Analytical Study of the Orbital Motion of a Spacecraft with a Variable Electric Charge

The work considers the orbital motion of a spacecraft with a variable electric charge in the gravitational and magnetic fields of the Earth. The geomagnetic field is modeled as a “direct magnetic dipole.” A nonlinear nonautonomous system of differential equations of motion of the spacecraft’s center of mass written in Cartesian and spherical coordinate systems is derived. Based on analysis of the differential system, simple harmonic laws for spacecraft charge variation are proposed to increase and decrease the orbital altitude. Using the small parameter method, an asymptotic solution is obtained for the system of differential equations describing the motion of a spacecraft launched into a circular orbit of arbitrary inclination with the proposed laws of charge variation. A computer simulation of the orbital motion of a spacecraft with variable electric charge is carried out. Good agreement is shown between the analytical results and the results of numerical simulation based on the nonlinear differential system.