Artificial Controlling of the Collinear Liberation Points Using Lorentz Force in the Restricted Three-Body Problem

Abstract

This work studies the possibility of generating artificial collinear liberation points for the planar circular restricted three-body problem using Lorentz force affecting a charged spacecraft due to the magnetic field of a planet. It is considered to be a magnetic dipole inclined by angle α with the spin axis of the planet. The acceleration components for Lorentz force are first derived in an inertial planet-center coordinate system. Then, they are transformed into the rotating coordinate system of the three-body system, with the planet naturally the smaller primary in a planet-Sun system. The equations for the liberation points are derived including the charge per unit mass as the controlling parameter. Finally, the values of the charge per unit mass required for controlling the collinear liberation point positions are derived. A numerical application for the Sun-Jupiter system is introduced and the relation between the position of the artificial liberation point and the charge per unit mass is presented graphically.