EFFECTS OF MASS VARIATION OF MAIN BODIES ON ORBITS AROUND TRIANGULAR LIBRATION POINTS IN THE RESTRICTED THREE-BODY PROBLEM
JAGADISH SINGH *
Department of Mathematics, Faculty of Science, Ahmadu Bello University, P.M.B 2222 Sokoto Road, Zaria, Nigeria
Department of Mathematics, Statistics and Computer Science, College of Science, University of Agriculture, P.M.B. 2373, North-Bank, Makurdi, Nigeria
*Author to whom correspondence should be addressed.
The effects of isotropic mass variation of a binary system on orbits and orbital elements of a test particle around triangular libration points in the frame of the restricted three-body problem, is examined. The motion of the main bodies is described by the Gyld´en-Mestschersky equation while their mass variation occurs in accordance with the unified Mestschersky law. It is seen that the change in the frequencies, orbital period, eccentricities and the semi-minor and major axes, of long and short orbits, are influenced by the mass parameter of the binary and a constant of a particular integral of the Gyld´en-Mestschersky equation. For increasing mass ratio, the orientations, sizes, shapes and positions of the orbits differ, while for increasing orbital period, the test particle spirals towards the libration point. Further, we observe that the triangular libration points are enclosed by the orbits, for some parametric values. In particular, for very small values of the governing parameters, the orbits almost completely collapse and motion around the libration point becomes restricted. Due to the variations, the eccentricity can be less, equal to, or greater than one, and so the orbits can be elliptic, parabolic or hyperbolic types. Also, the lengths of the semi-axes do not exist for some values of as they are either zero or imaginary. This study validates that planetary orbits are changing due to stellar mass loss. These results differ from the case when the main bodies have constant masses.
Keywords: R3BP, Variable masses, Orbits