Orientation of a Satellite Located at the Libration Point in the Restricted Three-Body Problem

In this paper the initial results of an investigation of the motion of a rigid body located at the libration point in the planar, restricted three-body problem are given. This problem was analyzed in part by Kane and Marsh (1971), Markeev (1967a,b). However the present investigation is formulated in terms of hamiltonian mechanics. The final results will by used to study nonlinear effects connected with the gravitational influence of the “second” central body.

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GEOMETRY OF HOMOCLINIC CONNECTIONS IN A PLANAR CIRCULAR RESTRICTED THREE-BODY PROBLEM

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127407017744 ◽

2007 ◽

Vol 17 (04) ◽

pp. 1151-1169 ◽

Cited By ~ 16

Author(s):

MARIAN GIDEA ◽

JOSEP J. MASDEMONT

Keyword(s):

Symbolic Dynamics ◽

Body Problem ◽

Invariant Manifolds ◽

Libration Point ◽

Homoclinic Orbits ◽

Restricted Three Body Problem ◽

Three Body Problem ◽

Lyapunov Orbits ◽

Homoclinic Connections ◽

Three Body

The stable and unstable invariant manifolds associated with Lyapunov orbits about the libration point L1between the primaries in the planar circular restricted three-body problem with equal masses are considered. The behavior of the intersections of these invariant manifolds for values of the energy between that of L1and the other collinear libration points L2, L3is studied using symbolic dynamics. Homoclinic orbits are classified according to the number of turns about the primaries.

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A Framework for Constructing Transfers Linking Periodic Libration Point Orbits in the Spatial Circular Restricted Three-Body Problem

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127416300135 ◽

2016 ◽

Vol 26 (05) ◽

pp. 1630013 ◽

Cited By ~ 8

Author(s):

Amanda F. Haapala ◽

Kathleen C. Howell

Keyword(s):

Body Problem ◽

Libration Point ◽

Mass Parameter ◽

Solar Radiation Pressure ◽

Restricted Three Body Problem ◽

Three Body Problem ◽

Libration Point Orbits ◽

The Earth ◽

Three Body ◽

Fidelity Model

The Earth–Moon libration points are of interest for future missions and have been proposed for both storage of propellant and supplies for lunar missions and as locations to establish space-based facilities for human missions. Thus, further development of an available transport network in the vicinity of the Moon is valuable. In this investigation, a methodology to search for transfers between periodic lunar libration point orbits is developed, and a catalog of these transfers is established, assuming the dynamics associated with the Earth–Moon circular restricted three-body problem. Maneuver-free transfers, i.e. heteroclinic and homoclinic connections, are considered, as well as transfers that require relatively small levels of [Formula: see text]. Considering the evolution of Earth–Moon transfers as the mass parameter is reduced, a relationship emerges between the available transfers in the Earth–Moon system and maneuver-free transfers that exist within the Hill three-body problem. The correlation between transfers in these systems is examined and offers insight into the existence of solutions within the catalog. To demonstrate the persistence of the catalog transfers in a higher-fidelity model, several solutions are transitioned to a Sun–Earth–Moon ephemeris model with the inclusion of solar radiation pressure and lunar gravity harmonics. The defining characteristics are preserved in the high-fidelity model, validating both the techniques employed for this investigation and the solutions computed within the catalog.

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Transfers from the Earth to $$L_2$$ Halo orbits in the Earth–Moon bicircular problem

Celestial Mechanics and Dynamical Astronomy ◽

10.1007/s10569-021-10054-4 ◽

2021 ◽

Vol 133 (11-12) ◽

Author(s):

José J. Rosales ◽

Àngel Jorba ◽

Marc Jorba-Cuscó

Keyword(s):

Direct Effect ◽

Body Problem ◽

Time Dependent ◽

Restricted Three Body Problem ◽

The Sun ◽

Three Body Problem ◽

Halo Orbits ◽

The Earth ◽

Gravitational Influence ◽

Three Body

AbstractThis paper deals with direct transfers from the Earth to Halo orbits related to the translunar point. The gravitational influence of the Sun as a fourth body is taken under consideration by means of the Bicircular Problem (BCP), which is a periodic time dependent perturbation of the Restricted Three Body Problem (RTBP) that includes the direct effect of the Sun on the spacecraft. In this model, the Halo family is quasi-periodic. Here we show how the effect of the Sun bends the stable manifolds of the quasi-periodic Halo orbits in a way that allows for direct transfers.

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