The stable regions of the triangular libration points of the planets

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Libration, Orbital Resonances (Celestial Mechanics), Planets, Three Body Problem, Orbit Calculation, Solar System

Scientific paper

The stability and actual stable areas of the triangular libration points in the restricted three-body problem involving the sun, a planet, and a small body is investigated for the solar system planets, excluding Pluto. A large stable region is found to exist around each triangular libration point of the outer planets. For Jupiter, the size of this region is about 2/3 d. For Saturn, Uranus, and Neptune the sizes are about 4/5 d. These triangular libration points can keep the small body in large areas for a long time, and the variations of the orbital elements a, e, and i of the small body around the libration points are nearly periodical and their variational periods are very long. The triangular libration points of earth or Mars are not stable against the perturbation of the other planets. The small body cannot long stay in the vicinity of the triangular libration points of earth and Mars. A relatively small stable region exists around each triangular libration point of Mercury and Venus.

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