The Restricted 2+2 Body Problem: Parametric Variation of the Equilibrium States of the Minor Bodies and Their Attracting Regions

Table 1

Sun-Jupiter-binary asteroids (case A).

(a) Collinear equilibrium solutions (𝑆_1,𝐿𝑖^𝑗𝑘,𝑆_2,𝐿𝑖^𝑗𝑘),𝑖=1,2,3𝑗,𝑘=1,2𝑗≠𝑘.

	𝑥1,𝐿𝑖^𝑗𝑘	𝑦1,𝐿𝑖^𝑗𝑘	𝑥2,𝐿𝑖^𝑗𝑘	𝑦2,𝐿𝑖^𝑗𝑘	Jacobian constant 𝐶 (10^−15)	Stability
(𝑆1,𝐿1^12,𝑆2,𝐿1^12)	−1.0688315127	0	−1.0688265629	0	3.037482	U
(𝑆1𝐿1^21,𝑆2,𝐿1^21)	−1.0688295327	0	−1.0688344827	0	3.037482	U
(𝑆1,𝐿2^12,𝑆2,𝐿2^12)	−0.9323665174	0	−0.9323618589	0	3.038764	U
(𝑆1,𝐿2^21,𝑆2,𝐿2^21)	−0.9323646541	0	−0.9323693124	0	3.038764	U
(𝑆1,𝐿3^12,𝑆2,𝐿3^12)	1.0003960615	0	1.0004029939	0	3.000966	U
(𝑆1,𝐿3^21,𝑆2,𝐿3^21)	1.0003988345	0	1.0003919022	0	3.000966	U

(b) Inline (𝑆_1,IN𝐿𝑖^𝑗𝑘, 𝑆_2,IN𝐿𝑖^𝑗𝑘) and perpendicular (𝑆_{1,PER𝐿𝑖}^𝑗𝑘, 𝑆_{2,PER𝐿𝑖}^𝑗𝑘) equilibrium solutions, 𝑖=4,5,𝑗,𝑘=1,2𝑗≠𝑘

	𝑥1,IN𝐿𝑖^𝑗𝑘	𝑦1,IN𝐿𝑖^𝑗𝑘	𝑥2,IN𝐿𝑖^𝑗𝑘	𝑦2,IN𝐿𝑖^𝑗𝑘	Jacobian constant 𝐶 (10^−15)	Stability
(𝑆1,IN𝐿4^12,𝑆2,IN𝐿4^12)	−0.4990468176	0.8660266052	−0.4990433524	0.8660205977	2.999844	U
(𝑆1,IN𝐿4^21,𝑆2,IN𝐿4^21)	−0.4990454315	0.8660242022	−0.4990488967	0.8660302098	2.999844	U
(𝑆1,IN𝐿5^12,𝑆2,IN𝐿5^12)	−0.4990468176	−0.8660266052	−0.4990433524	−0.8660205977	2.999844	U
(𝑆1,IN𝐿5^21,𝑆2,IN𝐿5^21)	−0.4990454315	−0.8660242022	−0.4990488967	−0.8660302098	2.999844	U
	𝑥1,PER𝐿𝑖^𝑗𝑘	𝑦1,PER𝐿𝑖^𝑗𝑘	𝑥2,PER𝐿𝑖^𝑗𝑘	𝑦2,PER𝐿𝑖^𝑗𝑘	Jacobian constant 𝐶 (10^−15)	Stability
(𝑆1,PER𝐿4^12,𝑆2,PER𝐿4^12)	−0.4990595557	0.8660176565	−0.4989923934	0.8660563936	2.999844	S
(𝑆1,PER𝐿4^21,𝑆2,PER𝐿4^21)	−0.4990326917	0.8660331517	−0.4990998494	0.8659944131	2.999844	S
(𝑆1,PER𝐿5^12,𝑆2,PER𝐿5^12)	−0.4990595557	−0.8660176565	−0.4989923934	−0.8660563936	2.999844	S
(𝑆1,PER𝐿5^21,𝑆2,PER𝐿5^21)	−0.4990326917	−0.8660331517	−0.4990998494	−0.8659944131	2.999844	S