Open AccessOn motions around the collinear libration points in the elliptic restricted three‐body problem
Author(s) -
Hou X. Y.,
Liu L.
Publication year - 2011
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2011.18970.x
Subject(s) - physics , eccentricity (behavior) , lissajous curve , libration (molecule) , three body problem , halo orbit , lagrangian point , literal (mathematical logic) , celestial mechanics , elliptic orbit , halo , classical mechanics , orbital mechanics , amplitude , series (stratigraphy) , orbital elements , motion (physics) , geometry , astrophysics , astronomy , point (geometry) , mathematics , optics , satellite , algorithm , galaxy , political science , law , biology , paleontology
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.