Artificial Triangular Points by Lorentz Force in the Restricted Three-Body Problem

Abstract

The restricted three body problem was outlined. The acceleration due to planetary magnetic field, in terms of space craft's orbital elements, was analysed. The conditions for calculating the liberation points including the mutual gravitational attraction and the effect of Lorentz acceleration were derived for the case of circular planer restricted three bodies. The stability of the solution for the artificial Lorentz triangular liberation points was studied. Finally, numerical investigation for the case of Sun-Jupiter system was calculated as case study. The results show the ability of changing the position of the triangular liberation points by an order from 10-7 to 10-6 for the dimensionless x, y coordinates and distance r from Jupiter. This is equivalent to about hundreds of Kilometers which is considerable.