Invariant manifolds near $$L_1$$ and $$L_2$$ in the quasi-bicircular problem
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Published:2023-03-11
Issue:2
Volume:135
Page:
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ISSN:0923-2958
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Container-title:Celestial Mechanics and Dynamical Astronomy
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language:en
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Short-container-title:Celest Mech Dyn Astron
Author:
Rosales José J.ORCID,
Jorba Àngel,
Jorba-Cuscó Marc
Abstract
AbstractThe quasi-bicircular problem (QBCP) is a periodic time-dependent perturbation of the Earth–Moon restricted three-body problem (RTBP) that accounts for the effect of the Sun. It is based on using a periodic solution of the Earth–Moon–Sun three-body problem to write the equations of motion of the infinitesimal particle. The paper focuses on the dynamics near the $$L_1$$
L
1
and $$L_2$$
L
2
points of the Earth–Moon system in the QBCP. By means of a periodic time-dependent reduction to the center manifold, we show the existence of two families of quasi-periodic Lyapunov orbits around $$L_1$$
L
1
(resp. $$L_2$$
L
2
) with two basic frequencies. The first of these two families is contained in the Earth–Moon plane and undergoes an out-of-plane (quasi-periodic) pitchfork bifurcation giving rise to a family of quasi-periodic Halo orbits. This analysis is complemented with the continuation of families of 2D tori. In particular, the planar and vertical Lyapunov families are continued, and their stability analyzed. Finally, examples of invariant manifolds associated with invariant 2D tori around the $$L_2$$
L
2
that pass close to the Earth are shown. This phenomenon is not observed in the RTBP and opens the room to direct transfers from the Earth to the Earth–Moon $$L_2$$
L
2
region.
Funder
H2020 Marie Skłodowska-Curie Actions
Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R &D
Publisher
Springer Science and Business Media LLC
Subject
Space and Planetary Science,Astronomy and Astrophysics,Applied Mathematics,Computational Mathematics,Mathematical Physics,Modeling and Simulation
Reference28 articles.
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