Abstract
Robe's restricted three-body problem is reanalyzed with a view to incorporate a new assumption, namely that the configuration of the fluid body is that described by an hydrostatic equilibrium figure (Roche's ellipsoid). In the concomitant gravitational field a full treatment of the buoyancy force is given. The pertinent equations of motion are derived, the linear stability of the equilibrium solution is studied and the connection between the effect of the buoyancy forces and a perturbation of the Coriolis force is pointed out.
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References
Chandrasekhar, S.: 1987,Ellipsoidal Figures of Equilibrium, Dover Publications Inc., New York.
Robe, H. A. G.: 1977, ‘A New Kind of Three-Body Problem’,Celest. Mech. 16, 343–351.
Shrivastava, A. K. and Garain, D.: 1991, ‘Effect of Perturbation on the Location of Libration Point in the Robe Restricted Problem of Three Bodies’,Celest. Mech. 51, 67–73.
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Plastino, A.R., Plastino, A. Robe's restricted three-body problem revisited. Celestial Mech Dyn Astr 61, 197–206 (1995). https://doi.org/10.1007/BF00048515
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DOI: https://doi.org/10.1007/BF00048515