Spacecraft charging is a naturally occurring phenomenon in the space plasma environment, which in most cases is undesirable due to the deleterious effect on on-board electronics. Based on the fundamental physical principle that a moving charged particle experiences the Lorentz force in a magnetic field, one can deduce that an electrostatically charged spacecraft in Earth orbit is subjected to the Lorentz force in the Earth’s magnetic field. Early studies of spacecraft charging conclude that the natural spacecraft charging level may reach to about 10-8 C/kg and the induced Lorentz force with such charging level is insufficient to perturb the orbit and attitude of satellite significantly. The concept of Lorentzaugmented orbits is analogous to the motion of charged dust grains in planetary magnetic fields, After the launch of artificial satellites, the phenomenon of spacecraft surface charging was discovered and found to be omnipresent, and therefore the motion of electrically charged artificial satellites affected by the Lorentz force. However, much research relating to charged spacecraft are conducted by space-plasma physicists, and the primary purpose of their research is to attenuate the hazardous electromagnetic radiation effect caused by surface charging. Contrary to previous studies that concentrate on passive mitigation of the charge, a new concept of active application of the charge of spacecraft has been proposed by Peck in recent years . Such conception spacecraft is referred to as Lorentz spacecraft, an artificially charged space vehicle that intentionally generates net charge on its surface to induce Lorentz force via interaction with the planetary magnetic field. If the charging level is several orders of magnitude larger than natural charging level or even higher, the induced Lorentz force could be utilized as propellantless electromagnetic propulsion for orbital maneuvers and attitude control. The Lorentz force acting on an electrostatically charged spacecraft may provide a useful thrust for controlling a spacecraft’s orbit and attitude control . In this work, the Lorentz force has been developed as a function of the orbital elements. The orbital perturbations of a charged spacecraft by Lorentz force in the Earth’s magnetic field, which is modeled as a titled dipole is investigated using the Gauss variation of the Lagrange planetary Equations. The perturbations in the orbital elements depend on the value of the charge to mass ratio (q/m). The dynamical models of the Relative motion are developed that leads to approximate analytical solutions for the motion of a charged spacecraft subject to Lorentz force. The modeled derived when the chief spacecraft’s reference orbit is either circular or elliptical, and the deputy spacecraft is capable of established electrostatic charge. The numerical results show that the effects of the Lorentz force on the spacecraft are to change intrack position or/and plane orbit. The results investigated the approximation of the trajectory an estimate the reachable of the Lorentz spacecraft for short time intervals with different ration (q/m) for different orbits in LEO.
 Peck MA. Prospects and challenges for Lorentz-augmen-ted orbits. In: AIAA guidance, navigation, and control conference and exhibit, San Francisco, California, 15–18 August 2005, paper no. IAA-2005-5995.  Abdel-Aziz, Yehiaand M. Shoaib, Attitude dynamics and control of spacecraft usinggeomagnetic Lorentz force. Research in Astronomy and Astrophysics (RAA) Vol 15 No. 1, 127-144, 2015.
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