Abstract
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.
Highlights
Spacecraft charging occurred during the orbital motion of the spacecraft in the space plasma and charged particle moving relative to Earth’s magnetic field in the direction perpendicular to its velocity, creating a current along its orbital path
The main goal to maintain an electrostatic charge on the surface of the spacecraft, creating Lorentz force due to the interaction between the local magnetic field and the velocity of the spacecraft, by developing the effect of Lorentz force for both magnetic and electric fields to increase the level of charging on the spacecraft surface using Ion collector
The effect of Electromagnetic field when we increase the level of charging in the spacecraft surface as shown in Figures (4,5,6,7) for different values of charge to mass ratio (2×10-4, 2×10-3, 2×10-2, 2×10-1 Coulombs per kilogram (C/kg)) on relative trajectory, (x-y) plane, (y-z) plane, and (x-z) plane after 10 periods
Summary
Spacecraft charging occurred during the orbital motion of the spacecraft in the space plasma and charged particle moving relative to Earth’s magnetic field in the direction perpendicular to its velocity, creating a current along its orbital path. Studies of spacecraft charging conclude that the Natural spacecraft charging level may reach about 10 -8 C/kg (Vokrouhlicky 1989) Due to these limitations, the Lorentz force with such charging level is insufficient to perturb the orbit or attitude of satellite significantly, where the charge to mass ratio required to the Lorentz force for orbital maneuvering in low-Earth orbit (LEO) about 10-5 C/kg G.E. Pollock et al [7] developed the relative motion of a charged spacecraft under perturbations from the Lorentz force through interactions with the planetary magnetosphere. Gao [10] investigated a nonlinear dynamical model for relative motion assuming that the first satellite generates a rotating magnetic dipole while a constantly charging second satellite moves close to the artificial magnetic field of the chief satellite.
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