Equilibrating the Effects of Gravity-Gradient Potential on the Orbits of Lorentz Triaxial Spacecraft

In this paper, the effects of gravity-gradient potential on a spacecraft of arbitrary shape are outlined. The potential expressing the planet’s gravity-gradient torque on a triaxial spacecraft is formed. The planet’s shape is considered oblate spheroidal, and the dimensions of the spacecraft are assumed small compared to its distance from the center of the planet. The radial, transverse and normal components of the Lorentz force, in terms of orbital elements, are constructed. The variations in the orbital elements due to both gravity-gradient potential and Lorentz force are derived. The charges per unit mass needed to balance such perturbation are obtained. The symmetrical results in mathematical equations are obvious. The International Space Station (ISS) is used as an example to test our model. A three-dimensional diagram was plotted to illustrate the charge per unit mass with the shape and size of the orbits.