Abstract
A new kind of restricted 3-body problem is considered. One body,m 1, is a rigid spherical shell filled with an homogeneous incompressible fluid of density ρ1. The second one,m 2, is a mass point outside the shell andm 3 a small solid sphere of density ρ3 supposed movinginside the shell and subjected to the attraction ofm 2 and the buoyancy force due to the fluid ρ1. 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 ρ1 and ρ3 are equal. In each case, the domain of stability is investigated for the whole range of the parameters characterizing the problem.
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Robe, H.A.G. A new kind of 3-body problem. Celestial Mechanics 16, 343–351 (1977). https://doi.org/10.1007/BF01232659
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DOI: https://doi.org/10.1007/BF01232659