We consider the Robe’s restricted three-body problem in which the bigger primary is assumed to be a hydrostatic equilibrium figure as an oblate spheroid filled with a homogeneous incompressible fluid, around which a circular motion is described by the second primary, that is a finite straight segment. The aim of this note is to investigate the effect of oblateness and length parameters on the motion of an infinitesimal body that lies inside the bigger primary. The locations of the equilibrium points are approximated by the series expansions and it is found that two collinear equilibrium points lying on the line segment joining the centers of the primaries, exist. The non- collinear equilibrium points lie on a circle and are infinite in number. No out-of-plane equilibrium point exists. Based on the linear stability analysis, it is observed that the collinear equilibrium points can be stable under certain conditions whereas the non-collinear ones are always unstable.
Kaur, Bhavneet; Chauhan, Shipra; and Kumar, Dinesh
Outcomes of Aspheric Primaries in Robe’s Circular Restricted Three-body Problem,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 16,
1, Article 25.
Available at: https://digitalcommons.pvamu.edu/aam/vol16/iss1/25