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Invariant manifolds near $L_{1}$ and $L_{2}$ in the Quasi-bicircular Problem

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The 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 $L_1$ and $L_2$ 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 $L_1$ (resp. $L_2$) 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 $L_2$ 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 $L_2$ region.

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Celestial Mechanics and Dynamical Astronomy, 2023, vol. 135

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cc by (c) José J. Rosales de Cáceres et al., 2023

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Invariant manifolds near $L_{1}$ and $L_{2}$ in the Quasi-bicircular Problem