Abstract
The linear stability of equilibrium points of a test particle of infinitesimal mass in the framework of Robe's circular restricted three-body problem, as in Hallan and Rana, together with effect of variation in masses of the primaries with time according to the combined Meshcherskii law, is investigated. It is seen that, due to a small perturbation in the centrifugal force and an arbitrary constant of a particular integral of the Gylden-Meshcherskii problem, every point on the line joining the centers of the primaries is an equilibrium point provided they lie within the shell. Further, a number of pairs of equilibrium points lying on the -plane and forming triangles with the centers of the shell and the second primary exist, for some values of . The points collinear with the center of the shell are found to be stable under some conditions and the range of stability depends on the small perturbations and , while the triangular points are unstable. Illustrative numerical exploration is given to indicate significant improvement of the problem in Hallan and Rana.
Highlights
The classical restricted three-body problem (RTBP) assumes that the masses of the participating bodies are constant and do not change with time during mechanical motion
Gelf ’gat [4] examined the restricted problem of three-body of variable masses in which the primary bodies move within the framework of the Gylden-Meshcherskii problem (GMP) and established the existence of five libration points analogous to the classical libration points
We extend the work of Hallan and Rana [10] assuming that the masses of the primaries vary with time in accordance with the unified Meshcherskii [3] law and their motion determined by the GMP
Summary
The classical restricted three-body problem (RTBP) assumes that the masses of the participating bodies are constant and do not change with time during mechanical motion. Singh and Leke [5] studied the stability of the equilibrium points when the luminous primaries move within the framework of the GMP and vary their masses in accordance with the unified Meshcherskii law. A third body of infinitesimal mass m3 is a small solid sphere of density ρ3 that moves inside the shell He discussed the linear stability of an equilibrium point of the problem obtained in two cases. Shrivastava and Garain [9] investigated the effect of small perturbation in the Coriolis and centrifugal forces on the location of libration point in the Robe [8] circular restricted problem of three bodies when the shell is empty. The emergence of more equilibrium points near the center of the shell and infinite number of triangular equilibrium points is observed
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