The stable regions of the triangular libration points of the planets
Abstract
The problem of the stable regions of the triangular libration points of the restricted threebody problem is discussed from the viewpoint of 1/1 orbital resonance. An estimated analytical epression, d = 2/3μ, is derived, where d corresponds to the size of the stable region and μ is the mass ratio of the restricted threebody problem. Based on the above conclusions, considering a model closer to the Solar System and adopting the sympletic integrator SI6 A developed recently for the Hamiltonian system, we investigate the stabilities and the corresponding stable regions of the triangular libration points of the restricted threebody problem consisting of the Sun, the planet in the Solar System (excluding Pluto), and a small body and we obtain some quantitative results about the practical stable regions of these libration points. The results show that the practical stable regions corresponding to each outer planet (excluding Pluto) are approximate to the corresponding d, and for Mercury and Venus the sizes of the stable regions are about onefourth of the corresponding d, but the points corresponding to Earth and Mars are not stable.
 Publication:

Icarus
 Pub Date:
 November 1992
 DOI:
 10.1016/00191035(92)900242
 Bibcode:
 1992Icar..100..136Z
 Keywords:

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