A New Kind of 3Body Problem
Abstract
A new kind of restricted 3body problem is considered. One body,m _{1}, is a rigid spherical shell filled with an homogeneous incompressible fluid of density ρ_{1}. The second one,m _{2}, is a mass point outside the shell andm _{3} a small solid sphere of density ρ_{3} supposed movinginside the shell and subjected to the attraction ofm _{2} and the buoyancy force due to the fluid ρ_{1}. There exists a solution withm _{3} at the center of the shell whilem _{2} describes a Keplerian orbit around it. The linear stability of this configuration is studied assuming the mass ofm _{3} to beinfinitesimal. Explicitly two cases are considered. In the first case, the orbit ofm _{2} aroundm _{1} is circular. In the second case, this orbit is elliptic but the shell is empty (i.e. no fluid inside it) or the densities ρ_{1} and ρ_{3} are equal. In each case, the domain of stability is investigated for the whole range of the parameters characterizing the problem.
 Publication:

Celestial Mechanics
 Pub Date:
 November 1977
 DOI:
 10.1007/BF01232659
 Bibcode:
 1977CeMec..16..343R
 Keywords:

 Earth Core;
 EarthMoon System;
 Lunar Gravitation;
 Orbital Mechanics;
 Satellite Orbits;
 Three Body Problem;
 Artificial Satellites;
 Circular Orbits;
 Elliptical Orbits;
 Equations Of Motion;
 Liquid Filled Shells;
 Astronomy