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

Table 2

Earth-Moon-dual satellite system (case B).

(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^−20)	Stability
(𝑆1,𝐿1^12,𝑆2,𝐿1^12)	−1.1556481286	0	−1.1556481033	0	3.772852	U
(𝑆1𝐿1^21,𝑆2,𝐿1^21)	−1.1556481114	0	−1.1556481366	0	3.772852	U
(𝑆1,𝐿2^12,𝑆2,𝐿2^12)	−0.8369586858	0	−0.8369586639	0	3.792084	U
(𝑆1,𝐿2^21,𝑆2,𝐿2^21)	−0.8369586709	0	−0.8369586928	0	3.792084	U
(𝑆1,𝐿3^12,𝑆2,𝐿3^12)	1.0050589472	0	1.0050589812	0	3.582608	U
(𝑆1,𝐿3^21,𝑆2,𝐿3^21)	1.0050589703	0	1.0050589363	0	3.582608	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^−20)	Stability
(𝑆1,IN𝐿4^12,𝑆2,IN𝐿4^12)	−0.4878582696	0.8660254139	−0.4878582526	0.8660253842	3.553904	U
(𝑆1,IN𝐿4^21,𝑆2,IN𝐿4^21)	−0.4878582580	0.8660253937	−0.4878582749	0.8660254234	3.553904	U
(𝑆1,IN𝐿5^12,𝑆2,IN𝐿5^12)	−0.4878582696	−0.8660254139	−0.4878582526	−0.8660253842	3.553904	U
(𝑆1,IN𝐿5^21,𝑆2,IN𝐿5^21)	−0.4878582580	−0.8660253937	−0.4878582749	−0.8660254234	3.553904	U
	𝑥1,PER𝐿𝑖^𝑗𝑘	𝑦1,PER𝐿𝑖^𝑗𝑘	𝑥2,PER𝐿𝑖^𝑗𝑘	𝑦2,PER𝐿𝑖^𝑗𝑘	Jacobian constant 𝐶 (10^−20)	Stability
(𝑆1,PER𝐿4^12,𝑆2,PER𝐿4^12)	−0.4878583121	0.8660253762	−0.4878581701	0.8660254572	3.553904	S
(𝑆1,PER𝐿4^21,𝑆2,PER𝐿4^21)	−0.4878582155	0.8660254313	−0.4878583575	0.8660253504	3.553904	S
(𝑆1,PER𝐿5^12,𝑆2,PER𝐿5^12)	−0.4878583121	−0.8660253762	−0.4878581701	−0.8660254572	3.553904	S
(𝑆1,PER𝐿5^21,𝑆2,PER𝐿5^21)	−0.4878582155	−0.8660254313	−0.4878583575	−0.8660253504	3.553904	S