On the axisymmetric restricted five-body problem within the frame of variable mass: The convex case

Abstract

The present manuscript reveals the existence and stability of the libration points (LPs) in the axisymmetric restricted five-body problem (AR5BP) in which the mass of the fifth particle varies with respect to time as per Jeans' law. It has been assumed that the four bodies P i with masses m i , i = 1, 2, ..., 4 (with m 3 = m 4 = m) form an axisymmetric convex configuration. The systems of differential equations which govern the motion of the test particle (whose mass is variable) moving under the gravitational influence of the four primaries, have been presented, indeed, these equations are different from those of the test particle with constant mass in the AR5BP. We have determined the in-plane and out-of-plane LPs along with their linear stability. Furthermore, it is observed that the existence of these LPs depends † Corresponding Author