Stability and velocity sensitivities of libration points in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary

Singh, Jagadish; Tyokyaa, Richard K.

doi:10.1016/j.newast.2022.101917

Cited by 8 publications

(1 citation statement)

References 28 publications

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“…There is only one value of µ , say µ c in 0, 1 2 for which vanishes. The triangular points are stable for 0 < µ < µ c and unstable for µ c < µ ≤ 1 2 by 33 . Now, we are interested in the discriminant being zero at the critical point.…”

Section: Com/scientificreports/mentioning

confidence: 93%

Albedo effects in the ER3BP with an oblate primary, a triaxial secondary and a potential due to belt

Singh

Richard²

2023

Sci Rep

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We have examined the effects of Albedo in the Elliptic Restricted Three-Body Problem (ER3BP) with an oblate primary, a triaxial secondary, and potential due to belt for the Earth–Moon system. We have found that as the perturbed parameters increases, the possible boundary regions of the primary come closer to one other, allowing particles to travel from one region to the next freely and possibly merge the permissible regions. Our study has revealed that the formation of triangular libration points depends on the Albedo effects, semi-major axis, the Eccentricity of the orbits, triaxiality, and the potential due to the belt. As the parameters mentioned above increase, the triangular positions $${L}_{4}$$ L 4 and $${L}_{5}$$ L 5 move towards the center of origin in cases 1, 2, 3, and 4 and away from the center of the origin in cases 5, 6, and 7. Considering the range of a stable and unstable libration point for the problem under study given as $$0<\mu <{\mu }_{c}$$ 0 < μ < μ c for stable libration points and $${\mu }_{c}\leq\mu \le \frac{1}{2}$$ μ c ≤ μ ≤ 1 2 for unstable libration points, our study has established that the triangular libration points are respectively stable and unstable for cases 1, 2, and 6 and cases 3, 4, 5, and 7. Our study has also revealed that each set of values has at least one characteristic complex root with a positive real part. Hence, the triangular libration points for the Earth–Moon system are unstable in the sense of Lyapunov. The Earth–Moon system's Poincare Surface of Section (PSS) has demonstrated that a slight change in the initial conditions, the semi-major axis, and the Eccentricity of the orbits have affected the system's behavior dramatically. Further, it is seen that a chaotic dynamical behavior of the system results into either regular or irregular orbits.

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Section: Com/scientificreports/mentioning

confidence: 93%