Semi-Analytical Solution for Formation Flying Spacecraft Subject to Electromagnetic Acceleration

The generation of Lorentz force is limited by the local magnetic field and the relative velocity of the spacecraft. As a result of this constraint, the Lorentz force cannot completely take place of the traditional propulsion technologies. In recent years, studying the Lorentz force provided by modulating spacecraft electrostatic charge (magnetic and electric fields) has become a possible good means to control the spacecraft without fuel consumption or reduce the fuel cost. Most of the previous studies concerned the Lorentz force of the magnetic field only. In this paper, we developed a combination of Lorentz forces provided by modulating spacecraft's electrostatic charge (magnetic and electric fields) that can be used to keep the desired relative distances and orientations. We are derived nonlinear dynamic models of satellite relative motion considering J2 perturbation, and Lorentz forces to develop a mathematical model for a new technique establishing increase the level of charging in the spacecraft surface. These solutions indicate that the principal effects of the Lorentz force on a spacecraft can be used to correct the drift in the relative position of formation flying due to the effect of Second zonal harmonics, where the magnitude of charge to mass ratio is the key player for the correction of this drift. Numerical results for different examples of formation flying confirmed the capability of Lorentz force to correct the drift in relative position. These corrections depend on the value of charge to mass ratio and magnitude of the relative position.