Artificial equilibrium points in the low-thrust restricted three-body problem

The magnitude and direction of the required acceleration creating the artificial equilibrium point (AEP) in the low-thrust restricted three-dimensional space problem are investigated. A nonequilibrium point is turned into AEP by applying the appropriate continuous control acceleration. The nondimensional magnitude of acceleration is found in terms of the sun-earth system and the required acceleration is obtained by assuming that other planets such as Mars and Venus are not near the spacecraft with negligible effect. The stability of each AEP is found by linearizing the equations of motion and carrying out a linear stability analysis. The results show that for a small mass-ratio system such as the Sun-Earth system, there are stable regions of AEPs with very small control acceleration that are defined in space missions.