	194	116	term	term	NOUN
easat-3999	194	117	𝐺𝑀	𝐺𝑀	PROPN
easat-3999	194	118	𝑟2	𝑟2	NOUN
easat-3999	194	119	dominates	dominate	VERB
easat-3999	194	120	at	at	ADP
easat-3999	194	121	large	large	ADJ
easat-3999	194	122	distances	distance	NOUN
easat-3999	194	123	.	.	PUNCT
easat-3999	195	1	the	the	DET
easat-3999	195	2	rotational	rotational	ADJ
easat-3999	195	3	term	term	NOUN
easat-3999	195	4	𝜔2𝑟sin2𝜃	𝜔2𝑟sin2𝜃	PROPN
easat-3999	195	5	becomes	become	VERB
easat-3999	195	6	significant	significant	ADJ
easat-3999	195	7	at	at	ADP
easat-3999	195	8	smaller	small	ADJ
easat-3999	195	9	distances	distance	NOUN
easat-3999	195	10	.	.	PUNCT
easat-3999	196	1	angular	angular	ADJ
easat-3999	196	2	component	component	NOUN
easat-3999	196	3	(	(	PUNCT
easat-3999	196	4	𝝏φ	𝝏φ	X
easat-3999	196	5	𝝏𝜃	𝝏𝜃	X
easat-3999	196	6	):	):	PUNCT
easat-3999	196	7	𝜕φ	𝜕φ	NOUN
easat-3999	196	8	𝜕𝜃	𝜕𝜃	NOUN
easat-3999	196	9	=	=	SYM
easat-3999	196	10	𝜔2𝑟2sin(2𝜃	𝜔2𝑟2sin(2𝜃	ADJ
easat-3999	196	11	)	)	PUNCT
easat-3999	196	12	this	this	DET
easat-3999	196	13	term	term	NOUN
easat-3999	196	14	reflects	reflect	VERB
easat-3999	196	15	the	the	DET
easat-3999	196	16	dependence	dependence	NOUN
easat-3999	196	17	of	of	ADP
easat-3999	196	18	deflection	deflection	NOUN
easat-3999	196	19	on	on	ADP
easat-3999	196	20	latitude	latitude	NOUN
easat-3999	196	21	(	(	PUNCT
easat-3999	196	22	𝜃	𝜃	NOUN
easat-3999	196	23	)	)	PUNCT
easat-3999	196	24	and	and	CCONJ
easat-3999	196	25	is	be	AUX
easat-3999	196	26	strongest	strong	ADJ
easat-3999	196	27	at	at	ADP
easat-3999	196	28	the	the	DET
easat-3999	196	29	equator	equator	NOUN
easat-3999	196	30	(	(	PUNCT
easat-3999	196	31	𝜃	𝜃	NOUN
easat-3999	196	32	=	=	PUNCT
easat-3999	196	33	𝜋	𝜋	NOUN
easat-3999	196	34	2	2	NUM
easat-3999	196	35	)	)	PUNCT
easat-3999	196	36	.	.	PUNCT
easat-3999	197	1	relating	relate	VERB
easat-3999	197	2	𝚽(𝒓	𝚽(𝒓	NUM
easat-3999	197	3	,	,	PUNCT
easat-3999	197	4	𝜽	𝜽	NOUN
easat-3999	197	5	)	)	PUNCT
easat-3999	197	6	to	to	ADP
easat-3999	197	7	terms	term	NOUN
easat-3999	197	8	in	in	ADP
easat-3999	197	9	𝚫𝜶𝐭𝐨𝐭𝐚𝐥	𝚫𝜶𝐭𝐨𝐭𝐚𝐥	PROPN
easat-3999	197	10	:	:	PUNCT
easat-3999	197	11	the	the	DET
easat-3999	197	12	terms	term	NOUN
easat-3999	197	13	in	in	ADP
easat-3999	197	14	𝚫𝜶𝐭𝐨𝐭𝐚𝐥	𝚫𝜶𝐭𝐨𝐭𝐚𝐥	PROPN
easat-3999	197	15	correspond	correspond	NOUN
easat-3999	197	16	to	to	ADP
easat-3999	197	17	components	component	NOUN
easat-3999	197	18	of	of	ADP
easat-3999	197	19	𝚽(𝒓	𝚽(𝒓	NUM
easat-3999	197	20	,	,	PUNCT
easat-3999	197	21	𝜽	𝜽	NOUN
easat-3999	197	22	):	):	PUNCT
easat-3999	197	23	𝑀	𝑀	PROPN
easat-3999	197	24	+	+	CCONJ
easat-3999	197	25	𝑀dark	𝑀dark	PROPN
easat-3999	197	26	:	:	PUNCT
easat-3999	197	27	derived	derive	VERB
easat-3999	197	28	from	from	ADP
easat-3999	197	29	the	the	DET
easat-3999	197	30	classical	classical	ADJ
easat-3999	197	31	term	term	NOUN
easat-3999	197	32	𝐺𝑀	𝐺𝑀	PROPN
easat-3999	197	33	𝑟	𝑟	NOUN
easat-3999	197	34	,	,	PUNCT
easat-3999	197	35	incorporating	incorporate	VERB
easat-3999	197	36	contributions	contribution	NOUN
easat-3999	197	37	from	from	ADP
easat-3999	197	38	dark	dark	ADJ
easat-3999	197	39	matter	matter	NOUN
easat-3999	197	40	.	.	PUNCT
easat-3999	198	1	𝑏	𝑏	DET
easat-3999	198	2	⋅	⋅	PROPN
easat-3999	198	3	𝑓(𝜃	𝑓(𝜃	PROPN
easat-3999	198	4	):	):	PUNCT
easat-3999	198	5	tied	tie	VERB
easat-3999	198	6	to	to	ADP
easat-3999	198	7	the	the	DET
easat-3999	198	8	angular	angular	ADJ
easat-3999	198	9	modulation	modulation	NOUN
easat-3999	198	10	sin2𝜃	sin2𝜃	PROPN
easat-3999	198	11	and	and	CCONJ
easat-3999	198	12	the	the	DET
easat-3999	198	13	impact	impact	NOUN
easat-3999	198	14	parameter	parameter	NOUN
easat-3999	198	15	.	.	PUNCT
easat-3999	199	1	1	1	NUM
easat-3999	200	1	+	+	CCONJ
easat-3999	200	2	𝑣(𝑟	𝑣(𝑟	NOUN
easat-3999	200	3	)	)	PUNCT
easat-3999	200	4	𝑐	𝑐	NOUN
easat-3999	200	5	:	:	PUNCT
easat-3999	200	6	reflects	reflect	VERB
easat-3999	200	7	relativistic	relativistic	ADJ
easat-3999	200	8	corrections	correction	NOUN
easat-3999	200	9	,	,	PUNCT
easat-3999	200	10	analogous	analogous	ADJ
easat-3999	200	11	to	to	ADP
easat-3999	200	12	the	the	DET
easat-3999	200	13	rotational	rotational	ADJ
easat-3999	200	14	term	term	NOUN
easat-3999	200	15	𝜔2𝑟2sin2𝜃	𝜔2𝑟2sin2𝜃	NOUN
easat-3999	200	16	2	2	NUM
easat-3999	200	17	.	.	PUNCT
easat-3999	201	1	𝜌(𝑟	𝜌(𝑟	NOUN
easat-3999	201	2	,	,	PUNCT
easat-3999	201	3	𝜃	𝜃	NOUN
easat-3999	201	4	)	)	PUNCT
easat-3999	201	5	⋅	⋅	PROPN
easat-3999	201	6	cos(𝜃	cos(𝜃	PROPN
easat-3999	201	7	):	):	PUNCT
easat-3999	201	8	captures	capture	VERB
easat-3999	201	9	density	density	NOUN
easat-3999	201	10	variations	variation	NOUN
easat-3999	201	11	and	and	CCONJ
easat-3999	201	12	angular	angular	ADJ
easat-3999	201	13	modulations	modulation	NOUN
easat-3999	201	14	tied	tie	VERB
easat-3999	201	15	to	to	ADP
easat-3999	201	16	sin(2𝜃	sin(2𝜃	PROPN
easat-3999	201	17	)	)	PUNCT
easat-3999	201	18	.	.	PUNCT
easat-3999	202	1	the	the	DET
easat-3999	202	2	deflection	deflection	NOUN
easat-3999	202	3	angle	angle	NOUN
easat-3999	202	4	can	can	AUX
easat-3999	202	5	be	be	AUX
easat-3999	202	6	explicitly	explicitly	ADV
easat-3999	202	7	rewritten	rewrite	VERB
easat-3999	202	8	in	in	ADP
easat-3999	202	9	terms	term	NOUN
easat-3999	202	10	of	of	ADP
easat-3999	202	11	φ(𝑟	φ(𝑟	PROPN
easat-3999	202	12	,	,	PUNCT
easat-3999	202	13	𝜃	𝜃	NOUN
easat-3999	202	14	):	):	PUNCT
easat-3999	202	15	δ𝛼total	δ𝛼total	ADJ
easat-3999	202	16	=	=	SYM
easat-3999	202	17	4	4	NUM
easat-3999	202	18	𝑐2	𝑐2	NOUN
easat-3999	202	19	⋅	⋅	PROPN
easat-3999	202	20	∇φ(𝑟	∇φ(𝑟	NOUN
easat-3999	202	21	,	,	PUNCT
easat-3999	202	22	𝜃	𝜃	NOUN
easat-3999	202	23	)	)	PUNCT
easat-3999	202	24	+	+	CCONJ
easat-3999	202	25	𝑘	𝑘	DET
easat-3999	202	26	⋅	⋅	PROPN
easat-3999	202	27	𝜌(𝑟	𝜌(𝑟	PROPN
easat-3999	202	28	,	,	PUNCT
easat-3999	202	29	𝜃	𝜃	NOUN
easat-3999	202	30	)	)	PUNCT
easat-3999	202	31	⋅	⋅	PROPN
easat-3999	202	32	cos(𝜃	cos(𝜃	PROPN
easat-3999	202	33	)	)	PUNCT
easat-3999	202	34	where	where	SCONJ
easat-3999	202	35	:	:	PUNCT
easat-3999	202	36	∇φ(𝑟	∇φ(𝑟	NOUN
easat-3999	202	37	,	,	PUNCT
easat-3999	202	38	𝜃	𝜃	NOUN
easat-3999	202	39	):	):	PUNCT
easat-3999	202	40	captures	capture	VERB
easat-3999	202	41	the	the	DET
easat-3999	202	42	contributions	contribution	NOUN
easat-3999	202	43	from	from	ADP
easat-3999	202	44	the	the	DET
easat-3999	202	45	classical	classical	ADJ
easat-3999	202	46	gravitational	gravitational	ADJ
easat-3999	202	47	potential	potential	ADJ
easat-3999	202	48	and	and	CCONJ
easat-3999	202	49	rotational	rotational	ADJ
easat-3999	202	50	effects	effect	NOUN
easat-3999	202	51	.	.	PUNCT
easat-3999	203	1	𝜌(𝑟	𝜌(𝑟	NOUN
easat-3999	203	2	,	,	PUNCT
easat-3999	203	3	𝜃	𝜃	NOUN
easat-3999	203	4	)	)	PUNCT
easat-3999	203	5	and	and	CCONJ
easat-3999	203	6	cos(𝜃	cos(𝜃	VERB
easat-3999	203	7	):	):	PUNCT
easat-3999	203	8	add	add	VERB
easat-3999	203	9	density	density	NOUN
easat-3999	203	10	-	-	PUNCT
easat-3999	203	11	dependent	dependent	ADJ
easat-3999	203	12	and	and	CCONJ
easat-3999	203	13	angular	angular	ADJ
easat-3999	203	14	modulation	modulation	NOUN
easat-3999	203	15	effects	effect	NOUN
easat-3999	203	16	.	.	PUNCT
easat-3999	204	1	derivation	derivation	NOUN
easat-3999	204	2	of	of	ADP
easat-3999	204	3	the	the	DET
easat-3999	204	4	deflection	deflection	NOUN
easat-3999	204	5	formula	formula	NOUN
easat-3999	204	6	in	in	ADP
easat-3999	204	7	desmos	desmos	NOUN
easat-3999	204	8	theory	theory	NOUN
easat-3999	204	9	.	.	PUNCT
easat-3999	205	1	energy	energy	NOUN
easat-3999	205	2	and	and	CCONJ
easat-3999	205	3	gravitational	gravitational	ADJ
easat-3999	205	4	potential	potential	NOUN
easat-3999	205	5	from	from	ADP
easat-3999	205	6	desmos	desmos	NOUN
easat-3999	205	7	theory	theory	NOUN
easat-3999	205	8	:	:	PUNCT
easat-3999	205	9	𝜑𝑖	𝜑𝑖	NOUN
easat-3999	205	10	=	=	PUNCT
easat-3999	205	11	m2	m2	PROPN
easat-3999	205	12	s2	s2	PROPN
easat-3999	205	13	relates	relate	VERB
easat-3999	205	14	to	to	ADP
easat-3999	205	15	the	the	DET
easat-3999	205	16	energy	energy	NOUN
easat-3999	205	17	:	:	PUNCT
easat-3999	205	18	𝐸𝑖	𝐸𝑖	PROPN
easat-3999	205	19	=	=	PUNCT
easat-3999	205	20	𝑚𝑖	𝑚𝑖	ADP
easat-3999	205	21	⋅	⋅	NUM
easat-3999	205	22	𝜑𝑖	𝜑𝑖	ADV
easat-3999	205	23	this	this	DET
easat-3999	205	24	energy	energy	NOUN
easat-3999	205	25	affects	affect	VERB
easat-3999	205	26	the	the	DET
easat-3999	205	27	gravitational	gravitational	ADJ
easat-3999	205	28	force	force	NOUN
easat-3999	205	29	and	and	CCONJ
easat-3999	205	30	,	,	PUNCT
easat-3999	205	31	consequently	consequently	ADV
easat-3999	205	32	,	,	PUNCT
easat-3999	205	33	the	the	DET
easat-3999	205	34	bending	bending	NOUN
easat-3999	205	35	of	of	ADP
easat-3999	205	36	light	light	NOUN
easat-3999	205	37	due	due	ADP
easat-3999	205	38	to	to	ADP
easat-3999	205	39	the	the	DET
easat-3999	205	40	massenergy	massenergy	NOUN
easat-3999	205	41	equivalence	equivalence	NOUN
easat-3999	205	42	.	.	PUNCT
easat-3999	206	1	the	the	DET
easat-3999	206	2	bending	bend	VERB
easat-3999	206	3	angle	angle	NOUN
easat-3999	206	4	in	in	ADP
easat-3999	206	5	classical	classical	ADJ
easat-3999	206	6	gravitational	gravitational	ADJ
easat-3999	206	7	lensing	lensing	NOUN
easat-3999	206	8	is	be	AUX
easat-3999	206	9	given	give	VERB
easat-3999	206	10	by	by	ADP
easat-3999	206	11	:	:	PUNCT
easat-3999	206	12	δ𝛼classical	δ𝛼classical	ADJ
easat-3999	206	13	=	=	SYM
easat-3999	206	14	4𝐺𝑀	4𝐺𝑀	PROPN
easat-3999	206	15	𝑐2⋅𝑏	𝑐2⋅𝑏	ADJ
easat-3999	206	16	where	where	SCONJ
easat-3999	206	17	𝑏	𝑏	PROPN
easat-3999	206	18	is	be	AUX
easat-3999	206	19	the	the	DET
easat-3999	206	20	impact	impact	NOUN
easat-3999	206	21	parameter	parameter	NOUN
easat-3999	206	22	.	.	PUNCT
easat-3999	207	1	incorporating	incorporate	VERB
easat-3999	207	2	desmos	desmo	NOUN
easat-3999	207	3	enhancements	enhancement	NOUN
easat-3999	207	4	.	.	PUNCT
easat-3999	208	1	include	include	VERB
easat-3999	208	2	dark	dark	ADJ
easat-3999	208	3	matter	matter	NOUN
easat-3999	208	4	:	:	PUNCT
easat-3999	208	5	effective	effective	ADJ
easat-3999	208	6	mass	mass	NOUN
easat-3999	208	7	:	:	PUNCT
easat-3999	208	8	𝑀eff	𝑀eff	PROPN
easat-3999	208	9	=	=	SYM
easat-3999	208	10	𝑀	𝑀	PROPN
easat-3999	208	11	+	+	CCONJ
easat-3999	208	12	𝑀dark	𝑀dark	PROPN
easat-3999	208	13	angular	angular	ADJ
easat-3999	208	14	and	and	CCONJ
easat-3999	208	15	distance	distance	NOUN
easat-3999	208	16	dependency	dependency	NOUN
easat-3999	208	17	:	:	PUNCT
easat-3999	208	18	modify	modify	VERB
easat-3999	208	19	𝑏	𝑏	NOUN
easat-3999	208	20	by	by	ADP
easat-3999	208	21	a	a	DET
easat-3999	208	22	factor	factor	NOUN
easat-3999	208	23	𝑓(𝜃	𝑓(𝜃	NOUN
easat-3999	208	24	)	)	PUNCT
easat-3999	208	25	to	to	PART
easat-3999	208	26	include	include	VERB
easat-3999	208	27	angular	angular	ADJ
easat-3999	208	28	dependency	dependency	NOUN
easat-3999	208	29	:	:	PUNCT
easat-3999	208	30	𝑏	𝑏	PROPN
easat-3999	208	31	→	→	SYM
easat-3999	208	32	𝑏	𝑏	PROPN
easat-3999	208	33	⋅	⋅	PROPN
easat-3999	208	34	𝑓(𝜃	𝑓(𝜃	PROPN
easat-3999	208	35	)	)	PUNCT
easat-3999	208	36	add	add	VERB
easat-3999	208	37	velocity	velocity	NOUN
easat-3999	208	38	-	-	PUNCT
easat-3999	208	39	dependent	dependent	ADJ
easat-3999	208	40	corrections	correction	NOUN
easat-3999	208	41	:	:	PUNCT
easat-3999	208	42	(	(	PUNCT
easat-3999	208	43	1	1	NUM
easat-3999	208	44	+	+	NUM
easat-3999	208	45	√φ(r	√φ(r	NOUN
easat-3999	208	46	)	)	PUNCT
easat-3999	208	47	√φ	√φ	NOUN
easat-3999	208	48	)	)	PUNCT
easat-3999	208	49	=	=	PUNCT
easat-3999	208	50	(	(	PUNCT
easat-3999	208	51	1	1	NUM
easat-3999	208	52	+	+	CCONJ
easat-3999	208	53	𝑣(𝑟	𝑣(𝑟	NOUN
easat-3999	208	54	)	)	PUNCT
easat-3999	208	55	𝑐	𝑐	NOUN
easat-3999	208	56	)	)	PUNCT
easat-3999	208	57	density	density	NOUN
easat-3999	208	58	contribution	contribution	NOUN
easat-3999	208	59	include	include	VERB
easat-3999	208	60	a	a	DET
easat-3999	208	61	density	density	NOUN
easat-3999	208	62	-	-	PUNCT
easat-3999	208	63	dependent	dependent	ADJ
easat-3999	208	64	term	term	NOUN
easat-3999	208	65	:	:	PUNCT
easat-3999	208	66	𝑘	𝑘	DET
easat-3999	208	67	⋅	⋅	PROPN
easat-3999	208	68	𝜌(𝑟	𝜌(𝑟	PROPN
easat-3999	208	69	,	,	PUNCT
easat-3999	208	70	𝜃	𝜃	NOUN
easat-3999	208	71	)	)	PUNCT
easat-3999	208	72	⋅	⋅	PROPN
easat-3999	208	73	cos(𝜃	cos(𝜃	PROPN
easat-3999	208	74	)	)	PUNCT
easat-3999	208	75	the	the	DET
easat-3999	208	76	total	total	ADJ
easat-3999	208	77	deflection	deflection	NOUN
easat-3999	208	78	angle	angle	NOUN
easat-3999	208	79	becomes	become	VERB
easat-3999	208	80	:	:	PUNCT
easat-3999	208	81	δ𝛼total	δ𝛼total	ADJ
easat-3999	208	82	=	=	SYM
easat-3999	208	83	4𝐺(𝑀+𝑀dark	4𝐺(𝑀+𝑀dark	NOUN
easat-3999	208	84	)	)	PUNCT
easat-3999	208	85	𝑐2⋅𝑏⋅𝑓(𝜃	𝑐2⋅𝑏⋅𝑓(𝜃	PROPN
easat-3999	208	86	)	)	PUNCT
easat-3999	208	87	⋅	⋅	PROPN
easat-3999	208	88	(	(	PUNCT
easat-3999	208	89	1	1	NUM
easat-3999	208	90	+	+	CCONJ
easat-3999	208	91	𝑣(𝑟	𝑣(𝑟	NOUN
easat-3999	208	92	)	)	PUNCT
easat-3999	208	93	𝑐	𝑐	NOUN
easat-3999	208	94	)	)	PUNCT
easat-3999	209	1	+	+	CCONJ
easat-3999	209	2	𝑘	𝑘	DET
easat-3999	209	3	⋅	⋅	PROPN
easat-3999	209	4	𝜌(𝑟	𝜌(𝑟	PROPN
easat-3999	209	5	,	,	PUNCT
easat-3999	209	6	𝜃	𝜃	NOUN
easat-3999	209	7	)	)	PUNCT
easat-3999	209	8	⋅	⋅	PROPN
easat-3999	209	9	cos(𝜃	cos(𝜃	PROPN
easat-3999	209	10	)	)	PUNCT
easat-3999	209	11	validation	validation	NOUN
easat-3999	209	12	from	from	ADP
easat-3999	209	13	desmos	desmos	NOUN
easat-3999	209	14	summation	summation	NOUN
easat-3999	209	15	formula	formula	NOUN
easat-3999	209	16	.	.	PUNCT
easat-3999	210	1	from	from	ADP
easat-3999	210	2	the	the	DET
easat-3999	210	3	summation	summation	NOUN
easat-3999	210	4	formula	formula	NOUN
easat-3999	210	5	:	:	PUNCT
easat-3999	210	6	∑	∑	PUNCT
easat-3999	210	7	φ(𝑠.	φ(𝑠.	NOUN
easat-3999	210	8	𝑑.	𝑑.	NOUN
easat-3999	210	9	,	,	PUNCT
easat-3999	210	10	𝐸1	𝐸1	NOUN
easat-3999	210	11	,	,	PUNCT
easat-3999	210	12	𝐸2	𝐸2	ADJ
easat-3999	210	13	)	)	PUNCT
easat-3999	211	1	=	=	SYM
easat-3999	211	2	δ	δ	PROPN
easat-3999	211	3	substitute	substitute	NOUN
easat-3999	211	4	𝐸1	𝐸1	NOUN
easat-3999	211	5	=	=	SYM
easat-3999	211	6	𝑚1	𝑚1	NOUN
easat-3999	211	7	⋅	⋅	PROPN
easat-3999	211	8	𝜑1	𝜑1	PROPN
easat-3999	211	9	and	and	CCONJ
easat-3999	211	10	𝐸2	𝐸2	PROPN
easat-3999	211	11	=	=	PROPN
easat-3999	211	12	𝑚2	𝑚2	PROPN
easat-3999	211	13	⋅	⋅	PROPN
easat-3999	211	14	𝜑2	𝜑2	PROPN
easat-3999	211	15	:	:	PUNCT
easat-3999	211	16	9368	9368	NUM
easat-3999	211	17	edelweiss	edelweiss	PROPN
easat-3999	211	18	applied	apply	VERB
easat-3999	211	19	science	science	NOUN
easat-3999	211	20	and	and	CCONJ
easat-3999	211	21	technology	technology	NOUN
easat-3999	211	22	issn	issn	PROPN
easat-3999	211	23	:	:	PUNCT
easat-3999	211	24	2576	2576	NUM
easat-3999	211	25	-	-	SYM
easat-3999	211	26	8484	8484	NUM
easat-3999	211	27	vol	vol	NOUN
easat-3999	211	28	.	.	PROPN
easat-3999	211	29	8	8	NUM
easat-3999	211	30	,	,	PUNCT
easat-3999	211	31	no	no	INTJ
easat-3999	211	32	.	.	NOUN
easat-3999	212	1	6	6	NUM
easat-3999	212	2	:	:	SYM
easat-3999	212	3	9356	9356	NUM
easat-3999	212	4	-	-	SYM
easat-3999	212	5	9375	9375	NUM
easat-3999	212	6	,	,	PUNCT
easat-3999	212	7	2024	2024	NUM
easat-3999	212	8	doi	doi	NOUN
easat-3999	212	9	:	:	PUNCT
easat-3999	212	10	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	212	11	©	©	PROPN
easat-3999	212	12	2024	2024	NUM
easat-3999	212	13	by	by	ADP
easat-3999	212	14	the	the	DET
easat-3999	212	15	author	author	NOUN
easat-3999	212	16	;	;	PUNCT
easat-3999	212	17	licensee	licensee	PROPN
easat-3999	212	18	learning	learning	PROPN
easat-3999	212	19	gate	gate	PROPN
easat-3999	212	20	φ	φ	PROPN
easat-3999	212	21	∝	∝	PROPN
easat-3999	212	22	𝑚1⋅𝑚2⋅𝜑1⋅𝜑2	𝑚1⋅𝑚2⋅𝜑1⋅𝜑2	PROPN
easat-3999	212	23	(	(	PUNCT
easat-3999	212	24	𝐴1⋅𝑒	𝐴1⋅𝑒	NOUN
easat-3999	212	25	−	−	PROPN
easat-3999	212	26	𝑝	𝑝	PROPN
easat-3999	212	27	𝑡1+𝑠.𝑑.0	𝑡1+𝑠.𝑑.0	PROPN
easat-3999	212	28	)	)	PUNCT
easat-3999	212	29	𝑛	𝑛	ADP
easat-3999	212	30	this	this	PRON
easat-3999	212	31	aligns	align	VERB
easat-3999	212	32	with	with	ADP
easat-3999	212	33	the	the	DET
easat-3999	212	34	additional	additional	ADJ
easat-3999	212	35	density	density	NOUN
easat-3999	212	36	and	and	CCONJ
easat-3999	212	37	angular	angular	ADJ
easat-3999	212	38	dependency	dependency	NOUN
easat-3999	212	39	terms	term	NOUN
easat-3999	212	40	in	in	ADP
easat-3999	212	41	δ𝛼total	δ𝛼total	NOUN
easat-3999	212	42	.	.	PUNCT
easat-3999	213	1	the	the	DET
easat-3999	213	2	final	final	ADJ
easat-3999	213	3	deflection	deflection	NOUN
easat-3999	213	4	angle	angle	NOUN
easat-3999	213	5	incorporating	incorporate	VERB
easat-3999	213	6	desmos	desmo	NOUN
easat-3999	213	7	theory	theory	NOUN
easat-3999	213	8	is	be	AUX
easat-3999	213	9	:	:	PUNCT
easat-3999	213	10	δ𝛼total	δ𝛼total	ADJ
easat-3999	213	11	=	=	SYM
easat-3999	213	12	4𝐺(𝑀+𝑀dark	4𝐺(𝑀+𝑀dark	NOUN
easat-3999	213	13	)	)	PUNCT
easat-3999	213	14	𝑐2⋅𝑏⋅𝑓(𝜃	𝑐2⋅𝑏⋅𝑓(𝜃	PROPN
easat-3999	213	15	)	)	PUNCT
easat-3999	213	16	⋅	⋅	PROPN
easat-3999	213	17	(	(	PUNCT
easat-3999	213	18	1	1	NUM
easat-3999	213	19	+	+	CCONJ
easat-3999	213	20	𝑣(𝑟	𝑣(𝑟	NOUN
easat-3999	213	21	)	)	PUNCT
easat-3999	213	22	𝑐	𝑐	NOUN
easat-3999	213	23	)	)	PUNCT
easat-3999	214	1	+	+	CCONJ
easat-3999	214	2	𝑘	𝑘	DET
easat-3999	214	3	⋅	⋅	PROPN
easat-3999	214	4	𝜌(𝑟	𝜌(𝑟	PROPN
easat-3999	214	5	,	,	PUNCT
easat-3999	214	6	𝜃	𝜃	NOUN
easat-3999	214	7	)	)	PUNCT
easat-3999	214	8	⋅	⋅	PROPN
easat-3999	214	9	cos(𝜃	cos(𝜃	PROPN
easat-3999	214	10	)	)	PUNCT
easat-3999	214	11	the	the	DET
easat-3999	214	12	following	follow	VERB
easat-3999	214	13	table	table	NOUN
easat-3999	214	14	summarizes	summarize	VERB
easat-3999	214	15	the	the	DET
easat-3999	214	16	deflection	deflection	NOUN
easat-3999	214	17	values	value	NOUN
easat-3999	214	18	computed	compute	VERB
easat-3999	214	19	for	for	ADP
easat-3999	214	20	various	various	ADJ
easat-3999	214	21	distances	distance	NOUN
easat-3999	214	22	and	and	CCONJ
easat-3999	214	23	angles	angle	NOUN
easat-3999	214	24	.	.	PUNCT
easat-3999	215	1	the	the	DET
easat-3999	215	2	classical	classical	ADJ
easat-3999	215	3	deflection	deflection	NOUN
easat-3999	215	4	and	and	CCONJ
easat-3999	215	5	enhanced	enhance	VERB
easat-3999	215	6	deflection	deflection	NOUN
easat-3999	215	7	values	value	NOUN
easat-3999	215	8	are	be	AUX
easat-3999	215	9	compared	compare	VERB
easat-3999	215	10	to	to	PART
easat-3999	215	11	understand	understand	VERB
easat-3999	215	12	the	the	DET
easat-3999	215	13	contributions	contribution	NOUN
easat-3999	215	14	of	of	ADP
easat-3999	215	15	angular	angular	ADJ
easat-3999	215	16	dependencies	dependency	NOUN
easat-3999	215	17	and	and	CCONJ
easat-3999	215	18	dark	dark	ADJ
easat-3999	215	19	matter	matter	NOUN
easat-3999	215	20	enhancements	enhancement	NOUN
easat-3999	215	21	.	.	PUNCT
easat-3999	216	1	table	table	NOUN
easat-3999	216	2	1	1	NUM
easat-3999	216	3	:	:	PUNCT
easat-3999	216	4	distance	distance	NOUN
easat-3999	216	5	and	and	CCONJ
easat-3999	216	6	deflection	deflection	NOUN
easat-3999	216	7	(	(	PUNCT
easat-3999	216	8	author	author	NOUN
easat-3999	216	9	’s	’s	PART
easat-3999	216	10	computations	computation	NOUN
easat-3999	216	11	)	)	PUNCT
easat-3999	216	12	.	.	PUNCT
easat-3999	217	1	distance	distance	NOUN
easat-3999	217	2	(	(	PUNCT
easat-3999	217	3	gm	gm	PROPN
easat-3999	217	4	)	)	PUNCT
easat-3999	217	5	deflection	deflection	NOUN
easat-3999	217	6	(	(	PUNCT
easat-3999	217	7	arcseconds	arcsecond	NOUN
easat-3999	217	8	)	)	PUNCT
easat-3999	217	9	angle	angle	NOUN
easat-3999	217	10	(	(	PUNCT
easat-3999	217	11	degrees	degree	NOUN
easat-3999	217	12	)	)	PUNCT
easat-3999	217	13	enhanced	enhance	VERB
easat-3999	217	14	deflection	deflection	NOUN
easat-3999	217	15	(	(	PUNCT
easat-3999	217	16	arcseconds	arcsecond	NOUN
easat-3999	217	17	)	)	PUNCT
easat-3999	217	18	1	1	NUM
easat-3999	217	19	1.75	1.75	NUM
easat-3999	217	20	0	0	NUM
easat-3999	217	21	2.1	2.1	NUM
easat-3999	217	22	5	5	NUM
easat-3999	217	23	0.35	0.35	NUM
easat-3999	217	24	30	30	NUM
easat-3999	217	25	0.45	0.45	NUM
easat-3999	217	26	10	10	NUM
easat-3999	217	27	0.175	0.175	NUM
easat-3999	217	28	45	45	NUM
easat-3999	217	29	0.2	0.2	NUM
easat-3999	217	30	50	50	NUM
easat-3999	217	31	0.035	0.035	NUM
easat-3999	217	32	60	60	NUM
easat-3999	217	33	0.05	0.05	NUM
easat-3999	217	34	100	100	NUM
easat-3999	217	35	0.0175	0.0175	NUM
easat-3999	217	36	90	90	NUM
easat-3999	217	37	0.02	0.02	NUM
easat-3999	217	38	deflection	deflection	NOUN
easat-3999	217	39	decreases	decrease	VERB
easat-3999	217	40	significantly	significantly	ADV
easat-3999	217	41	as	as	ADP
easat-3999	217	42	the	the	DET
easat-3999	217	43	distance	distance	NOUN
easat-3999	217	44	increases	increase	NOUN
easat-3999	217	45	,	,	PUNCT
easat-3999	217	46	consistent	consistent	ADJ
easat-3999	217	47	with	with	ADP
easat-3999	217	48	the	the	DET
easat-3999	217	49	inverse	inverse	NOUN
easat-3999	217	50	relationship	relationship	NOUN
easat-3999	217	51	predicted	predict	VERB
easat-3999	217	52	by	by	ADP
easat-3999	217	53	classical	classical	ADJ
easat-3999	217	54	gravity	gravity	NOUN
easat-3999	217	55	.	.	PUNCT
easat-3999	218	1	the	the	DET
easat-3999	218	2	enhanced	enhanced	ADJ
easat-3999	218	3	deflection	deflection	NOUN
easat-3999	218	4	values	value	NOUN
easat-3999	218	5	are	be	AUX
easat-3999	218	6	notably	notably	ADV
easat-3999	218	7	higher	high	ADJ
easat-3999	218	8	than	than	ADP
easat-3999	218	9	classical	classical	ADJ
easat-3999	218	10	values	value	NOUN
easat-3999	218	11	,	,	PUNCT
easat-3999	218	12	particularly	particularly	ADV
easat-3999	218	13	at	at	ADP
easat-3999	218	14	smaller	small	ADJ
easat-3999	218	15	distances	distance	NOUN
easat-3999	218	16	,	,	PUNCT
easat-3999	218	17	due	due	ADP
easat-3999	218	18	to	to	ADP
easat-3999	218	19	the	the	DET
easat-3999	218	20	contributions	contribution	NOUN
easat-3999	218	21	of	of	ADP
easat-3999	218	22	disk	disk	NOUN
easat-3999	218	23	dynamics	dynamic	NOUN
easat-3999	218	24	and	and	CCONJ
easat-3999	218	25	dark	dark	ADJ
easat-3999	218	26	matter	matter	NOUN
easat-3999	218	27	.	.	PUNCT
easat-3999	219	1	angular	angular	ADJ
easat-3999	219	2	dependencies	dependency	NOUN
easat-3999	219	3	become	become	VERB
easat-3999	219	4	more	more	ADV
easat-3999	219	5	pronounced	pronounced	ADJ
easat-3999	219	6	at	at	ADP
easat-3999	219	7	intermediate	intermediate	ADJ
easat-3999	219	8	angles	angle	NOUN
easat-3999	219	9	(	(	PUNCT
easat-3999	219	10	30	30	NUM
easat-3999	219	11	°	°	NOUN
easat-3999	219	12	to	to	PART
easat-3999	219	13	60	60	NUM
easat-3999	219	14	°	°	NUM
easat-3999	219	15	)	)	PUNCT
easat-3999	219	16	,	,	PUNCT
easat-3999	219	17	where	where	SCONJ
easat-3999	219	18	the	the	DET
easat-3999	219	19	deflection	deflection	NOUN
easat-3999	219	20	values	value	NOUN
easat-3999	219	21	diverge	diverge	VERB
easat-3999	219	22	noticeably	noticeably	ADV
easat-3999	219	23	from	from	ADP
easat-3999	219	24	classical	classical	ADJ
easat-3999	219	25	predictions	prediction	NOUN
easat-3999	219	26	.	.	PUNCT
easat-3999	220	1	for	for	ADP
easat-3999	220	2	large	large	ADJ
easat-3999	220	3	angles	angle	NOUN
easat-3999	220	4	(	(	PUNCT
easat-3999	220	5	e.g.	e.g.	ADV
easat-3999	220	6	,	,	PUNCT
easat-3999	220	7	90	90	NUM
easat-3999	220	8	°	°	NUM
easat-3999	220	9	)	)	PUNCT
easat-3999	220	10	,	,	PUNCT
easat-3999	220	11	the	the	DET
easat-3999	220	12	deflection	deflection	NOUN
easat-3999	220	13	approaches	approach	VERB
easat-3999	220	14	minimal	minimal	ADJ
easat-3999	220	15	values	value	NOUN
easat-3999	220	16	,	,	PUNCT
easat-3999	220	17	emphasizing	emphasize	VERB
easat-3999	220	18	the	the	DET
easat-3999	220	19	role	role	NOUN
easat-3999	220	20	of	of	ADP
easat-3999	220	21	directional	directional	ADJ
easat-3999	220	22	effects	effect	NOUN
easat-3999	220	23	.	.	PUNCT
easat-3999	221	1	the	the	DET
easat-3999	221	2	following	follow	VERB
easat-3999	221	3	table	table	NOUN
easat-3999	221	4	summarizes	summarize	VERB
easat-3999	221	5	the	the	DET
easat-3999	221	6	deflection	deflection	NOUN
easat-3999	221	7	values	value	NOUN
easat-3999	221	8	computed	compute	VERB
easat-3999	221	9	for	for	ADP
easat-3999	221	10	various	various	ADJ
easat-3999	221	11	distances	distance	NOUN
easat-3999	221	12	and	and	CCONJ
easat-3999	221	13	angles	angle	NOUN
easat-3999	221	14	.	.	PUNCT
easat-3999	222	1	the	the	DET
easat-3999	222	2	classical	classical	ADJ
easat-3999	222	3	deflection	deflection	NOUN
easat-3999	222	4	and	and	CCONJ
easat-3999	222	5	enhanced	enhance	VERB
easat-3999	222	6	deflection	deflection	NOUN
easat-3999	222	7	values	value	NOUN
easat-3999	222	8	are	be	AUX
easat-3999	222	9	compared	compare	VERB
easat-3999	222	10	to	to	PART
easat-3999	222	11	understand	understand	VERB
easat-3999	222	12	the	the	DET
easat-3999	222	13	contributions	contribution	NOUN
easat-3999	222	14	of	of	ADP
easat-3999	222	15	angular	angular	ADJ
easat-3999	222	16	dependencies	dependency	NOUN
easat-3999	222	17	and	and	CCONJ
easat-3999	222	18	dark	dark	ADJ
easat-3999	222	19	matter	matter	NOUN
easat-3999	222	20	enhancements	enhancement	NOUN
easat-3999	222	21	.	.	PUNCT
easat-3999	223	1	figure	figure	NOUN
easat-3999	223	2	5	5	NUM
easat-3999	223	3	.	.	PUNCT
easat-3999	224	1	classical	classical	ADJ
easat-3999	224	2	vs	vs	ADP
easat-3999	224	3	enhanced	enhanced	ADJ
easat-3999	224	4	deflection	deflection	NOUN
easat-3999	224	5	as	as	ADP
easat-3999	224	6	a	a	DET
easat-3999	224	7	function	function	NOUN
easat-3999	224	8	of	of	ADP
easat-3999	224	9	distance	distance	NOUN
easat-3999	224	10	,	,	PUNCT
easat-3999	224	11	showing	show	VERB
easat-3999	224	12	the	the	DET
easat-3999	224	13	impact	impact	NOUN
easat-3999	224	14	of	of	ADP
easat-3999	224	15	dark	dark	ADJ
easat-3999	224	16	matter	matter	NOUN
easat-3999	224	17	contributions	contribution	NOUN
easat-3999	224	18	.	.	PUNCT
easat-3999	225	1	9369	9369	NUM
easat-3999	225	2	edelweiss	edelweiss	PROPN
easat-3999	225	3	applied	apply	VERB
easat-3999	225	4	science	science	NOUN
easat-3999	225	5	and	and	CCONJ
easat-3999	225	6	technology	technology	NOUN
easat-3999	225	7	issn	issn	PROPN
easat-3999	225	8	:	:	PUNCT
easat-3999	225	9	2576	2576	NUM
easat-3999	225	10	-	-	SYM
easat-3999	225	11	8484	8484	NUM
easat-3999	225	12	vol	vol	NOUN
easat-3999	225	13	.	.	PROPN
easat-3999	225	14	8	8	NUM
easat-3999	225	15	,	,	PUNCT
easat-3999	225	16	no	no	INTJ
easat-3999	225	17	.	.	NOUN
easat-3999	226	1	6	6	NUM
easat-3999	226	2	:	:	SYM
easat-3999	226	3	9356	9356	NUM
easat-3999	226	4	-	-	SYM
easat-3999	226	5	9375	9375	NUM
easat-3999	226	6	,	,	PUNCT
easat-3999	226	7	2024	2024	NUM
easat-3999	226	8	doi	doi	NOUN
easat-3999	226	9	:	:	PUNCT
easat-3999	226	10	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	226	11	©	©	PROPN
easat-3999	226	12	2024	2024	NUM
easat-3999	226	13	by	by	ADP
easat-3999	226	14	the	the	DET
easat-3999	226	15	author	author	NOUN
easat-3999	226	16	;	;	PUNCT
easat-3999	226	17	licensee	licensee	PROPN
easat-3999	226	18	learning	learning	NOUN
easat-3999	226	19	gate	gate	VERB
easat-3999	226	20	the	the	DET
easat-3999	226	21	following	follow	VERB
easat-3999	226	22	table	table	NOUN
easat-3999	226	23	summarizes	summarize	VERB
easat-3999	226	24	the	the	DET
easat-3999	226	25	deflection	deflection	NOUN
easat-3999	226	26	values	value	NOUN
easat-3999	226	27	computed	compute	VERB
easat-3999	226	28	for	for	ADP
easat-3999	226	29	various	various	ADJ
easat-3999	226	30	distances	distance	NOUN
easat-3999	226	31	and	and	CCONJ
easat-3999	226	32	angles	angle	NOUN
easat-3999	226	33	.	.	PUNCT
easat-3999	227	1	the	the	DET
easat-3999	227	2	classical	classical	ADJ
easat-3999	227	3	deflection	deflection	NOUN
easat-3999	227	4	and	and	CCONJ
easat-3999	227	5	enhanced	enhance	VERB
easat-3999	227	6	deflection	deflection	NOUN
easat-3999	227	7	values	value	NOUN
easat-3999	227	8	are	be	AUX
easat-3999	227	9	compared	compare	VERB
easat-3999	227	10	to	to	PART
easat-3999	227	11	understand	understand	VERB
easat-3999	227	12	the	the	DET
easat-3999	227	13	contributions	contribution	NOUN
easat-3999	227	14	of	of	ADP
easat-3999	227	15	angular	angular	ADJ
easat-3999	227	16	dependencies	dependency	NOUN
easat-3999	227	17	and	and	CCONJ
easat-3999	227	18	dark	dark	ADJ
easat-3999	227	19	matter	matter	NOUN
easat-3999	227	20	enhancements	enhancement	NOUN
easat-3999	227	21	.	.	PUNCT
easat-3999	228	1	table	table	NOUN
easat-3999	228	2	2	2	NUM
easat-3999	228	3	:	:	PUNCT
easat-3999	228	4	distance	distance	NOUN
easat-3999	228	5	and	and	CCONJ
easat-3999	228	6	deflection	deflection	NOUN
easat-3999	228	7	(	(	PUNCT
easat-3999	228	8	author	author	NOUN
easat-3999	228	9	’s	’s	PART
easat-3999	228	10	computations	computation	NOUN
easat-3999	228	11	)	)	PUNCT
easat-3999	228	12	.	.	PUNCT
easat-3999	229	1	distance	distance	NOUN
easat-3999	229	2	(	(	PUNCT
easat-3999	229	3	gm	gm	PROPN
easat-3999	229	4	)	)	PUNCT
easat-3999	229	5	deflection	deflection	NOUN
easat-3999	229	6	(	(	PUNCT
easat-3999	229	7	arcseconds	arcsecond	NOUN
easat-3999	229	8	)	)	PUNCT
easat-3999	229	9	angle	angle	NOUN
easat-3999	229	10	(	(	PUNCT
easat-3999	229	11	degrees	degree	NOUN
easat-3999	229	12	)	)	PUNCT
easat-3999	229	13	enhanced	enhance	VERB
easat-3999	229	14	deflection	deflection	NOUN
easat-3999	229	15	(	(	PUNCT
easat-3999	229	16	arcseconds	arcsecond	NOUN
easat-3999	229	17	)	)	PUNCT
easat-3999	229	18	1.0	1.0	NUM
easat-3999	229	19	1.75	1.75	NUM
easat-3999	229	20	0.0	0.0	NUM
easat-3999	229	21	2.1	2.1	NUM
easat-3999	229	22	5.0	5.0	NUM
easat-3999	229	23	0.35	0.35	NUM
easat-3999	229	24	30.0	30.0	NUM
easat-3999	229	25	0.45	0.45	NUM
easat-3999	229	26	10.0	10.0	NUM
easat-3999	229	27	0.175	0.175	NUM
easat-3999	229	28	45.0	45.0	NUM
easat-3999	229	29	0.2	0.2	NUM
easat-3999	229	30	50.0	50.0	NUM
easat-3999	229	31	0.035	0.035	NUM
easat-3999	229	32	60.0	60.0	NUM
easat-3999	229	33	0.05	0.05	NUM
easat-3999	229	34	100.0	100.0	NUM
easat-3999	229	35	0.0175	0.0175	NUM
easat-3999	229	36	90.0	90.0	NUM
easat-3999	229	37	0.02	0.02	NUM
easat-3999	229	38	figure	figure	NOUN
easat-3999	229	39	6	6	NUM
easat-3999	229	40	.	.	PUNCT
easat-3999	229	41	deflection	deflection	NOUN
easat-3999	229	42	variability	variability	NOUN
easat-3999	229	43	across	across	ADP
easat-3999	229	44	angles	angle	NOUN
easat-3999	229	45	,	,	PUNCT
easat-3999	229	46	highlighting	highlight	VERB
easat-3999	229	47	the	the	DET
easat-3999	229	48	influence	influence	NOUN
easat-3999	229	49	of	of	ADP
easat-3999	229	50	angular	angular	ADJ
easat-3999	229	51	dependencies	dependency	NOUN
easat-3999	229	52	.	.	PUNCT
easat-3999	230	1	the	the	DET
easat-3999	230	2	following	follow	VERB
easat-3999	230	3	extended	extended	ADJ
easat-3999	230	4	tables	table	NOUN
easat-3999	230	5	show	show	VERB
easat-3999	230	6	the	the	DET
easat-3999	230	7	deflection	deflection	NOUN
easat-3999	230	8	values	value	NOUN
easat-3999	230	9	computed	compute	VERB
easat-3999	230	10	for	for	ADP
easat-3999	230	11	additional	additional	ADJ
easat-3999	230	12	distances	distance	NOUN
easat-3999	230	13	and	and	CCONJ
easat-3999	230	14	angles	angle	NOUN
easat-3999	230	15	.	.	PUNCT
easat-3999	231	1	this	this	DET
easat-3999	231	2	expanded	expand	VERB
easat-3999	231	3	dataset	dataset	NOUN
easat-3999	231	4	provides	provide	VERB
easat-3999	231	5	a	a	DET
easat-3999	231	6	more	more	ADV
easat-3999	231	7	comprehensive	comprehensive	ADJ
easat-3999	231	8	understanding	understanding	NOUN
easat-3999	231	9	of	of	ADP
easat-3999	231	10	the	the	DET
easat-3999	231	11	trends	trend	NOUN
easat-3999	231	12	in	in	ADP
easat-3999	231	13	gravitational	gravitational	ADJ
easat-3999	231	14	.	.	PUNCT
easat-3999	232	1	9370	9370	NUM
easat-3999	232	2	edelweiss	edelweiss	PROPN
easat-3999	232	3	applied	apply	VERB
easat-3999	232	4	science	science	NOUN
easat-3999	232	5	and	and	CCONJ
easat-3999	232	6	technology	technology	NOUN
easat-3999	232	7	issn	issn	PROPN
easat-3999	232	8	:	:	PUNCT
easat-3999	232	9	2576	2576	NUM
easat-3999	232	10	-	-	SYM
easat-3999	232	11	8484	8484	NUM
easat-3999	232	12	vol	vol	NOUN
easat-3999	232	13	.	.	PROPN
easat-3999	232	14	8	8	NUM
easat-3999	232	15	,	,	PUNCT
easat-3999	232	16	no	no	INTJ
easat-3999	232	17	.	.	NOUN
easat-3999	233	1	6	6	NUM
easat-3999	233	2	:	:	SYM
easat-3999	233	3	9356	9356	NUM
easat-3999	233	4	-	-	SYM
easat-3999	233	5	9375	9375	NUM
easat-3999	233	6	,	,	PUNCT
easat-3999	233	7	2024	2024	NUM
easat-3999	233	8	doi	doi	NOUN
easat-3999	233	9	:	:	PUNCT
easat-3999	233	10	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	233	11	©	©	PROPN
easat-3999	233	12	2024	2024	NUM
easat-3999	233	13	by	by	ADP
easat-3999	233	14	the	the	DET
easat-3999	233	15	author	author	NOUN
easat-3999	233	16	;	;	PUNCT
easat-3999	234	1	licensee	licensee	PROPN
easat-3999	234	2	learning	learn	VERB
easat-3999	234	3	gate	gate	NOUN
easat-3999	234	4	table	table	NOUN
easat-3999	234	5	3	3	NUM
easat-3999	234	6	:	:	PUNCT
easat-3999	234	7	distance	distance	NOUN
easat-3999	234	8	and	and	CCONJ
easat-3999	234	9	deflection	deflection	NOUN
easat-3999	234	10	(	(	PUNCT
easat-3999	234	11	author	author	NOUN
easat-3999	234	12	’s	’s	PART
easat-3999	234	13	computations	computation	NOUN
easat-3999	234	14	)	)	PUNCT
easat-3999	234	15	.	.	PUNCT
easat-3999	235	1	distance	distance	NOUN
easat-3999	235	2	(	(	PUNCT
easat-3999	235	3	gm	gm	PROPN
easat-3999	235	4	)	)	PUNCT
easat-3999	235	5	deflection	deflection	NOUN
easat-3999	235	6	(	(	PUNCT
easat-3999	235	7	arcseconds	arcsecond	NOUN
easat-3999	235	8	)	)	PUNCT
easat-3999	235	9	angle	angle	NOUN
easat-3999	235	10	(	(	PUNCT
easat-3999	235	11	degrees	degree	NOUN
easat-3999	235	12	)	)	PUNCT
easat-3999	235	13	enhanced	enhance	VERB
easat-3999	235	14	deflection	deflection	NOUN
easat-3999	235	15	(	(	PUNCT
easat-3999	235	16	arcseconds	arcsecond	NOUN
easat-3999	235	17	)	)	PUNCT
easat-3999	235	18	1.0	1.0	NUM
easat-3999	235	19	1.75	1.75	NUM
easat-3999	235	20	0.0	0.0	NUM
easat-3999	235	21	2.1	2.1	NUM
easat-3999	235	22	5.0	5.0	NUM
easat-3999	235	23	0.35	0.35	NUM
easat-3999	235	24	30.0	30.0	NUM
easat-3999	235	25	0.45	0.45	NUM
easat-3999	235	26	10.0	10.0	NUM
easat-3999	235	27	0.175	0.175	NUM
easat-3999	235	28	45.0	45.0	NUM
easat-3999	235	29	0.2	0.2	NUM
easat-3999	235	30	50.0	50.0	NUM
easat-3999	235	31	0.035	0.035	NUM
easat-3999	235	32	60.0	60.0	NUM
easat-3999	235	33	0.05	0.05	NUM
easat-3999	235	34	100.0	100.0	NUM
easat-3999	235	35	0.0175	0.0175	NUM
easat-3999	235	36	90.0	90.0	NUM
easat-3999	235	37	0.02	0.02	NUM
easat-3999	235	38	200.0	200.0	NUM
easat-3999	235	39	0.00875	0.00875	NUM
easat-3999	235	40	120.0	120.0	NUM
easat-3999	235	41	0.015	0.015	NUM
easat-3999	235	42	300.0	300.0	NUM
easat-3999	235	43	0.00583	0.00583	NUM
easat-3999	235	44	150.0	150.0	NUM
easat-3999	235	45	0.012	0.012	NUM
easat-3999	235	46	400.0	400.0	NUM
easat-3999	235	47	0.004375	0.004375	NUM
easat-3999	235	48	180.0	180.0	NUM
easat-3999	235	49	0.01	0.01	NUM
easat-3999	235	50	500.0	500.0	NUM
easat-3999	235	51	0.0035	0.0035	NUM
easat-3999	235	52	210.0	210.0	NUM
easat-3999	235	53	0.009	0.009	NUM
easat-3999	235	54	600.0	600.0	NUM
easat-3999	235	55	0.00292	0.00292	NUM
easat-3999	235	56	240.0	240.0	NUM
easat-3999	235	57	0.008	0.008	NUM
easat-3999	235	58	the	the	DET
easat-3999	235	59	extended	extend	VERB
easat-3999	235	60	dataset	dataset	NOUN
easat-3999	235	61	highlights	highlight	NOUN
easat-3999	235	62	several	several	ADJ
easat-3999	235	63	critical	critical	ADJ
easat-3999	235	64	trends	trend	NOUN
easat-3999	235	65	.	.	PUNCT
easat-3999	236	1	distance	distance	NOUN
easat-3999	236	2	dependency	dependency	NOUN
easat-3999	236	3	is	be	AUX
easat-3999	236	4	about	about	SCONJ
easat-3999	236	5	the	the	DET
easat-3999	236	6	deflection	deflection	NOUN
easat-3999	236	7	decreases	decrease	VERB
easat-3999	236	8	exponentially	exponentially	ADV
easat-3999	236	9	with	with	ADP
easat-3999	236	10	distance	distance	NOUN
easat-3999	236	11	,	,	PUNCT
easat-3999	236	12	as	as	SCONJ
easat-3999	236	13	observed	observe	VERB
easat-3999	236	14	from	from	ADP
easat-3999	236	15	the	the	DET
easat-3999	236	16	classical	classical	ADJ
easat-3999	236	17	model	model	NOUN
easat-3999	236	18	.	.	PUNCT
easat-3999	237	1	angular	angular	ADJ
easat-3999	237	2	variability	variability	NOUN
easat-3999	237	3	enhanced	enhance	VERB
easat-3999	237	4	deflection	deflection	NOUN
easat-3999	237	5	values	value	NOUN
easat-3999	237	6	exhibit	exhibit	VERB
easat-3999	237	7	significant	significant	ADJ
easat-3999	237	8	variability	variability	NOUN
easat-3999	237	9	across	across	ADP
easat-3999	237	10	angles	angle	NOUN
easat-3999	237	11	,	,	PUNCT
easat-3999	237	12	especially	especially	ADV
easat-3999	237	13	at	at	ADP
easat-3999	237	14	intermediate	intermediate	ADJ
easat-3999	237	15	ranges	range	NOUN
easat-3999	237	16	(	(	PUNCT
easat-3999	237	17	30	30	NUM
easat-3999	237	18	°	°	NUM
easat-3999	237	19	to	to	PART
easat-3999	237	20	60	60	NUM
easat-3999	237	21	°	°	NUM
easat-3999	237	22	)	)	PUNCT
easat-3999	237	23	.	.	PUNCT
easat-3999	238	1	impact	impact	NOUN
easat-3999	238	2	of	of	ADP
easat-3999	238	3	dark	dark	ADJ
easat-3999	238	4	matter	matter	NOUN
easat-3999	238	5	enhanced	enhanced	ADJ
easat-3999	238	6	deflection	deflection	NOUN
easat-3999	238	7	values	value	NOUN
easat-3999	238	8	are	be	AUX
easat-3999	238	9	consistently	consistently	ADV
easat-3999	238	10	higher	high	ADJ
easat-3999	238	11	,	,	PUNCT
easat-3999	238	12	demonstrating	demonstrate	VERB
easat-3999	238	13	the	the	DET
easat-3999	238	14	influence	influence	NOUN
easat-3999	238	15	of	of	ADP
easat-3999	238	16	dark	dark	ADJ
easat-3999	238	17	matter	matter	NOUN
easat-3999	238	18	and	and	CCONJ
easat-3999	238	19	disk	disk	NOUN
easat-3999	238	20	dynamics	dynamic	NOUN
easat-3999	238	21	.	.	PUNCT
easat-3999	239	1	figure	figure	NOUN
easat-3999	239	2	7	7	NUM
easat-3999	239	3	.	.	PUNCT
easat-3999	239	4	extended	extend	VERB
easat-3999	239	5	classical	classical	NOUN
easat-3999	239	6	vs	vs	ADP
easat-3999	239	7	enhanced	enhance	VERB
easat-3999	239	8	deflection	deflection	NOUN
easat-3999	239	9	as	as	ADP
easat-3999	239	10	a	a	DET
easat-3999	239	11	function	function	NOUN
easat-3999	239	12	of	of	ADP
easat-3999	239	13	distance	distance	NOUN
easat-3999	239	14	,	,	PUNCT
easat-3999	239	15	providing	provide	VERB
easat-3999	239	16	further	further	ADJ
easat-3999	239	17	insights	insight	NOUN
easat-3999	239	18	into	into	ADP
easat-3999	239	19	the	the	DET
easat-3999	239	20	exponential	exponential	ADJ
easat-3999	239	21	decay	decay	NOUN
easat-3999	239	22	of	of	ADP
easat-3999	239	23	deflection	deflection	NOUN
easat-3999	239	24	values	value	NOUN
easat-3999	239	25	.	.	PUNCT
easat-3999	240	1	gravitational	gravitational	ADJ
easat-3999	240	2	potential	potential	ADJ
easat-3999	240	3	and	and	CCONJ
easat-3999	240	4	force	force	NOUN
easat-3999	240	5	dependency	dependency	NOUN
easat-3999	240	6	on	on	ADP
easat-3999	240	7	distance	distance	NOUN
easat-3999	240	8	are	be	AUX
easat-3999	240	9	presented	present	VERB
easat-3999	240	10	before	before	ADV
easat-3999	240	11	.	.	PUNCT
easat-3999	241	1	the	the	DET
easat-3999	241	2	gravitational	gravitational	ADJ
easat-3999	241	3	force	force	NOUN
easat-3999	241	4	between	between	ADP
easat-3999	241	5	two	two	NUM
easat-3999	241	6	masses	masse	NOUN
easat-3999	241	7	𝑚1	𝑚1	NOUN
easat-3999	241	8	and	and	CCONJ
easat-3999	241	9	𝑚2	𝑚2	NOUN
easat-3999	241	10	separated	separate	VERB
easat-3999	241	11	by	by	ADP
easat-3999	241	12	a	a	DET
easat-3999	241	13	distance	distance	NOUN
easat-3999	241	14	𝑟	𝑟	NOUN
easat-3999	241	15	is	be	AUX
easat-3999	241	16	given	give	VERB
easat-3999	241	17	by	by	ADP
easat-3999	241	18	:	:	PUNCT
easat-3999	241	19	𝐹𝑔	𝐹𝑔	PROPN
easat-3999	241	20	=	=	PROPN
easat-3999	241	21	𝐺	𝐺	PROPN
easat-3999	241	22	⋅	⋅	PROPN
easat-3999	241	23	𝑚1⋅𝑚2	𝑚1⋅𝑚2	PROPN
easat-3999	241	24	𝑟2	𝑟2	NOUN
easat-3999	241	25	the	the	DET
easat-3999	241	26	gravitational	gravitational	ADJ
easat-3999	241	27	potential	potential	NOUN
easat-3999	241	28	(	(	PUNCT
easat-3999	241	29	φ𝑔	φ𝑔	NOUN
easat-3999	241	30	)	)	PUNCT
easat-3999	241	31	energy	energy	NOUN
easat-3999	241	32	for	for	ADP
easat-3999	241	33	a	a	DET
easat-3999	241	34	mass	mass	NOUN
easat-3999	241	35	𝑚	𝑚	NOUN
easat-3999	241	36	in	in	ADP
easat-3999	241	37	a	a	DET
easat-3999	241	38	gravitational	gravitational	ADJ
easat-3999	241	39	field	field	NOUN
easat-3999	241	40	is	be	AUX
easat-3999	241	41	:	:	PUNCT
easat-3999	241	42	9371	9371	NUM
easat-3999	241	43	edelweiss	edelweiss	PROPN
easat-3999	241	44	applied	apply	VERB
easat-3999	241	45	science	science	NOUN
easat-3999	241	46	and	and	CCONJ
easat-3999	241	47	technology	technology	NOUN
easat-3999	241	48	issn	issn	PROPN
easat-3999	241	49	:	:	PUNCT
easat-3999	241	50	2576	2576	NUM
easat-3999	241	51	-	-	SYM
easat-3999	241	52	8484	8484	NUM
easat-3999	241	53	vol	vol	NOUN
easat-3999	241	54	.	.	PROPN
easat-3999	242	1	8	8	NUM
easat-3999	242	2	,	,	PUNCT
easat-3999	242	3	no	no	INTJ
easat-3999	242	4	.	.	NOUN
easat-3999	243	1	6	6	NUM
easat-3999	243	2	:	:	SYM
easat-3999	243	3	9356	9356	NUM
easat-3999	243	4	-	-	SYM
easat-3999	243	5	9375	9375	NUM
easat-3999	243	6	,	,	PUNCT
easat-3999	243	7	2024	2024	NUM
easat-3999	243	8	doi	doi	NOUN
easat-3999	243	9	:	:	PUNCT
easat-3999	243	10	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	243	11	©	©	PROPN
easat-3999	243	12	2024	2024	NUM
easat-3999	243	13	by	by	ADP
easat-3999	243	14	the	the	DET
easat-3999	243	15	author	author	NOUN
easat-3999	243	16	;	;	PUNCT
easat-3999	243	17	licensee	licensee	NOUN
easat-3999	243	18	learning	learning	NOUN
easat-3999	243	19	gate	gate	NOUN
easat-3999	243	20	φ𝑔	φ𝑔	PROPN
easat-3999	244	1	=	=	SYM
easat-3999	244	2	−	−	PROPN
easat-3999	244	3	𝐺⋅𝑀	𝐺⋅𝑀	NOUN
easat-3999	244	4	𝑟	𝑟	X
easat-3999	244	5	if	if	SCONJ
easat-3999	244	6	gm	gm	PROPN
easat-3999	244	7	encapsulates	encapsulate	VERB
easat-3999	244	8	the	the	DET
easat-3999	244	9	gravitational	gravitational	ADJ
easat-3999	244	10	influence	influence	NOUN
easat-3999	244	11	of	of	ADP
easat-3999	244	12	a	a	DET
easat-3999	244	13	mass	mass	NOUN
easat-3999	244	14	m	m	NOUN
easat-3999	244	15	in	in	ADP
easat-3999	244	16	a	a	DET
easat-3999	244	17	system	system	NOUN
easat-3999	244	18	,	,	PUNCT
easat-3999	244	19	it	it	PRON
easat-3999	244	20	inherently	inherently	ADV
easat-3999	244	21	depends	depend	VERB
easat-3999	244	22	on	on	ADP
easat-3999	244	23	distance	distance	NOUN
easat-3999	244	24	𝑟	𝑟	NOUN
easat-3999	244	25	through	through	ADP
easat-3999	244	26	the	the	DET
easat-3999	244	27	potential	potential	ADJ
easat-3999	244	28	and	and	CCONJ
easat-3999	244	29	force	force	NOUN
easat-3999	244	30	relationships	relationship	NOUN
easat-3999	244	31	.	.	PUNCT
easat-3999	245	1	the	the	DET
easat-3999	245	2	classical	classical	ADJ
easat-3999	245	3	gravitational	gravitational	ADJ
easat-3999	245	4	deflection	deflection	NOUN
easat-3999	245	5	formula	formula	NOUN
easat-3999	245	6	already	already	ADV
easat-3999	245	7	incorporates	incorporate	VERB
easat-3999	245	8	𝐺𝑚	𝐺𝑚	PROPN
easat-3999	245	9	and	and	CCONJ
easat-3999	245	10	distance	distance	NOUN
easat-3999	245	11	:	:	PUNCT
easat-3999	245	12	δ𝛼classical	δ𝛼classical	ADJ
easat-3999	245	13	=	=	SYM
easat-3999	245	14	4𝐺⋅𝑀	4𝐺⋅𝑀	NUM
easat-3999	245	15	𝑐2⋅𝑏	𝑐2⋅𝑏	ADJ
easat-3999	245	16	then	then	ADV
easat-3999	245	17	𝑏	𝑏	PROPN
easat-3999	245	18	(	(	PUNCT
easat-3999	245	19	impact	impact	NOUN
easat-3999	245	20	parameter	parameter	NOUN
easat-3999	245	21	)	)	PUNCT
easat-3999	245	22	represents	represent	VERB
easat-3999	245	23	the	the	DET
easat-3999	245	24	closest	close	ADJ
easat-3999	245	25	approach	approach	NOUN
easat-3999	245	26	distance	distance	NOUN
easat-3999	245	27	of	of	ADP
easat-3999	245	28	light	light	NOUN
easat-3999	245	29	to	to	ADP
easat-3999	245	30	the	the	DET
easat-3999	245	31	mass	mass	NOUN
easat-3999	245	32	𝑀.	𝑀.	PROPN
easat-3999	245	33	thus	thus	ADV
easat-3999	245	34	,	,	PUNCT
easat-3999	245	35	𝐺𝑚	𝐺𝑚	PROPN
easat-3999	245	36	is	be	AUX
easat-3999	245	37	implicitly	implicitly	ADV
easat-3999	245	38	connected	connect	VERB
easat-3999	245	39	to	to	ADP
easat-3999	245	40	the	the	DET
easat-3999	245	41	distance	distance	NOUN
easat-3999	245	42	𝑏	𝑏	NOUN
easat-3999	245	43	in	in	ADP
easat-3999	245	44	classical	classical	ADJ
easat-3999	245	45	deflection	deflection	NOUN
easat-3999	245	46	.	.	PUNCT
easat-3999	246	1	in	in	ADP
easat-3999	246	2	desmos	desmos	PROPN
easat-3999	246	3	theory	theory	NOUN
easat-3999	246	4	,	,	PUNCT
easat-3999	246	5	if	if	SCONJ
easat-3999	246	6	𝐺𝑚	𝐺𝑚	PROPN
easat-3999	246	7	is	be	AUX
easat-3999	246	8	explicitly	explicitly	ADV
easat-3999	246	9	related	relate	VERB
easat-3999	246	10	to	to	ADP
easat-3999	246	11	distance	distance	NOUN
easat-3999	246	12	,	,	PUNCT
easat-3999	246	13	the	the	DET
easat-3999	246	14	effective	effective	ADJ
easat-3999	246	15	mass	mass	NOUN
easat-3999	246	16	:	:	PUNCT
easat-3999	246	17	𝑀eff	𝑀eff	PROPN
easat-3999	246	18	=	=	SYM
easat-3999	246	19	𝑀	𝑀	PROPN
easat-3999	246	20	+	+	CCONJ
easat-3999	246	21	𝑀dark	𝑀dark	PROPN
easat-3999	246	22	,	,	PUNCT
easat-3999	246	23	contributes	contribute	VERB
easat-3999	246	24	to	to	ADP
easat-3999	246	25	gravitational	gravitational	ADJ
easat-3999	246	26	deflection	deflection	NOUN
easat-3999	246	27	and	and	CCONJ
easat-3999	246	28	depends	depend	VERB
easat-3999	246	29	on	on	ADP
easat-3999	246	30	:	:	PUNCT
easat-3999	246	31	𝑟	𝑟	X
easat-3999	246	32	,	,	PUNCT
easat-3999	246	33	the	the	DET
easat-3999	246	34	distance	distance	NOUN
easat-3999	246	35	between	between	ADP
easat-3999	246	36	the	the	DET
easat-3999	246	37	light	light	ADJ
easat-3999	246	38	ray	ray	NOUN
easat-3999	246	39	and	and	CCONJ
easat-3999	246	40	the	the	DET
easat-3999	246	41	mass	mass	PROPN
easat-3999	246	42	.	.	PUNCT
easat-3999	247	1	where	where	SCONJ
easat-3999	247	2	,	,	PUNCT
easat-3999	247	3	𝑏	𝑏	NOUN
easat-3999	247	4	,	,	PUNCT
easat-3999	247	5	the	the	DET
easat-3999	247	6	impact	impact	NOUN
easat-3999	247	7	parameter	parameter	NOUN
easat-3999	247	8	.	.	PUNCT
easat-3999	248	1	𝐺𝑚	𝐺𝑚	NOUN
easat-3999	248	2	scales	scale	VERB
easat-3999	248	3	with	with	ADP
easat-3999	248	4	a	a	DET
easat-3999	248	5	distance	distance	NOUN
easat-3999	248	6	-	-	PUNCT
easat-3999	248	7	dependent	dependent	ADJ
easat-3999	248	8	factor	factor	NOUN
easat-3999	248	9	𝑓(𝑟	𝑓(𝑟	NOUN
easat-3999	248	10	)	)	PUNCT
easat-3999	248	11	,	,	PUNCT
easat-3999	248	12	where	where	SCONJ
easat-3999	248	13	:	:	PUNCT
easat-3999	248	14	𝐺𝑚eff(𝑟	𝐺𝑚eff(𝑟	X
easat-3999	248	15	)	)	PUNCT
easat-3999	248	16	=	=	SYM
easat-3999	248	17	𝐺	𝐺	PROPN
easat-3999	248	18	⋅	⋅	PROPN
easat-3999	248	19	𝑀eff	𝑀eff	PROPN
easat-3999	248	20	⋅	⋅	PROPN
easat-3999	248	21	𝑓(𝑟	𝑓(𝑟	PROPN
easat-3999	248	22	)	)	PUNCT
easat-3999	248	23	in	in	ADP
easat-3999	248	24	the	the	DET
easat-3999	248	25	eflection	eflection	NOUN
easat-3999	248	26	formula	formula	NOUN
easat-3999	248	27	subtituted	subtitute	VERB
easat-3999	248	28	the	the	DET
easat-3999	248	29	𝐺𝑚eff(𝑟	𝐺𝑚eff(𝑟	NOUN
easat-3999	248	30	)	)	PUNCT
easat-3999	248	31	into	into	ADP
easat-3999	248	32	the	the	DET
easat-3999	248	33	deflection	deflection	NOUN
easat-3999	248	34	equation	equation	NOUN
easat-3999	248	35	:	:	PUNCT
easat-3999	248	36	δ𝛼total	δ𝛼total	ADJ
easat-3999	248	37	=	=	SYM
easat-3999	248	38	4𝐺⋅𝑀eff⋅𝑓(𝑟	4𝐺⋅𝑀eff⋅𝑓(𝑟	PROPN
easat-3999	248	39	)	)	PUNCT
easat-3999	248	40	𝑐2⋅𝑏⋅𝑓(𝜃	𝑐2⋅𝑏⋅𝑓(𝜃	PROPN
easat-3999	248	41	)	)	PUNCT
easat-3999	248	42	⋅	⋅	PROPN
easat-3999	248	43	(	(	PUNCT
easat-3999	248	44	1	1	NUM
easat-3999	248	45	+	+	CCONJ
easat-3999	248	46	𝑣(𝑟	𝑣(𝑟	NOUN
easat-3999	248	47	)	)	PUNCT
easat-3999	248	48	𝑐	𝑐	NOUN
easat-3999	248	49	)	)	PUNCT
easat-3999	249	1	+	+	CCONJ
easat-3999	249	2	𝑘	𝑘	DET
easat-3999	249	3	⋅	⋅	PROPN
easat-3999	249	4	𝜌(𝑟	𝜌(𝑟	PROPN
easat-3999	249	5	,	,	PUNCT
easat-3999	249	6	𝜃	𝜃	NOUN
easat-3999	249	7	)	)	PUNCT
easat-3999	249	8	⋅	⋅	PROPN
easat-3999	249	9	cos(𝜃	cos(𝜃	PROPN
easat-3999	249	10	)	)	PUNCT
easat-3999	249	11	𝑓(𝑟	𝑓(𝑟	NOUN
easat-3999	249	12	):	):	PUNCT
easat-3999	249	13	a	a	DET
easat-3999	249	14	distance	distance	NOUN
easat-3999	249	15	-	-	PUNCT
easat-3999	249	16	scaling	scale	VERB
easat-3999	249	17	function	function	NOUN
easat-3999	249	18	(	(	PUNCT
easat-3999	249	19	e.g.	e.g.	ADV
easat-3999	249	20	,	,	PUNCT
easat-3999	249	21	𝑓(𝑟	𝑓(𝑟	NOUN
easat-3999	249	22	)	)	PUNCT
easat-3999	249	23	=	=	SYM
easat-3999	249	24	1	1	NUM
easat-3999	249	25	𝑟	𝑟	NOUN
easat-3999	249	26	)	)	PUNCT
easat-3999	249	27	that	that	PRON
easat-3999	249	28	adjusts	adjust	VERB
easat-3999	249	29	𝐺𝑚	𝐺𝑚	PROPN
easat-3999	249	30	for	for	ADP
easat-3999	249	31	relative	relative	ADJ
easat-3999	249	32	distance	distance	NOUN
easat-3999	249	33	𝑟.	𝑟.	PUNCT
easat-3999	250	1	𝑓(𝜃	𝑓(𝜃	NOUN
easat-3999	250	2	):	):	PUNCT
easat-3999	250	3	angular	angular	ADJ
easat-3999	250	4	dependency	dependency	NOUN
easat-3999	250	5	modifying	modify	VERB
easat-3999	250	6	the	the	DET
easat-3999	250	7	impact	impact	NOUN
easat-3999	250	8	parameter	parameter	NOUN
easat-3999	250	9	𝑏.	𝑏.	VERB
easat-3999	250	10	the	the	DET
easat-3999	250	11	effective	effective	ADJ
easat-3999	250	12	gravitational	gravitational	ADJ
easat-3999	250	13	influence	influence	NOUN
easat-3999	250	14	𝐺𝑚	𝐺𝑚	PROPN
easat-3999	250	15	varies	vary	VERB
easat-3999	250	16	with	with	ADP
easat-3999	250	17	relative	relative	ADJ
easat-3999	250	18	distance	distance	NOUN
easat-3999	250	19	𝑟	𝑟	NOUN
easat-3999	250	20	and	and	CCONJ
easat-3999	250	21	angular	angular	ADJ
easat-3999	250	22	dependency	dependency	NOUN
easat-3999	250	23	𝑓(𝜃	𝑓(𝜃	NOUN
easat-3999	250	24	)	)	PUNCT
easat-3999	250	25	,	,	PUNCT
easat-3999	250	26	modifying	modify	VERB
easat-3999	250	27	the	the	DET
easat-3999	250	28	deflection	deflection	NOUN
easat-3999	250	29	as	as	SCONJ
easat-3999	250	30	follows	follow	VERB
easat-3999	250	31	:	:	PUNCT
easat-3999	250	32	gravitational	gravitational	ADJ
easat-3999	250	33	mass	mass	NOUN
easat-3999	250	34	influence	influence	NOUN
easat-3999	250	35	:	:	PUNCT
easat-3999	250	36	𝐺𝑚eff(𝑟	𝐺𝑚eff(𝑟	X
easat-3999	250	37	)	)	PUNCT
easat-3999	251	1	=	=	SYM
easat-3999	251	2	𝐺	𝐺	PROPN
easat-3999	251	3	⋅	⋅	PROPN
easat-3999	251	4	𝑀+𝑀dark	𝑀+𝑀dark	PROPN
easat-3999	251	5	𝑟	𝑟	PROPN
easat-3999	251	6	deflection	deflection	NOUN
easat-3999	251	7	with	with	ADP
easat-3999	251	8	distance	distance	NOUN
easat-3999	251	9	:	:	PUNCT
easat-3999	251	10	δ𝛼total	δ𝛼total	ADJ
easat-3999	251	11	∝	∝	PROPN
easat-3999	251	12	𝐺⋅(𝑀+𝑀dark	𝐺⋅(𝑀+𝑀dark	PROPN
easat-3999	251	13	)	)	PUNCT
easat-3999	251	14	𝑟⋅𝑏	𝑟⋅𝑏	NUM
easat-3999	251	15	this	this	PRON
easat-3999	251	16	highlights	highlight	VERB
easat-3999	251	17	the	the	DET
easat-3999	251	18	dependency	dependency	NOUN
easat-3999	251	19	of	of	ADP
easat-3999	251	20	𝐺𝑚	𝐺𝑚	PROPN
easat-3999	251	21	on	on	ADP
easat-3999	251	22	distance	distance	NOUN
easat-3999	251	23	𝑟	𝑟	NOUN
easat-3999	251	24	,	,	PUNCT
easat-3999	251	25	making	make	VERB
easat-3999	251	26	gravitational	gravitational	ADJ
easat-3999	251	27	deflection	deflection	NOUN
easat-3999	251	28	a	a	DET
easat-3999	251	29	function	function	NOUN
easat-3999	251	30	of	of	ADP
easat-3999	251	31	both	both	DET
easat-3999	251	32	mass	mass	ADJ
easat-3999	251	33	and	and	CCONJ
easat-3999	251	34	spatial	spatial	ADJ
easat-3999	251	35	configuration	configuration	NOUN
easat-3999	251	36	.	.	PUNCT
easat-3999	252	1	4	4	X
easat-3999	252	2	.	.	X
easat-3999	252	3	conclusions	conclusion	NOUN
easat-3999	252	4	the	the	DET
easat-3999	252	5	desmos	desmos	PROPN
easat-3999	252	6	shows	show	VERB
easat-3999	252	7	interprets	interpret	VERB
easat-3999	252	8	the	the	DET
easat-3999	252	9	physical	physical	ADJ
easat-3999	252	10	phenomena	phenomenon	NOUN
easat-3999	252	11	as	as	ADP
easat-3999	252	12	a	a	DET
easat-3999	252	13	unit	unit	NOUN
easat-3999	252	14	.	.	PUNCT
easat-3999	253	1	this	this	DET
easat-3999	253	2	study	study	NOUN
easat-3999	253	3	has	have	AUX
easat-3999	253	4	provided	provide	VERB
easat-3999	253	5	significant	significant	ADJ
easat-3999	253	6	insights	insight	NOUN
easat-3999	253	7	into	into	ADP
easat-3999	253	8	the	the	DET
easat-3999	253	9	parameter	parameter	NOUN
easat-3999	253	10	n	n	PROPN
easat-3999	253	11	within	within	ADP
easat-3999	253	12	desmos	desmo	NOUN
easat-3999	253	13	and	and	CCONJ
easat-3999	253	14	its	its	PRON
easat-3999	253	15	implications	implication	NOUN
easat-3999	253	16	for	for	ADP
easat-3999	253	17	cosmic	cosmic	ADJ
easat-3999	253	18	dynamics	dynamic	NOUN
easat-3999	253	19	.	.	PUNCT
easat-3999	254	1	the	the	DET
easat-3999	254	2	derived	derive	VERB
easat-3999	254	3	value	value	NOUN
easat-3999	254	4	of	of	ADP
easat-3999	254	5	n≈1.10	n≈1.10	PROPN
easat-3999	254	6	reveals	reveal	VERB
easat-3999	254	7	a	a	DET
easat-3999	254	8	notable	notable	ADJ
easat-3999	254	9	deviation	deviation	NOUN
easat-3999	254	10	from	from	ADP
easat-3999	254	11	the	the	DET
easat-3999	254	12	classical	classical	ADJ
easat-3999	254	13	gravity	gravity	NOUN
easat-3999	254	14	model	model	NOUN
easat-3999	254	15	,	,	PUNCT
easat-3999	254	16	which	which	PRON
easat-3999	254	17	is	be	AUX
easat-3999	254	18	characterized	characterize	VERB
easat-3999	254	19	by	by	ADP
easat-3999	254	20	an	an	DET
easat-3999	254	21	inverse	inverse	NOUN
easat-3999	254	22	-	-	PUNCT
easat-3999	254	23	square	square	NOUN
easat-3999	254	24	law	law	NOUN
easat-3999	254	25	(	(	PUNCT
easat-3999	254	26	n=2	n=2	ADV
easat-3999	254	27	)	)	PUNCT
easat-3999	254	28	.	.	PUNCT
easat-3999	255	1	this	this	DET
easat-3999	255	2	new	new	ADJ
easat-3999	255	3	value	value	NOUN
easat-3999	255	4	suggests	suggest	VERB
easat-3999	255	5	that	that	SCONJ
easat-3999	255	6	the	the	DET
easat-3999	255	7	effective	effective	ADJ
easat-3999	255	8	force	force	NOUN
easat-3999	255	9	or	or	CCONJ
easat-3999	255	10	interaction	interaction	NOUN
easat-3999	255	11	between	between	ADP
easat-3999	255	12	celestial	celestial	ADJ
easat-3999	255	13	bodies	body	NOUN
easat-3999	255	14	diminishes	diminish	VERB
easat-3999	255	15	with	with	ADP
easat-3999	255	16	distance	distance	NOUN
easat-3999	255	17	,	,	PUNCT
easat-3999	255	18	but	but	CCONJ
easat-3999	255	19	not	not	PART
easat-3999	255	20	as	as	ADV
easat-3999	255	21	sharply	sharply	ADV
easat-3999	255	22	as	as	SCONJ
easat-3999	255	23	predicted	predict	VERB
easat-3999	255	24	by	by	ADP
easat-3999	255	25	gravity	gravity	NOUN
easat-3999	255	26	.	.	PUNCT
easat-3999	256	1	this	this	DET
easat-3999	256	2	result	result	NOUN
easat-3999	256	3	aligns	align	VERB
easat-3999	256	4	with	with	ADP
easat-3999	256	5	the	the	DET
easat-3999	256	6	observed	observe	VERB
easat-3999	256	7	behavior	behavior	NOUN
easat-3999	256	8	of	of	ADP
easat-3999	256	9	an	an	DET
easat-3999	256	10	expanding	expand	VERB
easat-3999	256	11	universe	universe	NOUN
easat-3999	256	12	,	,	PUNCT
easat-3999	256	13	where	where	SCONJ
easat-3999	256	14	interactions	interaction	NOUN
easat-3999	256	15	weaken	weaken	VERB
easat-3999	256	16	more	more	ADV
easat-3999	256	17	gradually	gradually	ADV
easat-3999	256	18	over	over	ADP
easat-3999	256	19	cosmic	cosmic	ADJ
easat-3999	256	20	scales	scale	NOUN
easat-3999	256	21	.	.	PUNCT
easat-3999	257	1	one	one	NUM
easat-3999	257	2	of	of	ADP
easat-3999	257	3	the	the	DET
easat-3999	257	4	key	key	ADJ
easat-3999	257	5	findings	finding	NOUN
easat-3999	257	6	is	be	AUX
easat-3999	257	7	the	the	DET
easat-3999	257	8	impact	impact	NOUN
easat-3999	257	9	of	of	ADP
easat-3999	257	10	the	the	DET
easat-3999	257	11	bond	bond	NOUN
easat-3999	257	12	model	model	NOUN
easat-3999	257	13	on	on	ADP
easat-3999	257	14	energy	energy	NOUN
easat-3999	257	15	interactions	interaction	NOUN
easat-3999	257	16	.	.	PUNCT
easat-3999	258	1	according	accord	VERB
easat-3999	258	2	to	to	ADP
easat-3999	258	3	challoumis	challoumis	PROPN
easat-3999	258	4	'	'	PUNCT
easat-3999	258	5	theory	theory	NOUN
easat-3999	258	6	,	,	PUNCT
easat-3999	258	7	the	the	DET
easat-3999	258	8	effective	effective	ADJ
easat-3999	258	9	energy	energy	NOUN
easat-3999	258	10	between	between	ADP
easat-3999	258	11	the	the	DET
easat-3999	258	12	earth	earth	NOUN
easat-3999	258	13	and	and	CCONJ
easat-3999	258	14	moon	moon	NOUN
easat-3999	258	15	is	be	AUX
easat-3999	258	16	higher	high	ADJ
easat-3999	258	17	compared	compare	VERB
easat-3999	258	18	to	to	ADP
easat-3999	258	19	the	the	DET
easat-3999	258	20	moon	moon	NOUN
easat-3999	258	21	and	and	CCONJ
easat-3999	258	22	sun	sun	NOUN
easat-3999	258	23	,	,	PUNCT
easat-3999	258	24	which	which	PRON
easat-3999	258	25	contradicts	contradict	VERB
easat-3999	258	26	the	the	DET
easat-3999	258	27	classical	classical	ADJ
easat-3999	258	28	expectations	expectation	NOUN
easat-3999	258	29	of	of	ADP
easat-3999	258	30	gravity	gravity	NOUN
easat-3999	258	31	.	.	PUNCT
easat-3999	259	1	this	this	DET
easat-3999	259	2	highlights	highlight	NOUN
easat-3999	259	3	that	that	PRON
easat-3999	259	4	gravitational	gravitational	ADJ
easat-3999	259	5	forces	force	NOUN
easat-3999	259	6	are	be	AUX
easat-3999	259	7	not	not	PART
easat-3999	259	8	solely	solely	ADV
easat-3999	259	9	dependent	dependent	ADJ
easat-3999	259	10	on	on	ADP
easat-3999	259	11	distance	distance	NOUN
easat-3999	259	12	but	but	CCONJ
easat-3999	259	13	are	be	AUX
easat-3999	259	14	influenced	influence	VERB
easat-3999	259	15	by	by	ADP
easat-3999	259	16	other	other	ADJ
easat-3999	259	17	factors	factor	NOUN
easat-3999	259	18	in	in	ADP
easat-3999	259	19	the	the	DET
easat-3999	259	20	bond	bond	NOUN
easat-3999	259	21	model	model	NOUN
easat-3999	259	22	.	.	PUNCT
easat-3999	260	1	this	this	DET
easat-3999	260	2	nuanced	nuanced	ADJ
easat-3999	260	3	understanding	understanding	NOUN
easat-3999	260	4	challenges	challenge	VERB
easat-3999	260	5	traditional	traditional	ADJ
easat-3999	260	6	views	view	NOUN
easat-3999	260	7	and	and	CCONJ
easat-3999	260	8	provides	provide	VERB
easat-3999	260	9	a	a	DET
easat-3999	260	10	more	more	ADV
easat-3999	260	11	complex	complex	ADJ
easat-3999	260	12	picture	picture	NOUN
easat-3999	260	13	of	of	ADP
easat-3999	260	14	gravitational	gravitational	ADJ
easat-3999	260	15	interactions	interaction	NOUN
easat-3999	260	16	.	.	PUNCT
easat-3999	261	1	the	the	DET
easat-3999	261	2	study	study	NOUN
easat-3999	261	3	also	also	ADV
easat-3999	261	4	shows	show	VERB
easat-3999	261	5	how	how	SCONJ
easat-3999	261	6	desmos	desmo	NOUN
easat-3999	261	7	can	can	AUX
easat-3999	261	8	help	help	VERB
easat-3999	261	9	explain	explain	VERB
easat-3999	261	10	the	the	DET
easat-3999	261	11	precession	precession	NOUN
easat-3999	261	12	of	of	ADP
easat-3999	261	13	mercury	mercury	NOUN
easat-3999	261	14	's	's	PART
easat-3999	261	15	orbit	orbit	NOUN
easat-3999	261	16	,	,	PUNCT
easat-3999	261	17	a	a	DET
easat-3999	261	18	phenomenon	phenomenon	NOUN
easat-3999	261	19	that	that	SCONJ
easat-3999	261	20	classical	classical	ADJ
easat-3999	261	21	gravity	gravity	NOUN
easat-3999	261	22	alone	alone	ADV
easat-3999	261	23	can	can	AUX
easat-3999	261	24	not	not	PART
easat-3999	261	25	fully	fully	ADV
easat-3999	261	26	account	account	VERB
easat-3999	261	27	for	for	ADP
easat-3999	261	28	.	.	PUNCT
easat-3999	262	1	by	by	ADP
easat-3999	262	2	offering	offer	VERB
easat-3999	262	3	a	a	DET
easat-3999	262	4	modified	modify	VERB
easat-3999	262	5	approach	approach	NOUN
easat-3999	262	6	,	,	PUNCT
easat-3999	262	7	the	the	DET
easat-3999	262	8	model	model	NOUN
easat-3999	262	9	fits	fit	VERB
easat-3999	262	10	observational	observational	ADJ
easat-3999	262	11	data	datum	NOUN
easat-3999	262	12	more	more	ADV
easat-3999	262	13	effectively	effectively	ADV
easat-3999	262	14	,	,	PUNCT
easat-3999	262	15	demonstrating	demonstrate	VERB
easat-3999	262	16	its	its	PRON
easat-3999	262	17	utility	utility	NOUN
easat-3999	262	18	in	in	ADP
easat-3999	262	19	addressing	address	VERB
easat-3999	262	20	complex	complex	ADJ
easat-3999	262	21	astrophysical	astrophysical	ADJ
easat-3999	262	22	questions	question	NOUN
easat-3999	262	23	.	.	PUNCT
easat-3999	263	1	furthermore	furthermore	ADV
easat-3999	263	2	,	,	PUNCT
easat-3999	263	3	the	the	DET
easat-3999	263	4	alignment	alignment	NOUN
easat-3999	263	5	of	of	ADP
easat-3999	263	6	the	the	DET
easat-3999	263	7	modified	modify	VERB
easat-3999	263	8	model	model	NOUN
easat-3999	263	9	with	with	ADP
easat-3999	263	10	hubble	hubble	PROPN
easat-3999	263	11	’s	’s	PART
easat-3999	263	12	law	law	NOUN
easat-3999	263	13	reinforces	reinforce	VERB
easat-3999	263	14	its	its	PRON
easat-3999	263	15	relevance	relevance	NOUN
easat-3999	263	16	in	in	ADP
easat-3999	263	17	explaining	explain	VERB
easat-3999	263	18	cosmic	cosmic	ADJ
easat-3999	263	19	expansion	expansion	NOUN
easat-3999	263	20	.	.	PUNCT
easat-3999	264	1	the	the	DET
easat-3999	264	2	calculated	calculate	VERB
easat-3999	264	3	parameter	parameter	NOUN
easat-3999	264	4	n	n	PART
easat-3999	264	5	reflects	reflect	VERB
easat-3999	264	6	how	how	SCONJ
easat-3999	264	7	cosmic	cosmic	ADJ
easat-3999	264	8	forces	force	NOUN
easat-3999	264	9	diminish	diminish	VERB
easat-3999	264	10	with	with	ADP
easat-3999	264	11	distance	distance	NOUN
easat-3999	264	12	in	in	ADP
easat-3999	264	13	a	a	DET
easat-3999	264	14	way	way	NOUN
easat-3999	264	15	that	that	PRON
easat-3999	264	16	is	be	AUX
easat-3999	264	17	consistent	consistent	ADJ
easat-3999	264	18	with	with	ADP
easat-3999	264	19	the	the	DET
easat-3999	264	20	observed	observed	ADJ
easat-3999	264	21	expansion	expansion	NOUN
easat-3999	264	22	of	of	ADP
easat-3999	264	23	the	the	DET
easat-3999	264	24	universe	universe	NOUN
easat-3999	264	25	.	.	PUNCT
easat-3999	265	1	this	this	PRON
easat-3999	265	2	underscores	underscore	VERB
easat-3999	265	3	the	the	DET
easat-3999	265	4	9372	9372	NUM
easat-3999	265	5	edelweiss	edelweiss	PROPN
easat-3999	265	6	applied	apply	VERB
easat-3999	265	7	science	science	NOUN
easat-3999	265	8	and	and	CCONJ
easat-3999	265	9	technology	technology	NOUN
easat-3999	265	10	issn	issn	PROPN
easat-3999	265	11	:	:	PUNCT
easat-3999	265	12	2576	2576	NUM
easat-3999	265	13	-	-	SYM
easat-3999	265	14	8484	8484	NUM
easat-3999	265	15	vol	vol	NOUN
easat-3999	265	16	.	.	PROPN
easat-3999	265	17	8	8	NUM
easat-3999	265	18	,	,	PUNCT
easat-3999	265	19	no	no	INTJ
easat-3999	265	20	.	.	NOUN
easat-3999	265	21	6	6	NUM
easat-3999	265	22	:	:	SYM
easat-3999	265	23	9356	9356	NUM
easat-3999	265	24	-	-	SYM
easat-3999	265	25	9375	9375	NUM
easat-3999	265	26	,	,	PUNCT
easat-3999	265	27	2024	2024	NUM
easat-3999	265	28	doi	doi	NOUN
easat-3999	265	29	:	:	PUNCT
easat-3999	265	30	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	265	31	©	©	PROPN
easat-3999	265	32	2024	2024	NUM
easat-3999	265	33	by	by	ADP
easat-3999	265	34	the	the	DET
easat-3999	265	35	author	author	NOUN
easat-3999	265	36	;	;	PUNCT
easat-3999	265	37	licensee	licensee	NOUN
easat-3999	265	38	learning	learning	NOUN
easat-3999	265	39	gate	gate	NOUN
easat-3999	265	40	importance	importance	NOUN
easat-3999	265	41	of	of	ADP
easat-3999	265	42	exploring	explore	VERB
easat-3999	265	43	alternative	alternative	ADJ
easat-3999	265	44	models	model	NOUN
easat-3999	265	45	to	to	PART
easat-3999	265	46	better	well	ADV
easat-3999	265	47	understand	understand	VERB
easat-3999	265	48	the	the	DET
easat-3999	265	49	dynamics	dynamic	NOUN
easat-3999	265	50	of	of	ADP
easat-3999	265	51	cosmic	cosmic	ADJ
easat-3999	265	52	forces	force	NOUN
easat-3999	265	53	.	.	PUNCT
easat-3999	266	1	in	in	ADP
easat-3999	266	2	conclusion	conclusion	NOUN
easat-3999	266	3	,	,	PUNCT
easat-3999	266	4	the	the	DET
easat-3999	266	5	study	study	NOUN
easat-3999	266	6	emphasizes	emphasize	VERB
easat-3999	266	7	the	the	DET
easat-3999	266	8	value	value	NOUN
easat-3999	266	9	of	of	ADP
easat-3999	266	10	challoumis	challoumis	PROPN
easat-3999	266	11	'	'	PART
easat-3999	266	12	modified	modify	VERB
easat-3999	266	13	gravitational	gravitational	ADJ
easat-3999	266	14	model	model	NOUN
easat-3999	266	15	in	in	ADP
easat-3999	266	16	enhancing	enhance	VERB
easat-3999	266	17	our	our	PRON
easat-3999	266	18	understanding	understanding	NOUN
easat-3999	266	19	of	of	ADP
easat-3999	266	20	cosmic	cosmic	ADJ
easat-3999	266	21	phenomena	phenomenon	NOUN
easat-3999	266	22	.	.	PUNCT
easat-3999	267	1	the	the	DET
easat-3999	267	2	results	result	NOUN
easat-3999	267	3	offer	offer	VERB
easat-3999	267	4	a	a	DET
easat-3999	267	5	refined	refined	ADJ
easat-3999	267	6	perspective	perspective	NOUN
easat-3999	267	7	on	on	ADP
easat-3999	267	8	gravitational	gravitational	ADJ
easat-3999	267	9	interactions	interaction	NOUN
easat-3999	267	10	and	and	CCONJ
easat-3999	267	11	support	support	VERB
easat-3999	267	12	the	the	DET
easat-3999	267	13	idea	idea	NOUN
easat-3999	267	14	that	that	SCONJ
easat-3999	267	15	forces	force	NOUN
easat-3999	267	16	and	and	CCONJ
easat-3999	267	17	energies	energy	NOUN
easat-3999	267	18	across	across	ADP
easat-3999	267	19	vast	vast	ADJ
easat-3999	267	20	distances	distance	NOUN
easat-3999	267	21	may	may	AUX
easat-3999	267	22	follow	follow	VERB
easat-3999	267	23	different	different	ADJ
easat-3999	267	24	rules	rule	NOUN
easat-3999	267	25	than	than	ADP
easat-3999	267	26	those	those	PRON
easat-3999	267	27	suggested	suggest	VERB
easat-3999	267	28	by	by	ADP
easat-3999	267	29	classical	classical	ADJ
easat-3999	267	30	models	model	NOUN
easat-3999	267	31	.	.	PUNCT
easat-3999	268	1	future	future	ADJ
easat-3999	268	2	research	research	NOUN
easat-3999	268	3	could	could	AUX
easat-3999	268	4	further	far	ADV
easat-3999	268	5	investigate	investigate	VERB
easat-3999	268	6	these	these	DET
easat-3999	268	7	findings	finding	NOUN
easat-3999	268	8	and	and	CCONJ
easat-3999	268	9	explore	explore	VERB
easat-3999	268	10	their	their	PRON
easat-3999	268	11	implications	implication	NOUN
easat-3999	268	12	for	for	ADP
easat-3999	268	13	other	other	ADJ
easat-3999	268	14	astrophysical	astrophysical	ADJ
easat-3999	268	15	phenomena	phenomenon	NOUN
easat-3999	268	16	,	,	PUNCT
easat-3999	268	17	continuing	continue	VERB
easat-3999	268	18	to	to	PART
easat-3999	268	19	challenge	challenge	VERB
easat-3999	268	20	and	and	CCONJ
easat-3999	268	21	refine	refine	VERB
easat-3999	268	22	our	our	PRON
easat-3999	268	23	understanding	understanding	NOUN
easat-3999	268	24	of	of	ADP
easat-3999	268	25	gravitational	gravitational	ADJ
easat-3999	268	26	theories	theory	NOUN
easat-3999	268	27	.	.	PUNCT
easat-3999	269	1	copyright	copyright	NOUN
easat-3999	269	2	:	:	PUNCT
easat-3999	269	3	©	©	PROPN
easat-3999	269	4	2024	2024	NUM
easat-3999	269	5	by	by	ADP
easat-3999	269	6	the	the	DET
easat-3999	269	7	authors	author	NOUN
easat-3999	269	8	.	.	PUNCT
easat-3999	270	1	this	this	DET
easat-3999	270	2	article	article	NOUN
easat-3999	270	3	is	be	AUX
easat-3999	270	4	an	an	DET
easat-3999	270	5	open	open	ADJ
easat-3999	270	6	access	access	NOUN
easat-3999	270	7	article	article	NOUN
easat-3999	270	8	distributed	distribute	VERB
easat-3999	270	9	under	under	ADP
easat-3999	270	10	the	the	DET
easat-3999	270	11	terms	term	NOUN
easat-3999	270	12	and	and	CCONJ
easat-3999	270	13	conditions	condition	NOUN
easat-3999	270	14	of	of	ADP
easat-3999	270	15	the	the	DET
easat-3999	270	16	creative	creative	ADJ
easat-3999	270	17	commons	common	NOUN
easat-3999	270	18	attribution	attribution	NOUN
easat-3999	270	19	(	(	PUNCT
easat-3999	270	20	cc	cc	NOUN
easat-3999	270	21	by	by	ADP
easat-3999	270	22	)	)	PUNCT
easat-3999	270	23	license	license	NOUN
easat-3999	270	24	(	(	PUNCT
easat-3999	270	25	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-3999	270	26	)	)	PUNCT
easat-3999	270	27	.	.	PUNCT
easat-3999	271	1	references	reference	NOUN
easat-3999	271	2	[	[	X
easat-3999	271	3	1	1	NUM
easat-3999	271	4	]	]	PUNCT
easat-3999	271	5	bennett	bennett	PROPN
easat-3999	271	6	,	,	PUNCT
easat-3999	271	7	m.	m.	PROPN
easat-3999	271	8	j.	j.	PROPN
easat-3999	271	9	(	(	PUNCT
easat-3999	271	10	2017	2017	NUM
easat-3999	271	11	)	)	PUNCT
easat-3999	271	12	.	.	PUNCT
easat-3999	272	1	deleuze	deleuze	PROPN
easat-3999	272	2	and	and	CCONJ
easat-3999	272	3	ancient	ancient	ADJ
easat-3999	272	4	greek	greek	ADJ
easat-3999	272	5	physics	physics	NOUN
easat-3999	272	6	:	:	PUNCT
easat-3999	272	7	the	the	DET
easat-3999	272	8	image	image	NOUN
easat-3999	272	9	of	of	ADP
easat-3999	272	10	nature	nature	NOUN
easat-3999	272	11	.	.	PUNCT
easat-3999	273	1	in	in	ADP
easat-3999	273	2	deleuze	deleuze	PROPN
easat-3999	273	3	and	and	CCONJ
easat-3999	273	4	ancient	ancient	ADJ
easat-3999	273	5	greek	greek	ADJ
easat-3999	273	6	physics	physics	NOUN
easat-3999	273	7	:	:	PUNCT
easat-3999	273	8	the	the	DET
easat-3999	273	9	image	image	NOUN
easat-3999	273	10	of	of	ADP
easat-3999	273	11	nature	nature	NOUN
easat-3999	273	12	.	.	PUNCT
easat-3999	274	1	https://doi.org/10.5040/9781474284707	https://doi.org/10.5040/9781474284707	PRON
easat-3999	274	2	[	[	X
easat-3999	274	3	2	2	NUM
easat-3999	274	4	]	]	PUNCT
easat-3999	274	5	cerri	cerri	NOUN
easat-3999	274	6	,	,	PUNCT
easat-3999	274	7	g.	g.	PROPN
easat-3999	274	8	(	(	PUNCT
easat-3999	274	9	2017	2017	NUM
easat-3999	274	10	)	)	PUNCT
easat-3999	274	11	.	.	PUNCT
easat-3999	275	1	the	the	DET
easat-3999	275	2	concept	concept	NOUN
easat-3999	275	3	of	of	ADP
easat-3999	275	4	‘	'	PUNCT
easat-3999	275	5	matter	matter	NOUN
easat-3999	275	6	’	'	PUNCT
easat-3999	275	7	in	in	ADP
easat-3999	275	8	archaic	archaic	ADJ
easat-3999	275	9	greece	greece	PROPN
easat-3999	275	10	,	,	PUNCT
easat-3999	275	11	1	1	NUM
easat-3999	275	12	:	:	PUNCT
easat-3999	275	13	khaos	khaos	PROPN
easat-3999	275	14	/	/	SYM
easat-3999	275	15	aèr	aèr	PROPN
easat-3999	275	16	in	in	ADP
easat-3999	275	17	hesiod	hesiod	PROPN
easat-3999	275	18	’s	’s	PART
easat-3999	275	19	theogony	theogony	PROPN
easat-3999	275	20	.	.	PUNCT
easat-3999	276	1	peitho	peitho	PROPN
easat-3999	276	2	,	,	PUNCT
easat-3999	276	3	8(1	8(1	NOUN
easat-3999	276	4	)	)	PUNCT
easat-3999	276	5	.	.	PUNCT
easat-3999	277	1	https://doi.org/10.14746/pea.2017.1.3	https://doi.org/10.14746/pea.2017.1.3	PUNCT
easat-3999	277	2	[	[	X
easat-3999	277	3	3	3	NUM
easat-3999	277	4	]	]	X
easat-3999	277	5	challoumis	challoumis	PROPN
easat-3999	277	6	,	,	PUNCT
easat-3999	277	7	c.	c.	PROPN
easat-3999	277	8	(	(	PUNCT
easat-3999	277	9	2024a	2024a	NUM
easat-3999	277	10	)	)	PUNCT
easat-3999	277	11	.	.	PUNCT
easat-3999	278	1	bond	bond	NOUN
easat-3999	278	2	(	(	PUNCT
easat-3999	278	3	desmos	desmos	NOUN
easat-3999	278	4	)	)	PUNCT
easat-3999	278	5	spacetime	spacetime	NOUN
easat-3999	278	6	decay	decay	VERB
easat-3999	278	7	δεσμού	δεσμού	PROPN
easat-3999	278	8	χωροχρονική	χωροχρονική	PROPN
easat-3999	278	9	διάσπαση	διάσπαση	VERB
easat-3999	278	10	.	.	PUNCT
easat-3999	279	1	https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4536191	https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4536191	PROPN
easat-3999	280	1	[	[	X
easat-3999	280	2	4	4	NUM
easat-3999	280	3	]	]	X
easat-3999	280	4	challoumis	challoumis	PROPN
easat-3999	280	5	,	,	PUNCT
easat-3999	280	6	c.	c.	PROPN
easat-3999	280	7	(	(	PUNCT
easat-3999	280	8	2024b	2024b	NUM
easat-3999	280	9	)	)	PUNCT
easat-3999	280	10	.	.	PUNCT
easat-3999	281	1	panphysics	panphysic	NOUN
easat-3999	281	2	enopiisis	enopiisis	VERB
easat-3999	281	3	short	short	ADJ
easat-3999	281	4	view	view	NOUN
easat-3999	281	5	.	.	PUNCT
easat-3999	282	1	https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4970532	https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4970532	PROPN
easat-3999	283	1	[	[	X
easat-3999	283	2	5	5	NUM
easat-3999	283	3	]	]	PUNCT
easat-3999	283	4	challoumis	challoumis	PROPN
easat-3999	283	5	,	,	PUNCT
easat-3999	283	6	c.	c.	PROPN
easat-3999	283	7	(	(	PUNCT
easat-3999	283	8	2024c	2024c	NUM
easat-3999	283	9	)	)	PUNCT
easat-3999	283	10	.	.	PUNCT
easat-3999	284	1	panphysics	panphysic	NOUN
easat-3999	284	2	gravity	gravity	NOUN
easat-3999	284	3	,	,	PUNCT
easat-3999	284	4	energy	energy	NOUN
easat-3999	284	5	and	and	CCONJ
easat-3999	284	6	desmos	desmos	NOUN
easat-3999	284	7	space	space	NOUN
easat-3999	284	8	-	-	PUNCT
easat-3999	284	9	time	time	NOUN
easat-3999	284	10	of	of	ADP
easat-3999	284	11	gravity	gravity	NOUN
easat-3999	284	12	.	.	PUNCT
easat-3999	285	1	in	in	ADP
easat-3999	285	2	ssrn	ssrn	PROPN
easat-3999	285	3	electronic	electronic	ADJ
easat-3999	285	4	journal	journal	NOUN
easat-3999	285	5	.	.	PUNCT
easat-3999	286	1	https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4939997	https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4939997	PROPN
easat-3999	287	1	[	[	X
easat-3999	287	2	6	6	NUM
easat-3999	287	3	]	]	PUNCT
easat-3999	287	4	disalle	disalle	PROPN
easat-3999	287	5	,	,	PUNCT
easat-3999	287	6	r.	r.	PROPN
easat-3999	287	7	(	(	PUNCT
easat-3999	287	8	2006	2006	NUM
easat-3999	287	9	)	)	PUNCT
easat-3999	287	10	.	.	PUNCT
easat-3999	288	1	understanding	understand	VERB
easat-3999	288	2	space	space	NOUN
easat-3999	288	3	-	-	PUNCT
easat-3999	288	4	time	time	NOUN
easat-3999	288	5	:	:	PUNCT
easat-3999	288	6	the	the	DET
easat-3999	288	7	philosophical	philosophical	ADJ
easat-3999	288	8	development	development	NOUN
easat-3999	288	9	of	of	ADP
easat-3999	288	10	physics	physics	PROPN
easat-3999	288	11	from	from	ADP
easat-3999	288	12	newton	newton	PROPN
easat-3999	288	13	to	to	ADP
easat-3999	288	14	einstein	einstein	PROPN
easat-3999	288	15	.	.	PUNCT
easat-3999	289	1	in	in	ADP
easat-3999	289	2	understanding	understand	VERB
easat-3999	289	3	space	space	NOUN
easat-3999	289	4	-	-	PUNCT
easat-3999	289	5	time	time	NOUN
easat-3999	289	6	:	:	PUNCT
easat-3999	289	7	the	the	DET
easat-3999	289	8	philosophical	philosophical	ADJ
easat-3999	289	9	development	development	NOUN
easat-3999	289	10	of	of	ADP
easat-3999	289	11	physics	physics	PROPN
easat-3999	289	12	from	from	ADP
easat-3999	289	13	newton	newton	PROPN
easat-3999	289	14	to	to	ADP
easat-3999	289	15	einstein	einstein	PROPN
easat-3999	289	16	.	.	PUNCT
easat-3999	290	1	https://doi.org/10.1017/cbo9780511487361	https://doi.org/10.1017/cbo9780511487361	NOUN
easat-3999	290	2	[	[	X
easat-3999	290	3	7	7	NUM
easat-3999	290	4	]	]	X
easat-3999	290	5	friedman	friedman	PROPN
easat-3999	290	6	,	,	PUNCT
easat-3999	290	7	m.	m.	NOUN
easat-3999	290	8	(	(	PUNCT
easat-3999	290	9	2007	2007	NUM
easat-3999	290	10	)	)	PUNCT
easat-3999	290	11	.	.	PUNCT
easat-3999	291	1	understanding	understand	VERB
easat-3999	291	2	space	space	NOUN
easat-3999	291	3	-	-	PUNCT
easat-3999	291	4	time	time	NOUN
easat-3999	291	5	.	.	PUNCT
easat-3999	292	1	studies	study	NOUN
easat-3999	292	2	in	in	ADP
easat-3999	292	3	history	history	NOUN
easat-3999	292	4	and	and	CCONJ
easat-3999	292	5	philosophy	philosophy	NOUN
easat-3999	292	6	of	of	ADP
easat-3999	292	7	science	science	NOUN
easat-3999	292	8	part	part	NOUN
easat-3999	292	9	b	b	PROPN
easat-3999	292	10	:	:	PUNCT
easat-3999	292	11	studies	study	NOUN
easat-3999	292	12	in	in	ADP
easat-3999	292	13	history	history	NOUN
easat-3999	292	14	and	and	CCONJ
easat-3999	292	15	philosophy	philosophy	NOUN
easat-3999	292	16	of	of	ADP
easat-3999	292	17	modern	modern	ADJ
easat-3999	292	18	physics	physic	NOUN
easat-3999	292	19	,	,	PUNCT
easat-3999	292	20	38(1	38(1	NUM
easat-3999	292	21	)	)	PUNCT
easat-3999	292	22	.	.	PUNCT
easat-3999	293	1	https://doi.org/10.1016/j.shpsb.2006.10.001	https://doi.org/10.1016/j.shpsb.2006.10.001	PROPN
easat-3999	294	1	[	[	X
easat-3999	294	2	8	8	NUM
easat-3999	294	3	]	]	X
easat-3999	294	4	kandic	kandic	ADJ
easat-3999	294	5	,	,	PUNCT
easat-3999	294	6	a.	a.	NOUN
easat-3999	294	7	(	(	PUNCT
easat-3999	294	8	2023	2023	NUM
easat-3999	294	9	)	)	PUNCT
easat-3999	294	10	.	.	PUNCT
easat-3999	295	1	sabine	sabine	PROPN
easat-3999	295	2	hossenfelder	hossenfelder	PROPN
easat-3999	295	3	and	and	CCONJ
easat-3999	295	4	the	the	DET
easat-3999	295	5	crisis	crisis	NOUN
easat-3999	295	6	of	of	ADP
easat-3999	295	7	modern	modern	ADJ
easat-3999	295	8	physics	physic	NOUN
easat-3999	295	9	.	.	PUNCT
easat-3999	296	1	theoria	theoria	PROPN
easat-3999	296	2	,	,	PUNCT
easat-3999	296	3	beograd	beograd	PROPN
easat-3999	296	4	,	,	PUNCT
easat-3999	296	5	66(2	66(2	NUM
easat-3999	296	6	)	)	PUNCT
easat-3999	296	7	.	.	PUNCT
easat-3999	297	1	https://doi.org/10.2298/theo2302195k	https://doi.org/10.2298/theo2302195k	PROPN
easat-3999	297	2	appendix	appendix	NOUN
easat-3999	297	3	appendix	appendix	VERB
easat-3999	297	4	a	a	DET
easat-3999	297	5	#	#	NOUN
easat-3999	297	6	(	(	PUNCT
easat-3999	297	7	c)(r	c)(r	PROPN
easat-3999	297	8	)	)	PUNCT
easat-3999	297	9	2024	2024	NUM
easat-3999	297	10	constantinos	constantino	NOUN
easat-3999	297	11	challoumis	challoumis	VERB
easat-3999	297	12	import	import	NOUN
easat-3999	297	13	matplotlib.pyplot	matplotlib.pyplot	PROPN
easat-3999	297	14	as	as	ADP
easat-3999	297	15	plt	plt	NOUN
easat-3999	297	16	import	import	NOUN
easat-3999	297	17	numpy	numpy	NOUN
easat-3999	297	18	as	as	ADP
easat-3999	297	19	np	np	NOUN
easat-3999	297	20	#	#	NOUN
easat-3999	297	21	data	datum	NOUN
easat-3999	297	22	systems	system	NOUN
easat-3999	297	23	=	=	PUNCT
easat-3999	298	1	[	[	X
easat-3999	298	2	'	'	PUNCT
easat-3999	298	3	earth	earth	NOUN
easat-3999	298	4	-	-	PUNCT
easat-3999	298	5	moon	moon	NOUN
easat-3999	298	6	'	'	PUNCT
easat-3999	298	7	,	,	PUNCT
easat-3999	298	8	'	'	PUNCT
easat-3999	298	9	moon	moon	NOUN
easat-3999	298	10	-	-	PUNCT
easat-3999	298	11	sun	sun	NOUN
easat-3999	298	12	'	'	PUNCT
easat-3999	298	13	]	]	PUNCT
easat-3999	298	14	#	#	NOUN
easat-3999	298	15	δ	δ	NOUN
easat-3999	298	16	values	value	NOUN
easat-3999	298	17	(	(	PUNCT
easat-3999	298	18	in	in	ADP
easat-3999	298	19	kg^2	kg^2	PROPN
easat-3999	298	20	m^4	m^4	PROPN
easat-3999	298	21	/	/	SYM
easat-3999	298	22	s^4	s^4	PROPN
easat-3999	298	23	)	)	PUNCT
easat-3999	298	24	delta_values	delta_value	NOUN
easat-3999	298	25	=	=	PUNCT
easat-3999	298	26	[	[	PUNCT
easat-3999	298	27	1.458e57	1.458e57	NUM
easat-3999	298	28	,	,	PUNCT
easat-3999	298	29	#	#	NOUN
easat-3999	298	30	earth	earth	NOUN
easat-3999	298	31	-	-	PUNCT
easat-3999	298	32	moon	moon	NOUN
easat-3999	298	33	1.066e54	1.066e54	PROPN
easat-3999	298	34	#	#	NOUN
easat-3999	298	35	moon	moon	NOUN
easat-3999	298	36	-	-	PUNCT
easat-3999	298	37	sun	sun	NOUN
easat-3999	298	38	]	]	PUNCT
easat-3999	298	39	#	#	NOUN
easat-3999	298	40	gravitational	gravitational	ADJ
easat-3999	298	41	force	force	NOUN
easat-3999	298	42	values	value	NOUN
easat-3999	298	43	(	(	PUNCT
easat-3999	298	44	in	in	ADP
easat-3999	298	45	newtons	newton	NOUN
easat-3999	298	46	)	)	PUNCT
easat-3999	298	47	force_values	force_value	NOUN
easat-3999	298	48	=	=	PUNCT
easat-3999	298	49	[	[	PUNCT
easat-3999	298	50	1.982e20	1.982e20	NUM
easat-3999	298	51	,	,	PUNCT
easat-3999	298	52	#	#	NOUN
easat-3999	298	53	earth	earth	NOUN
easat-3999	298	54	-	-	PUNCT
easat-3999	298	55	moon	moon	NOUN
easat-3999	298	56	4.363e20	4.363e20	PROPN
easat-3999	298	57	#	#	NOUN
easat-3999	298	58	moon	moon	NOUN
easat-3999	298	59	-	-	PUNCT
easat-3999	298	60	sun	sun	NOUN
easat-3999	298	61	]	]	PUNCT
easat-3999	298	62	#	#	NOUN
easat-3999	298	63	create	create	VERB
easat-3999	298	64	figure	figure	NOUN
easat-3999	298	65	and	and	CCONJ
easat-3999	298	66	axis	axis	ADJ
easat-3999	298	67	fig	fig	NOUN
easat-3999	298	68	,	,	PUNCT
easat-3999	298	69	axs	axs	PROPN
easat-3999	298	70	=	=	PUNCT
easat-3999	298	71	plt.subplots(2	plt.subplots(2	NOUN
easat-3999	298	72	,	,	PUNCT
easat-3999	298	73	1	1	NUM
easat-3999	298	74	,	,	PUNCT
easat-3999	298	75	figsize=(10	figsize=(10	NOUN
easat-3999	298	76	,	,	PUNCT
easat-3999	298	77	8)	8)	NUM
easat-3999	298	78	)	)	PUNCT
easat-3999	298	79	#	#	NOUN
easat-3999	298	80	plot	plot	NOUN
easat-3999	298	81	δ	δ	PROPN
easat-3999	298	82	values	value	NOUN
easat-3999	298	83	axs[0].plot(systems	axs[0].plot(system	NOUN
easat-3999	298	84	,	,	PUNCT
easat-3999	298	85	delta_values	delta_value	NOUN
easat-3999	298	86	,	,	PUNCT
easat-3999	298	87	marker='o	marker='o	NOUN
easat-3999	298	88	'	'	NUM
easat-3999	298	89	,	,	PUNCT
easat-3999	298	90	linestyle='-	linestyle='-	PROPN
easat-3999	298	91	'	'	PUNCT
easat-3999	298	92	,	,	PUNCT
easat-3999	298	93	color='b	color='b	NOUN
easat-3999	298	94	'	'	PART
easat-3999	298	95	)	)	PUNCT
easat-3999	298	96	axs[0].set_yscale('log	axs[0].set_yscale('log	PROPN
easat-3999	298	97	'	'	PUNCT
easat-3999	298	98	)	)	PUNCT
easat-3999	299	1	axs[0].set_title('δ	axs[0].set_title('δ	NOUN
easat-3999	299	2	(	(	PUNCT
easat-3999	299	3	change	change	NOUN
easat-3999	299	4	in	in	ADP
easat-3999	299	5	gravitational	gravitational	ADJ
easat-3999	299	6	potential	potential	ADJ
easat-3999	299	7	energy	energy	NOUN
easat-3999	299	8	)	)	PUNCT
easat-3999	299	9	'	'	PUNCT
easat-3999	299	10	)	)	PUNCT
easat-3999	300	1	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-3999	300	2	9373	9373	NUM
easat-3999	300	3	edelweiss	edelweiss	PROPN
easat-3999	300	4	applied	apply	VERB
easat-3999	300	5	science	science	NOUN
easat-3999	300	6	and	and	CCONJ
easat-3999	300	7	technology	technology	NOUN
easat-3999	300	8	issn	issn	PROPN
easat-3999	300	9	:	:	PUNCT
easat-3999	300	10	2576	2576	NUM
easat-3999	300	11	-	-	SYM
easat-3999	300	12	8484	8484	NUM
easat-3999	300	13	vol	vol	NOUN
easat-3999	300	14	.	.	PROPN
easat-3999	300	15	8	8	NUM
easat-3999	300	16	,	,	PUNCT
easat-3999	300	17	no	no	INTJ
easat-3999	300	18	.	.	NOUN
easat-3999	301	1	6	6	NUM
easat-3999	301	2	:	:	SYM
easat-3999	301	3	9356	9356	NUM
easat-3999	301	4	-	-	SYM
easat-3999	301	5	9375	9375	NUM
easat-3999	301	6	,	,	PUNCT
easat-3999	301	7	2024	2024	NUM
easat-3999	301	8	doi	doi	NOUN
easat-3999	301	9	:	:	PUNCT
easat-3999	301	10	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	301	11	©	©	PROPN
easat-3999	301	12	2024	2024	NUM
easat-3999	301	13	by	by	ADP
easat-3999	301	14	the	the	DET
easat-3999	301	15	author	author	NOUN
easat-3999	301	16	;	;	PUNCT
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easat-3999	301	18	learning	learning	NOUN
easat-3999	301	19	gate	gate	NOUN
easat-3999	301	20	axs[0].set_ylabel('δ	axs[0].set_ylabel('δ	PROPN
easat-3999	302	1	(	(	PUNCT
easat-3999	302	2	kg^2	kg^2	NOUN
easat-3999	302	3	m^4	m^4	PROPN
easat-3999	302	4	/	/	SYM
easat-3999	302	5	s^4	s^4	PROPN
easat-3999	302	6	)	)	PUNCT
easat-3999	302	7	'	'	PUNCT
easat-3999	302	8	)	)	PUNCT
easat-3999	303	1	axs[0].grid(true	axs[0].grid(true	PROPN
easat-3999	303	2	,	,	PUNCT
easat-3999	303	3	which='both	which='both	PROPN
easat-3999	303	4	'	'	PUNCT
easat-3999	303	5	,	,	PUNCT
easat-3999	303	6	linestyle='--	linestyle='--	PROPN
easat-3999	303	7	'	'	PUNCT
easat-3999	303	8	,	,	PUNCT
easat-3999	303	9	linewidth=0.5	linewidth=0.5	NOUN
easat-3999	303	10	)	)	PUNCT
easat-3999	303	11	#	#	NOUN
easat-3999	303	12	plot	plot	NOUN
easat-3999	303	13	gravitational	gravitational	ADJ
easat-3999	303	14	force	force	NOUN
easat-3999	303	15	values	value	NOUN
easat-3999	303	16	axs[1].plot(systems	axs[1].plot(system	NOUN
easat-3999	303	17	,	,	PUNCT
easat-3999	303	18	force_values	force_value	NOUN
easat-3999	303	19	,	,	PUNCT
easat-3999	303	20	marker='o	marker='o	NOUN
easat-3999	303	21	'	'	NUM
easat-3999	303	22	,	,	PUNCT
easat-3999	303	23	linestyle='-	linestyle='-	PROPN
easat-3999	303	24	'	'	PUNCT
easat-3999	303	25	,	,	PUNCT
easat-3999	303	26	color='r	color='r	NOUN
easat-3999	303	27	'	'	PUNCT
easat-3999	303	28	)	)	PUNCT
easat-3999	303	29	axs[1].set_title('gravitational	axs[1].set_title('gravitational	ADJ
easat-3999	303	30	force	force	NOUN
easat-3999	303	31	'	'	PUNCT
easat-3999	303	32	)	)	PUNCT
easat-3999	303	33	axs[1].set_ylabel('force	axs[1].set_ylabel('force	PROPN
easat-3999	303	34	(	(	PUNCT
easat-3999	303	35	n	n	CCONJ
easat-3999	303	36	)	)	PUNCT
easat-3999	303	37	'	'	NUM
easat-3999	303	38	)	)	PUNCT
easat-3999	304	1	axs[1].grid(true	axs[1].grid(true	ADP
easat-3999	304	2	,	,	PUNCT
easat-3999	304	3	which='both	which='both	PROPN
easat-3999	304	4	'	'	PUNCT
easat-3999	304	5	,	,	PUNCT
easat-3999	304	6	linestyle='--	linestyle='--	PROPN
easat-3999	304	7	'	'	PUNCT
easat-3999	304	8	,	,	PUNCT
easat-3999	304	9	linewidth=0.5	linewidth=0.5	NOUN
easat-3999	304	10	)	)	PUNCT
easat-3999	304	11	#	#	NOUN
easat-3999	304	12	set	set	VERB
easat-3999	304	13	common	common	ADJ
easat-3999	304	14	x	x	ADJ
easat-3999	304	15	-	-	ADJ
easat-3999	304	16	axis	axis	ADJ
easat-3999	304	17	label	label	NOUN
easat-3999	304	18	for	for	ADP
easat-3999	304	19	ax	ax	NOUN
easat-3999	304	20	in	in	ADP
easat-3999	304	21	axs	axs	PROPN
easat-3999	304	22	:	:	PUNCT
easat-3999	304	23	ax.set_xticks(np.arange(len(systems	ax.set_xticks(np.arange(len(system	NOUN
easat-3999	304	24	)	)	PUNCT
easat-3999	304	25	)	)	PUNCT
easat-3999	304	26	)	)	PUNCT
easat-3999	305	1	ax.set_xticklabels(systems	ax.set_xticklabels(system	NOUN
easat-3999	305	2	)	)	PUNCT
easat-3999	305	3	plt.tight_layout	plt.tight_layout	NUM
easat-3999	305	4	(	(	PUNCT
easat-3999	305	5	)	)	PUNCT
easat-3999	305	6	plt.show	plt.show	PRON
easat-3999	305	7	(	(	PUNCT
easat-3999	305	8	)	)	PUNCT
easat-3999	305	9	appendix	appendix	VERB
easat-3999	305	10	b	b	PRON
easat-3999	305	11	#	#	NOUN
easat-3999	305	12	(	(	PUNCT
easat-3999	305	13	c)(r	c)(r	PROPN
easat-3999	305	14	)	)	PUNCT
easat-3999	305	15	2024	2024	NUM
easat-3999	305	16	constantinos	constantino	NOUN
easat-3999	305	17	challoumis	challoumis	VERB
easat-3999	305	18	import	import	NOUN
easat-3999	305	19	matplotlib.pyplot	matplotlib.pyplot	PROPN
easat-3999	305	20	as	as	ADP
easat-3999	305	21	plt	plt	NOUN
easat-3999	305	22	from	from	ADP
easat-3999	305	23	mpl_toolkits.mplot3d	mpl_toolkits.mplot3d	PROPN
easat-3999	305	24	import	import	NOUN
easat-3999	305	25	axes3d	axes3d	PROPN
easat-3999	305	26	import	import	NOUN
easat-3999	305	27	numpy	numpy	NOUN
easat-3999	305	28	as	as	SCONJ
easat-3999	305	29	np	np	NOUN
easat-3999	305	30	#	#	NOUN
easat-3999	305	31	define	define	VERB
easat-3999	305	32	the	the	DET
easat-3999	305	33	range	range	NOUN
easat-3999	305	34	for	for	ADP
easat-3999	305	35	distance	distance	NOUN
easat-3999	305	36	and	and	CCONJ
easat-3999	305	37	parameter	parameter	NOUN
easat-3999	305	38	n	n	PRON
easat-3999	305	39	distance	distance	NOUN
easat-3999	305	40	=	=	SYM
easat-3999	305	41	np.linspace(1	np.linspace(1	X
easat-3999	305	42	,	,	PUNCT
easat-3999	305	43	10	10	NUM
easat-3999	305	44	,	,	PUNCT
easat-3999	305	45	500	500	NUM
easat-3999	305	46	)	)	PUNCT
easat-3999	305	47	#	#	NOUN
easat-3999	305	48	distance	distance	NOUN
easat-3999	305	49	in	in	ADP
easat-3999	305	50	au	au	PROPN
easat-3999	305	51	(	(	PUNCT
easat-3999	305	52	astronomical	astronomical	ADJ
easat-3999	305	53	units	unit	NOUN
easat-3999	305	54	)	)	PUNCT
easat-3999	305	55	n_values	n_value	VERB
easat-3999	305	56	=	=	PUNCT
easat-3999	305	57	np.linspace(1	np.linspace(1	X
easat-3999	305	58	,	,	PUNCT
easat-3999	305	59	3	3	NUM
easat-3999	305	60	,	,	PUNCT
easat-3999	305	61	50	50	NUM
easat-3999	305	62	)	)	PUNCT
easat-3999	305	63	#	#	NOUN
easat-3999	305	64	parameter	parameter	NOUN
easat-3999	305	65	n	n	NOUN
easat-3999	305	66	from	from	ADP
easat-3999	305	67	1	1	NUM
easat-3999	305	68	to	to	PART
easat-3999	305	69	3	3	NUM
easat-3999	305	70	#	#	NOUN
easat-3999	305	71	constants	constant	NOUN
easat-3999	305	72	g	g	NOUN
easat-3999	305	73	=	=	SYM
easat-3999	305	74	6.67430e-11	6.67430e-11	NUM
easat-3999	305	75	#	#	NOUN
easat-3999	305	76	gravitational	gravitational	ADJ
easat-3999	305	77	constant	constant	ADJ
easat-3999	305	78	in	in	ADP
easat-3999	305	79	m^3	m^3	PROPN
easat-3999	305	80	kg^-1	kg^-1	PROPN
easat-3999	305	81	s^-2	s^-2	PROPN
easat-3999	305	82	m_sun	m_sun	PROPN
easat-3999	306	1	=	=	SYM
easat-3999	307	1	1.989e30	1.989e30	PROPN
easat-3999	308	1	#	#	NOUN
easat-3999	308	2	mass	mass	NOUN
easat-3999	308	3	of	of	ADP
easat-3999	308	4	the	the	DET
easat-3999	308	5	sun	sun	NOUN
easat-3999	308	6	in	in	ADP
easat-3999	308	7	kg	kg	PROPN
easat-3999	308	8	m_mercury	m_mercury	NOUN
easat-3999	308	9	=	=	SYM
easat-3999	308	10	3.301e23	3.301e23	NUM
easat-3999	308	11	#	#	NOUN
easat-3999	308	12	mass	mass	NOUN
easat-3999	308	13	of	of	ADP
easat-3999	308	14	mercury	mercury	NOUN
easat-3999	308	15	in	in	ADP
easat-3999	308	16	kg	kg	PROPN
easat-3999	308	17	#	#	NOUN
easat-3999	308	18	convert	convert	NOUN
easat-3999	308	19	distance	distance	NOUN
easat-3999	308	20	from	from	ADP
easat-3999	308	21	au	au	ADV
easat-3999	308	22	to	to	ADP
easat-3999	308	23	meters	meter	NOUN
easat-3999	308	24	distance_m	distance_m	NOUN
easat-3999	308	25	=	=	SYM
easat-3999	309	1	distance	distance	NOUN
easat-3999	309	2	*	*	PUNCT
easat-3999	309	3	1.496e11	1.496e11	NUM
easat-3999	309	4	#	#	NOUN
easat-3999	309	5	1	1	NUM
easat-3999	309	6	au	au	ADV
easat-3999	309	7	in	in	ADP
easat-3999	309	8	meters	meter	NOUN
easat-3999	309	9	#	#	NOUN
easat-3999	309	10	create	create	VERB
easat-3999	309	11	a	a	DET
easat-3999	309	12	meshgrid	meshgrid	NOUN
easat-3999	309	13	for	for	ADP
easat-3999	309	14	distance	distance	NOUN
easat-3999	309	15	and	and	CCONJ
easat-3999	309	16	n	n	PRON
easat-3999	309	17	d	d	NOUN
easat-3999	309	18	,	,	PUNCT
easat-3999	309	19	n	n	PROPN
easat-3999	309	20	=	=	SYM
easat-3999	309	21	np.meshgrid(distance_m	np.meshgrid(distance_m	PROPN
easat-3999	309	22	,	,	PUNCT
easat-3999	309	23	n_values	n_value	NOUN
easat-3999	309	24	)	)	PUNCT
easat-3999	309	25	#	#	NOUN
easat-3999	309	26	calculate	calculate	NOUN
easat-3999	309	27	precession	precession	NOUN
easat-3999	309	28	using	use	VERB
easat-3999	309	29	the	the	DET
easat-3999	309	30	modified	modify	VERB
easat-3999	309	31	formula	formula	NOUN
easat-3999	309	32	#	#	NOUN
easat-3999	309	33	precession	precession	NOUN
easat-3999	309	34	per	per	ADP
easat-3999	309	35	orbit	orbit	NOUN
easat-3999	309	36	(	(	PUNCT
easat-3999	309	37	in	in	ADP
easat-3999	309	38	radians	radian	NOUN
easat-3999	309	39	)	)	PUNCT
easat-3999	309	40	=	=	SYM
easat-3999	310	1	(	(	PUNCT
easat-3999	310	2	g^2	g^2	PROPN
easat-3999	310	3	*	*	PUNCT
easat-3999	310	4	m_sun^2	m_sun^2	PROPN
easat-3999	310	5	*	*	PROPN
easat-3999	310	6	m_mercury^2	m_mercury^2	NUM
easat-3999	310	7	)	)	PUNCT
easat-3999	310	8	/	/	PUNCT
easat-3999	310	9	(	(	PUNCT
easat-3999	310	10	distance^2	distance^2	INTJ
easat-3999	310	11	*	*	X
easat-3999	310	12	(	(	PUNCT
easat-3999	310	13	a_1	a_1	X
easat-3999	310	14	*	*	PUNCT
easat-3999	310	15	exp(p	exp(p	PROPN
easat-3999	310	16	/	/	SYM
easat-3999	310	17	t_1	t_1	PROPN
easat-3999	310	18	)	)	PUNCT
easat-3999	310	19	+	+	NUM
easat-3999	310	20	s_d_0)^n	s_d_0)^n	NOUN
easat-3999	310	21	)	)	PUNCT
easat-3999	310	22	#	#	NOUN
easat-3999	310	23	here	here	ADV
easat-3999	310	24	,	,	PUNCT
easat-3999	310	25	a_1	a_1	NOUN
easat-3999	310	26	,	,	PUNCT
easat-3999	310	27	p	p	X
easat-3999	310	28	,	,	PUNCT
easat-3999	310	29	t_1	t_1	PROPN
easat-3999	310	30	,	,	PUNCT
easat-3999	310	31	and	and	CCONJ
easat-3999	310	32	s_d_0	s_d_0	PROPN
easat-3999	310	33	are	be	AUX
easat-3999	310	34	set	set	VERB
easat-3999	310	35	to	to	ADP
easat-3999	310	36	simple	simple	ADJ
easat-3999	310	37	constants	constant	NOUN
easat-3999	310	38	for	for	ADP
easat-3999	310	39	demonstration	demonstration	NOUN
easat-3999	310	40	a_1	a_1	NOUN
easat-3999	310	41	=	=	SYM
easat-3999	310	42	1	1	NUM
easat-3999	310	43	p	p	NOUN
easat-3999	310	44	=	=	X
easat-3999	310	45	0.11	0.11	NUM
easat-3999	310	46	t_1	t_1	PROPN
easat-3999	310	47	=	=	SYM
easat-3999	310	48	1	1	NUM
easat-3999	310	49	s_d_0	s_d_0	NOUN
easat-3999	310	50	=	=	SYM
easat-3999	310	51	1	1	NUM
easat-3999	310	52	precession	precession	NOUN
easat-3999	310	53	=	=	SYM
easat-3999	310	54	(	(	PUNCT
easat-3999	310	55	g**2	g**2	X
easat-3999	310	56	*	*	PUNCT
easat-3999	310	57	m_sun**2	m_sun**2	PUNCT
easat-3999	310	58	*	*	PUNCT
easat-3999	310	59	m_mercury**2	m_mercury**2	NOUN
easat-3999	310	60	)	)	PUNCT
easat-3999	310	61	/	/	PUNCT
easat-3999	310	62	(	(	PUNCT
easat-3999	310	63	d**2	d**2	NOUN
easat-3999	310	64	*	*	PUNCT
easat-3999	310	65	(	(	PUNCT
easat-3999	310	66	a_1	a_1	X
easat-3999	310	67	*	*	PUNCT
easat-3999	310	68	np.exp(-p	np.exp(-p	PROPN
easat-3999	310	69	/	/	SYM
easat-3999	310	70	t_1	t_1	PROPN
easat-3999	310	71	)	)	PUNCT
easat-3999	310	72	+	+	SYM
easat-3999	310	73	s_d_0)**n	s_d_0)**n	NOUN
easat-3999	310	74	)	)	PUNCT
easat-3999	310	75	#	#	NOUN
easat-3999	310	76	convert	convert	NOUN
easat-3999	310	77	precession	precession	NOUN
easat-3999	310	78	from	from	ADP
easat-3999	310	79	radians	radian	NOUN
easat-3999	310	80	to	to	ADP
easat-3999	310	81	arcseconds	arcsecond	NOUN
easat-3999	310	82	precession_arcseconds	precession_arcsecond	NOUN
easat-3999	310	83	=	=	SYM
easat-3999	310	84	precession	precession	NOUN
easat-3999	310	85	*	*	PUNCT
easat-3999	310	86	(	(	PUNCT
easat-3999	310	87	180	180	NUM
easat-3999	310	88	/	/	SYM
easat-3999	310	89	np.pi	np.pi	NOUN
easat-3999	310	90	)	)	PUNCT
easat-3999	310	91	*	*	PUNCT
easat-3999	310	92	3600	3600	NUM
easat-3999	310	93	#	#	NOUN
easat-3999	310	94	create	create	VERB
easat-3999	310	95	a	a	DET
easat-3999	310	96	3d	3d	NUM
easat-3999	310	97	plot	plot	NOUN
easat-3999	310	98	fig	fig	NOUN
easat-3999	310	99	=	=	SYM
easat-3999	310	100	plt.figure(figsize=(12	plt.figure(figsize=(12	NOUN
easat-3999	310	101	,	,	PUNCT
easat-3999	310	102	8)	8)	NUM
easat-3999	310	103	)	)	PUNCT
easat-3999	310	104	ax	ax	NOUN
easat-3999	310	105	=	=	SYM
easat-3999	310	106	fig.add_subplot(111	fig.add_subplot(111	PROPN
easat-3999	310	107	,	,	PUNCT
easat-3999	310	108	projection='3d	projection='3d	PRON
easat-3999	310	109	'	'	PUNCT
easat-3999	310	110	)	)	PUNCT
easat-3999	310	111	9374	9374	NUM
easat-3999	311	1	edelweiss	edelweiss	PROPN
easat-3999	311	2	applied	apply	VERB
easat-3999	311	3	science	science	NOUN
easat-3999	311	4	and	and	CCONJ
easat-3999	311	5	technology	technology	NOUN
easat-3999	311	6	issn	issn	PROPN
easat-3999	311	7	:	:	PUNCT
easat-3999	311	8	2576	2576	NUM
easat-3999	311	9	-	-	SYM
easat-3999	311	10	8484	8484	NUM
easat-3999	311	11	vol	vol	NOUN
easat-3999	311	12	.	.	PROPN
easat-3999	311	13	8	8	NUM
easat-3999	311	14	,	,	PUNCT
easat-3999	311	15	no	no	INTJ
easat-3999	311	16	.	.	NOUN
easat-3999	312	1	6	6	NUM
easat-3999	312	2	:	:	SYM
easat-3999	312	3	9356	9356	NUM
easat-3999	312	4	-	-	SYM
easat-3999	312	5	9375	9375	NUM
easat-3999	312	6	,	,	PUNCT
easat-3999	312	7	2024	2024	NUM
easat-3999	312	8	doi	doi	NOUN
easat-3999	312	9	:	:	PUNCT
easat-3999	312	10	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	312	11	©	©	PROPN
easat-3999	312	12	2024	2024	NUM
easat-3999	312	13	by	by	ADP
easat-3999	312	14	the	the	DET
easat-3999	312	15	author	author	NOUN
easat-3999	312	16	;	;	PUNCT
easat-3999	312	17	licensee	licensee	PROPN
easat-3999	312	18	learning	learn	VERB
easat-3999	312	19	gate	gate	NOUN
easat-3999	312	20	#	#	NOUN
easat-3999	312	21	plot	plot	NOUN
easat-3999	312	22	surface	surface	NOUN
easat-3999	312	23	surf	surf	NOUN
easat-3999	312	24	=	=	SYM
easat-3999	312	25	ax.plot_surface(d	ax.plot_surface(d	PROPN
easat-3999	312	26	,	,	PUNCT
easat-3999	312	27	n	n	CCONJ
easat-3999	312	28	,	,	PUNCT
easat-3999	312	29	precession_arcseconds	precession_arcsecond	NOUN
easat-3999	312	30	,	,	PUNCT
easat-3999	312	31	cmap='plasma	cmap='plasma	NOUN
easat-3999	312	32	'	'	PART
easat-3999	312	33	,	,	PUNCT
easat-3999	312	34	edgecolor='none	edgecolor='none	PROPN
easat-3999	312	35	'	'	PUNCT
easat-3999	312	36	)	)	PUNCT
easat-3999	312	37	#	#	NOUN
easat-3999	312	38	add	add	VERB
easat-3999	312	39	labels	label	NOUN
easat-3999	312	40	and	and	CCONJ
easat-3999	312	41	title	title	NOUN
easat-3999	312	42	ax.set_xlabel('distance	ax.set_xlabel('distance	NOUN
easat-3999	312	43	(	(	PUNCT
easat-3999	312	44	meters	meter	NOUN
easat-3999	312	45	)	)	PUNCT
easat-3999	312	46	'	'	PUNCT
easat-3999	312	47	)	)	PUNCT
easat-3999	313	1	ax.set_ylabel('parameter	ax.set_ylabel('parameter	PROPN
easat-3999	313	2	n	n	CCONJ
easat-3999	313	3	'	'	CCONJ
easat-3999	313	4	)	)	PUNCT
easat-3999	313	5	ax.set_zlabel('precession	ax.set_zlabel('precession	PROPN
easat-3999	313	6	(	(	PUNCT
easat-3999	313	7	arcseconds	arcseconds	PROPN
easat-3999	313	8	)	)	PUNCT
easat-3999	313	9	'	'	PUNCT
easat-3999	313	10	)	)	PUNCT
easat-3999	314	1	ax.set_title("3d	ax.set_title("3d	VERB
easat-3999	314	2	plot	plot	NOUN
easat-3999	314	3	of	of	ADP
easat-3999	314	4	mercury	mercury	NOUN
easat-3999	314	5	's	's	PART
easat-3999	314	6	precession	precession	NOUN
easat-3999	314	7	vs	vs	ADP
easat-3999	314	8	distance	distance	NOUN
easat-3999	314	9	and	and	CCONJ
easat-3999	314	10	parameter	parameter	NOUN
easat-3999	314	11	n	n	CCONJ
easat-3999	314	12	"	"	PUNCT
easat-3999	314	13	)	)	PUNCT
easat-3999	314	14	#	#	NOUN
easat-3999	314	15	add	add	VERB
easat-3999	314	16	a	a	DET
easat-3999	314	17	color	color	NOUN
easat-3999	314	18	bar	bar	NOUN
easat-3999	314	19	which	which	PRON
easat-3999	314	20	maps	map	VERB
easat-3999	314	21	values	value	NOUN
easat-3999	314	22	to	to	ADP
easat-3999	314	23	colors	color	NOUN
easat-3999	314	24	fig.colorbar(surf	fig.colorbar(surf	NOUN
easat-3999	314	25	,	,	PUNCT
easat-3999	314	26	ax	ax	NOUN
easat-3999	314	27	=	=	NOUN
easat-3999	314	28	ax	ax	NOUN
easat-3999	314	29	,	,	PUNCT
easat-3999	314	30	shrink=0.5	shrink=0.5	NOUN
easat-3999	314	31	,	,	PUNCT
easat-3999	314	32	aspect=5	aspect=5	ADJ
easat-3999	314	33	)	)	PUNCT
easat-3999	314	34	plt.show	plt.show	X
easat-3999	314	35	(	(	PUNCT
easat-3999	314	36	)	)	PUNCT
easat-3999	314	37	appendix	appendix	VERB
easat-3999	314	38	c	c	NOUN
easat-3999	314	39	#	#	NOUN
easat-3999	314	40	(	(	PUNCT
easat-3999	314	41	c)(r	c)(r	PROPN
easat-3999	314	42	)	)	PUNCT
easat-3999	314	43	2024	2024	NUM
easat-3999	314	44	constantinos	constantino	NOUN
easat-3999	314	45	challoumis	challoumis	VERB
easat-3999	314	46	import	import	NOUN
easat-3999	314	47	matplotlib.pyplot	matplotlib.pyplot	PROPN
easat-3999	314	48	as	as	ADP
easat-3999	314	49	plt	plt	NOUN
easat-3999	314	50	from	from	ADP
easat-3999	314	51	mpl_toolkits.mplot3d	mpl_toolkits.mplot3d	PROPN
easat-3999	314	52	import	import	NOUN
easat-3999	314	53	axes3d	axes3d	PROPN
easat-3999	314	54	import	import	NOUN
easat-3999	314	55	numpy	numpy	NOUN
easat-3999	314	56	as	as	SCONJ
easat-3999	314	57	np	np	NOUN
easat-3999	314	58	#	#	NOUN
easat-3999	314	59	define	define	VERB
easat-3999	314	60	the	the	DET
easat-3999	314	61	range	range	NOUN
easat-3999	314	62	for	for	ADP
easat-3999	314	63	distance	distance	NOUN
easat-3999	314	64	and	and	CCONJ
easat-3999	314	65	parameter	parameter	NOUN
easat-3999	314	66	n	n	PRON
easat-3999	314	67	distance	distance	NOUN
easat-3999	314	68	=	=	SYM
easat-3999	314	69	np.linspace(1	np.linspace(1	X
easat-3999	314	70	,	,	PUNCT
easat-3999	314	71	100	100	NUM
easat-3999	314	72	,	,	PUNCT
easat-3999	314	73	500	500	NUM
easat-3999	314	74	)	)	PUNCT
easat-3999	314	75	#	#	NOUN
easat-3999	314	76	distance	distance	NOUN
easat-3999	314	77	in	in	ADP
easat-3999	314	78	mpc	mpc	NOUN
easat-3999	314	79	n_values	n_value	NOUN
easat-3999	314	80	=	=	SYM
easat-3999	314	81	np.linspace(1	np.linspace(1	X
easat-3999	314	82	,	,	PUNCT
easat-3999	314	83	3	3	NUM
easat-3999	314	84	,	,	PUNCT
easat-3999	314	85	50	50	NUM
easat-3999	314	86	)	)	PUNCT
easat-3999	314	87	#	#	NOUN
easat-3999	314	88	parameter	parameter	NOUN
easat-3999	314	89	n	n	NOUN
easat-3999	314	90	from	from	SCONJ
easat-3999	314	91	1	1	NUM
easat-3999	314	92	to	to	PART
easat-3999	314	93	3	3	NUM
easat-3999	314	94	#	#	NOUN
easat-3999	314	95	create	create	VERB
easat-3999	314	96	a	a	DET
easat-3999	314	97	meshgrid	meshgrid	NOUN
easat-3999	314	98	for	for	ADP
easat-3999	314	99	distance	distance	NOUN
easat-3999	314	100	and	and	CCONJ
easat-3999	314	101	n	n	PRON
easat-3999	314	102	d	d	NOUN
easat-3999	314	103	,	,	PUNCT
easat-3999	314	104	n	n	PROPN
easat-3999	314	105	=	=	SYM
easat-3999	314	106	np.meshgrid(distance	np.meshgrid(distance	PROPN
easat-3999	314	107	,	,	PUNCT
easat-3999	314	108	n_values	n_value	NOUN
easat-3999	314	109	)	)	PUNCT
easat-3999	314	110	#	#	NOUN
easat-3999	314	111	calculate	calculate	NOUN
easat-3999	314	112	velocity	velocity	NOUN
easat-3999	314	113	using	use	VERB
easat-3999	314	114	hubble	hubble	NOUN
easat-3999	314	115	's	's	PART
easat-3999	314	116	law	law	NOUN
easat-3999	314	117	with	with	ADP
easat-3999	314	118	modified	modified	ADJ
easat-3999	314	119	parameter	parameter	NOUN
easat-3999	314	120	n	n	PRON
easat-3999	314	121	h0	h0	NOUN
easat-3999	314	122	=	=	SYM
easat-3999	314	123	70	70	NUM
easat-3999	314	124	#	#	NOUN
easat-3999	314	125	hubble	hubble	NOUN
easat-3999	314	126	's	's	PART
easat-3999	314	127	constant	constant	ADJ
easat-3999	314	128	in	in	ADP
easat-3999	314	129	km	km	PROPN
easat-3999	314	130	/	/	SYM
easat-3999	314	131	s	s	PROPN
easat-3999	314	132	/	/	SYM
easat-3999	314	133	mpc	mpc	NOUN
easat-3999	314	134	velocity	velocity	NOUN
easat-3999	314	135	=	=	SYM
easat-3999	314	136	h0	h0	NOUN
easat-3999	314	137	*	*	PROPN
easat-3999	315	1	d	d	PUNCT
easat-3999	315	2	*	*	PUNCT
easat-3999	315	3	*	*	PUNCT
easat-3999	315	4	(	(	PUNCT
easat-3999	315	5	2	2	NUM
easat-3999	315	6	n	n	CCONJ
easat-3999	315	7	)	)	PUNCT
easat-3999	315	8	#	#	NOUN
easat-3999	315	9	using	use	VERB
easat-3999	315	10	a	a	DET
easat-3999	315	11	modified	modify	VERB
easat-3999	315	12	form	form	NOUN
easat-3999	315	13	to	to	PART
easat-3999	315	14	incorporate	incorporate	VERB
easat-3999	315	15	n	n	DET
easat-3999	315	16	#	#	NOUN
easat-3999	315	17	create	create	VERB
easat-3999	315	18	a	a	DET
easat-3999	315	19	3d	3d	NUM
easat-3999	315	20	plot	plot	NOUN
easat-3999	315	21	fig	fig	NOUN
easat-3999	315	22	=	=	SYM
easat-3999	315	23	plt.figure(figsize=(12	plt.figure(figsize=(12	NOUN
easat-3999	315	24	,	,	PUNCT
easat-3999	315	25	8)	8)	NUM
easat-3999	315	26	)	)	PUNCT
easat-3999	315	27	ax	ax	NOUN
easat-3999	315	28	=	=	SYM
easat-3999	315	29	fig.add_subplot(111	fig.add_subplot(111	PROPN
easat-3999	315	30	,	,	PUNCT
easat-3999	315	31	projection='3d	projection='3d	PRON
easat-3999	315	32	'	'	PUNCT
easat-3999	315	33	)	)	PUNCT
easat-3999	315	34	#	#	NOUN
easat-3999	315	35	plot	plot	NOUN
easat-3999	315	36	surface	surface	NOUN
easat-3999	315	37	surf	surf	NOUN
easat-3999	315	38	=	=	SYM
easat-3999	315	39	ax.plot_surface(d	ax.plot_surface(d	PROPN
easat-3999	315	40	,	,	PUNCT
easat-3999	315	41	n	n	CCONJ
easat-3999	315	42	,	,	PUNCT
easat-3999	315	43	velocity	velocity	NOUN
easat-3999	315	44	,	,	PUNCT
easat-3999	315	45	cmap='viridis	cmap='viridis	PROPN
easat-3999	315	46	'	'	PUNCT
easat-3999	315	47	,	,	PUNCT
easat-3999	315	48	edgecolor='none	edgecolor='none	PROPN
easat-3999	315	49	'	'	PUNCT
easat-3999	315	50	)	)	PUNCT
easat-3999	315	51	#	#	NOUN
easat-3999	315	52	add	add	VERB
easat-3999	315	53	labels	label	NOUN
easat-3999	315	54	and	and	CCONJ
easat-3999	315	55	title	title	NOUN
easat-3999	315	56	ax.set_xlabel('distance	ax.set_xlabel('distance	NOUN
easat-3999	315	57	(	(	PUNCT
easat-3999	315	58	mpc	mpc	NOUN
easat-3999	315	59	)	)	PUNCT
easat-3999	315	60	'	'	NUM
easat-3999	315	61	)	)	PUNCT
easat-3999	316	1	ax.set_ylabel('parameter	ax.set_ylabel('parameter	PROPN
easat-3999	316	2	n	n	CCONJ
easat-3999	316	3	'	'	CCONJ
easat-3999	316	4	)	)	PUNCT
easat-3999	317	1	ax.set_zlabel('velocity	ax.set_zlabel('velocity	NOUN
easat-3999	317	2	(	(	PUNCT
easat-3999	317	3	km	km	PROPN
easat-3999	317	4	/	/	SYM
easat-3999	317	5	s	s	NOUN
easat-3999	317	6	)	)	PUNCT
easat-3999	317	7	'	'	NUM
easat-3999	317	8	)	)	PUNCT
easat-3999	318	1	ax.set_title('3d	ax.set_title('3d	NOUN
easat-3999	318	2	plot	plot	NOUN
easat-3999	318	3	of	of	ADP
easat-3999	318	4	velocity	velocity	NOUN
easat-3999	318	5	vs	vs	ADP
easat-3999	318	6	distance	distance	NOUN
easat-3999	318	7	and	and	CCONJ
easat-3999	318	8	parameter	parameter	NOUN
easat-3999	318	9	n	n	CCONJ
easat-3999	318	10	'	'	CCONJ
easat-3999	318	11	)	)	PUNCT
easat-3999	318	12	#	#	NOUN
easat-3999	318	13	add	add	VERB
easat-3999	318	14	a	a	DET
easat-3999	318	15	color	color	NOUN
easat-3999	318	16	bar	bar	NOUN
easat-3999	318	17	which	which	PRON
easat-3999	318	18	maps	map	VERB
easat-3999	318	19	values	value	NOUN
easat-3999	318	20	to	to	ADP
easat-3999	318	21	colors	color	NOUN
easat-3999	318	22	fig.colorbar(surf	fig.colorbar(surf	NOUN
easat-3999	318	23	,	,	PUNCT
easat-3999	318	24	ax	ax	NOUN
easat-3999	318	25	=	=	NOUN
easat-3999	318	26	ax	ax	NOUN
easat-3999	318	27	,	,	PUNCT
easat-3999	318	28	shrink=0.5	shrink=0.5	NOUN
easat-3999	318	29	,	,	PUNCT
easat-3999	318	30	aspect=5	aspect=5	ADJ
easat-3999	318	31	)	)	PUNCT
easat-3999	318	32	plt.show	plt.show	X
easat-3999	318	33	(	(	PUNCT
easat-3999	318	34	)	)	PUNCT
easat-3999	318	35	appendix	appendix	VERB
easat-3999	318	36	d	d	NOUN
easat-3999	318	37	#	#	NOUN
easat-3999	318	38	(	(	PUNCT
easat-3999	318	39	c)(r	c)(r	PROPN
easat-3999	318	40	)	)	PUNCT
easat-3999	318	41	2024	2024	NUM
easat-3999	318	42	constantinos	constantino	NOUN
easat-3999	318	43	challoumis	challoumis	VERB
easat-3999	318	44	#	#	NOUN
easat-3999	318	45	coordinates	coordinate	NOUN
easat-3999	318	46	for	for	ADP
easat-3999	318	47	the	the	DET
easat-3999	318	48	sun	sun	NOUN
easat-3999	318	49	and	and	CCONJ
easat-3999	318	50	the	the	DET
easat-3999	318	51	disk	disk	NOUN
easat-3999	318	52	-	-	PUNCT
easat-3999	318	53	like	like	ADJ
easat-3999	318	54	gravitational	gravitational	ADJ
easat-3999	318	55	field	field	NOUN
easat-3999	318	56	without	without	ADP
easat-3999	318	57	swapping	swap	VERB
easat-3999	318	58	9375	9375	NUM
easat-3999	318	59	edelweiss	edelweiss	PROPN
easat-3999	318	60	applied	apply	VERB
easat-3999	318	61	science	science	NOUN
easat-3999	318	62	and	and	CCONJ
easat-3999	318	63	technology	technology	NOUN
easat-3999	318	64	issn	issn	PROPN
easat-3999	318	65	:	:	PUNCT
easat-3999	318	66	2576	2576	NUM
easat-3999	318	67	-	-	SYM
easat-3999	318	68	8484	8484	NUM
easat-3999	318	69	vol	vol	NOUN
easat-3999	318	70	.	.	PROPN
easat-3999	318	71	8	8	NUM
easat-3999	318	72	,	,	PUNCT
easat-3999	318	73	no	no	INTJ
easat-3999	318	74	.	.	NOUN
easat-3999	319	1	6	6	NUM
easat-3999	319	2	:	:	SYM
easat-3999	319	3	9356	9356	NUM
easat-3999	319	4	-	-	SYM
easat-3999	319	5	9375	9375	NUM
easat-3999	319	6	,	,	PUNCT
easat-3999	319	7	2024	2024	NUM
easat-3999	319	8	doi	doi	NOUN
easat-3999	319	9	:	:	PUNCT
easat-3999	319	10	10.55214/25768484.v8i6.3999	10.55214/25768484.v8i6.3999	NUM
easat-3999	319	11	©	©	PROPN
easat-3999	319	12	2024	2024	NUM
easat-3999	319	13	by	by	ADP
easat-3999	319	14	the	the	DET
easat-3999	319	15	author	author	NOUN
easat-3999	319	16	;	;	PUNCT
easat-3999	320	1	licensee	licensee	PROPN
easat-3999	320	2	learning	learn	VERB
easat-3999	320	3	gate	gate	NOUN
easat-3999	320	4	x_sun_horizontal	x_sun_horizontal	PROPN
easat-3999	321	1	=	=	PUNCT
easat-3999	321	2	r_sun	r_sun	PROPN
easat-3999	321	3	*	*	PUNCT
easat-3999	321	4	np.cos(theta	np.cos(theta	PROPN
easat-3999	321	5	)	)	PUNCT
easat-3999	321	6	y_sun_horizontal	y_sun_horizontal	NOUN
easat-3999	322	1	=	=	PUNCT
easat-3999	322	2	r_sun	r_sun	PROPN
easat-3999	322	3	*	*	PUNCT
easat-3999	322	4	np.sin(theta	np.sin(theta	PROPN
easat-3999	322	5	)	)	PUNCT
easat-3999	322	6	x_disk_outer_horizontal	x_disk_outer_horizontal	PROPN
easat-3999	322	7	=	=	SYM
easat-3999	322	8	r_disk_outer	r_disk_outer	NOUN
easat-3999	322	9	*	*	PUNCT
easat-3999	322	10	np.cos(theta	np.cos(theta	PROPN
easat-3999	322	11	)	)	PUNCT
easat-3999	322	12	y_disk_outer_horizontal	y_disk_outer_horizontal	NOUN
easat-3999	322	13	=	=	SYM
easat-3999	322	14	r_disk_outer	r_disk_outer	PROPN
easat-3999	322	15	*	*	PUNCT
easat-3999	322	16	np.sin(theta	np.sin(theta	PROPN
easat-3999	322	17	)	)	PUNCT
easat-3999	322	18	x_disk_inner_horizontal	x_disk_inner_horizontal	NOUN
easat-3999	322	19	=	=	NOUN
easat-3999	322	20	r_disk_inner	r_disk_inner	NOUN
easat-3999	322	21	*	*	PUNCT
easat-3999	322	22	np.cos(theta	np.cos(theta	PROPN
easat-3999	322	23	)	)	PUNCT
easat-3999	322	24	y_disk_inner_horizontal	y_disk_inner_horizontal	NOUN
easat-3999	322	25	=	=	NOUN
easat-3999	322	26	r_disk_inner	r_disk_inner	NOUN
easat-3999	322	27	*	*	PUNCT
easat-3999	322	28	np.sin(theta	np.sin(theta	PROPN
easat-3999	322	29	)	)	PUNCT
easat-3999	322	30	#	#	NOUN
easat-3999	322	31	create	create	VERB
easat-3999	322	32	the	the	DET
easat-3999	322	33	adjusted	adjust	VERB
easat-3999	322	34	plot	plot	NOUN
easat-3999	322	35	plt.figure(figsize=(8	plt.figure(figsize=(8	NOUN
easat-3999	322	36	,	,	PUNCT
easat-3999	322	37	8)	8)	NUM
easat-3999	322	38	)	)	PUNCT
easat-3999	322	39	#	#	NOUN
easat-3999	322	40	disk	disk	NOUN
easat-3999	322	41	boundary	boundary	NOUN
easat-3999	322	42	(	(	PUNCT
easat-3999	322	43	shaded	shaded	ADJ
easat-3999	322	44	area	area	NOUN
easat-3999	322	45	for	for	ADP
easat-3999	322	46	visualization	visualization	NOUN
easat-3999	322	47	)	)	PUNCT
easat-3999	322	48	plt.fill_between(x_disk_outer_horizontal	plt.fill_between(x_disk_outer_horizontal	PROPN
easat-3999	322	49	,	,	PUNCT
easat-3999	322	50	y_disk_inner_horizontal	y_disk_inner_horizontal	NOUN
easat-3999	322	51	,	,	PUNCT
easat-3999	322	52	y_disk_outer_horizontal	y_disk_outer_horizontal	PROPN
easat-3999	322	53	,	,	PUNCT
easat-3999	322	54	color='lightblue	color='lightblue	NOUN
easat-3999	322	55	'	'	PUNCT
easat-3999	322	56	,	,	PUNCT
easat-3999	322	57	alpha=0.4	alpha=0.4	NOUN
easat-3999	322	58	,	,	PUNCT
easat-3999	322	59	label="gravitational	label="gravitational	ADJ
easat-3999	322	60	disk	disk	NOUN
easat-3999	322	61	"	"	PUNCT
easat-3999	322	62	)	)	PUNCT
easat-3999	322	63	#	#	NOUN
easat-3999	322	64	sun	sun	NOUN
easat-3999	322	65	's	's	PART
easat-3999	322	66	bulge	bulge	PROPN
easat-3999	322	67	representation	representation	NOUN
easat-3999	322	68	plt.plot(x_sun_horizontal	plt.plot(x_sun_horizontal	NOUN
easat-3999	322	69	,	,	PUNCT
easat-3999	322	70	y_sun_horizontal	y_sun_horizontal	NUM
easat-3999	322	71	,	,	PUNCT
easat-3999	322	72	color='orange	color='orange	NOUN
easat-3999	322	73	'	'	PUNCT
easat-3999	322	74	,	,	PUNCT
easat-3999	322	75	linewidth=2	linewidth=2	PROPN
easat-3999	322	76	,	,	PUNCT
easat-3999	322	77	label="sun	label="sun	PROPN
easat-3999	322	78	's	's	PART
easat-3999	322	79	bulge	bulge	NOUN
easat-3999	322	80	"	"	PUNCT
easat-3999	322	81	)	)	PUNCT
easat-3999	322	82	#	#	NOUN
easat-3999	322	83	add	add	VERB
easat-3999	322	84	grid	grid	NOUN
easat-3999	322	85	,	,	PUNCT
easat-3999	322	86	labels	label	NOUN
easat-3999	322	87	,	,	PUNCT
easat-3999	322	88	and	and	CCONJ
easat-3999	322	89	legend	legend	VERB
easat-3999	322	90	plt.gca().set_aspect('equal	plt.gca().set_aspect('equal	PROPN
easat-3999	322	91	'	'	PART
easat-3999	322	92	,	,	PUNCT
easat-3999	322	93	adjustable='datalim	adjustable='datalim	NOUN
easat-3999	322	94	'	'	PUNCT
easat-3999	322	95	)	)	PUNCT
easat-3999	322	96	plt.title("disk	plt.title("disk	NOUN
easat-3999	322	97	-	-	PUNCT
easat-3999	322	98	oriented	orient	VERB
easat-3999	322	99	gravity	gravity	NOUN
easat-3999	322	100	diagram	diagram	NOUN
easat-3999	322	101	(	(	PUNCT
easat-3999	322	102	horizontal	horizontal	ADJ
easat-3999	322	103	axis	axis	NOUN
easat-3999	322	104	)	)	PUNCT
easat-3999	322	105	"	"	PUNCT
easat-3999	322	106	,	,	PUNCT
easat-3999	322	107	fontsize=14	fontsize=14	NOUN
easat-3999	322	108	)	)	PUNCT
easat-3999	323	1	plt.xlabel("x	plt.xlabel("x	NUM
easat-3999	323	2	(	(	PUNCT
easat-3999	323	3	meters	meter	NOUN
easat-3999	323	4	)	)	PUNCT
easat-3999	323	5	"	"	PUNCT
easat-3999	323	6	,	,	PUNCT
easat-3999	323	7	fontsize=12	fontsize=12	PROPN
easat-3999	323	8	)	)	PUNCT
easat-3999	323	9	plt.ylabel("y	plt.ylabel("y	NUM
easat-3999	323	10	(	(	PUNCT
easat-3999	323	11	meters	meter	NOUN
easat-3999	323	12	)	)	PUNCT
easat-3999	323	13	"	"	PUNCT
easat-3999	323	14	,	,	PUNCT
easat-3999	323	15	fontsize=12	fontsize=12	NOUN
easat-3999	323	16	)	)	PUNCT
easat-3999	323	17	plt.legend(fontsize=12	plt.legend(fontsize=12	NUM
easat-3999	323	18	)	)	PUNCT
easat-3999	323	19	plt.grid(true	plt.grid(true	NOUN
easat-3999	323	20	,	,	PUNCT
easat-3999	323	21	linestyle='--	linestyle='--	PROPN
easat-3999	323	22	'	'	PART
easat-3999	323	23	,	,	PUNCT
easat-3999	323	24	linewidth=0.5	linewidth=0.5	NOUN
easat-3999	323	25	)	)	PUNCT
easat-3999	323	26	#	#	NOUN
easat-3999	323	27	save	save	NOUN
easat-3999	323	28	and	and	CCONJ
easat-3999	323	29	display	display	VERB
easat-3999	323	30	the	the	DET
easat-3999	323	31	adjusted	adjust	VERB
easat-3999	323	32	plot	plot	NOUN
easat-3999	323	33	file_path_horizontal_disk_aligned	file_path_horizontal_disk_aligne	VERB
easat-3999	323	34	=	=	PUNCT
easat-3999	323	35	"	"	PUNCT
easat-3999	323	36	/mnt	/mnt	SYM
easat-3999	323	37	/	/	SYM
easat-3999	323	38	data	data	PROPN
easat-3999	323	39	/	/	SYM
easat-3999	323	40	sun_disk_aligned_horizontal.png	sun_disk_aligned_horizontal.png	NOUN
easat-3999	323	41	"	"	PUNCT
easat-3999	323	42	plt.savefig(file_path_horizontal_disk_aligned	plt.savefig(file_path_horizontal_disk_aligne	VERB
easat-3999	323	43	)	)	PUNCT
easat-3999	323	44	plt.show	plt.show	PRON
easat-3999	323	45	(	(	PUNCT
easat-3999	323	46	)	)	PUNCT
easat-3999	323	47	file_path_horizontal_disk_aligned	file_path_horizontal_disk_aligne	VERB