On motions around the collinear libration points in the elliptic restricted three-body problem

Motions around the collinear libration points in the elliptic restricted three-body problem are studied. Literal expansions of the Lissajous orbits and the halo orbits are obtained. These expansions depend on two amplitude parameters and the orbital eccentricity of the two primaries. Numerical simul...

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Bibliographic Details
Published in:Monthly notices of the Royal Astronomical Society 2011-08, Vol.415 (4), p.3552-3560
Main Authors: Hou, X. Y., Liu, L.
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics
celestial mechanics
Computer simulation
Earth, ocean, space
Earth-Moon system
Eccentricity
Exact sciences and technology
Halos
Libration points
Mathematical models
Orbits
Series (mathematics)
Simulation
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Summary:Motions around the collinear libration points in the elliptic restricted three-body problem are studied. Literal expansions of the Lissajous orbits and the halo orbits are obtained. These expansions depend on two amplitude parameters and the orbital eccentricity of the two primaries. Numerical simulations are done to check the validity of these literal series and to compare them with the results in the circular restricted three-body problem. According to the properties of these literal expansions, three kinds of symmetric periodic orbits around the collinear libration points are discussed. Finally, applications of these results in the Earth-Moon system and the Sun-Earth+Moon system are discussed.
ISSN:0035-8711
1365-2966
DOI:10.1111/j.1365-2966.2011.18970.x