A new kind of 3-body problem |
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Authors: | H A G Robe |
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Institution: | (1) Institut d'Astrophysique, Université de Liège, B 4200 Cointe-Ougree, Belgium |
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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 1. The second one,m
2, is a mass point outside the shell andm
3 a small solid sphere of density 3 supposed movinginside the shell and subjected to the attraction ofm
2 and the buoyancy force due to the fluid 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 1 and 3 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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Keywords: | |
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