Stability of the Artificial Equilibrium Points in the Low-Thrust Restricted Three-Body Problem with Variable Mass

In this article, we have investigated the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem with variable mass. In this model of the low-thrust restricted three-body problem, we have considered both the primaries as point masses. The mass of the spacecraft varies with time according to Jeans' law (1928). We have introduced a new concept for creating the AEPs in the restricted three-body problem with variable mass using continuous constant acceleration. We have derived the equations of motion of the spacecraft after using the space-time transformations of Meshcherskii. The AEPs have been created by cancelling the gravitational and centrifugal forces with the constant continuous low-thrust at the non-equilibrium points. The positions of these AEPs will depend not only on magnitude but also on the constant directions of the low-thrust acceleration. We have analyzed the linear stability of the AEPs and found that all the AEPs are unstable. Finally, we have drawn the zero velocity curves (ZVCs) to determine the possible regions of motion in which the spacecraft is free to move.