Abstract
The present paper deals with the study of the motion’s properties of the infinitesimal variable mass body moving in the same orbital plan as two massive bodies (considered as primaries). It is assumed that the massive bodies have radiating effects, have oblate shapes, and are moving in circular orbits around their common center of mass. Using the procedures established by Singh and Abouelmagd, we determined the equations of motion of the infinitesimal body for which we assumed that under the effects of radiation and oblateness of the primaries, its mass varies following Jean’s law. We evaluated analytically and numerically the locations of equilibrium points and examined the stability of these equilibrium points. Finally, we found that all the points are unstable.
Highlights
In celestial mechanics and dynamical astronomy, the most studied problem was and remains the restricted three-body problem that we denote in the sequel by R3BP. e problem has been investigated when the orbits of the primaries are either circular or elliptic
Bhatnagar and Hallan [1] introduced a new type of perturbations in the classical R3BP, and they have shown that their problem has five libration points out of which three are unstable and two are stable
We studied the effects of the variation parameters α and β on the behavior of motion of the infinitesimal body in the restricted 3-body problem and when the mass of this infinitesimal body varies according to Jean’s law
Summary
In celestial mechanics and dynamical astronomy, the most studied problem was and remains the restricted three-body problem that we denote in the sequel by R3BP. e problem has been investigated when the orbits of the primaries are either circular or elliptic. Bhatnagar and Hallan [1] introduced a new type of perturbations in the classical R3BP (i.e., under Coriolis and centrifugal forces), and they have shown that their problem has five libration points out of which three are unstable and two are stable In their studies, Khanna and Bhatnagar [2] have been concerned by the existence and stability of equilibrium points in the circular R3BP, both with the triaxial shape and with the combination of the triaxial shape and the oblateness of the primaries. E authors supposed that the equatorial plane coincides with the orbital plane of motion In these conditions, they found three collinear libration points which are always unstable and two triangular libration points which are stable in some intervals like it has been shown by Szebehely [7] for the classical restricted threebody problem.
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