Spacecraft Electrostatic Force and Torque Expansions Yielding Appropriate Fidelity Measures

Abstract

Charged spacecraft experience electrostatic forces and torques from both charged neighboring spacecraft and the local space environment. These forces and torques can be used for a variety of novel touchless actuation concepts. In contrast to the multipole method which provides an expansion of the potential field, this paper presents a direct binomial series expansion of the forces and torques called the Appropriate Fidelity Measures (AFMs) method. A two-stage process is presented where first the force and torque vectors are expanded assuming a known charge distribution, followed by a second stage which provides an approximation of the charge distribution through the susceptibilities of the measures. AFMs provide a direct analytical solution and thus provide new insight for charged single- and two-body configurations. The accuracy of a truncated expansion is numerically studied and validated. With a second-order AFM solution, the errors drop below 5% at separations greater than $\sim $ 6 craft diameters. This new method is well-suited for control analysis due to the analytical solutions produced. An AFM solution of the torque on an axis-symmetric cylinder is developed that yields closed form analytic solutions that match prior numerically fit solutions.