Spacecraft relative dynamics under the influence of geomagnetic lorentz force

The motion of a charged satellite subjected to the Earth's magnetic field is considered. Lorentz force, which acts on charged particle when it is moving through the magnetic field, provides a new concepts of propellant-less electromagnetic propulsion. We derive a dynamical model of a charged spacecraft including the effect of Lorentz force in the vicinity of circular and elliptic orbit and consider its application to formation flight. Based on Hill-Clohessy-Wiltshire equations and Tschauner-Hempel equations, analytical approximations for the relative motion in Earth orbit are obtained. The analysis based on linearized equations in the equatorial case show that the stability of the periodic solutions. Numerical simulations revealed that the periodic solutions which are useful for the formation are obtained for both circular and elliptic reference orbits.The control strategy for the propellantless rendezvous and reconfiguration are developed.