Optimization of Sphere Population for Electrostatic Multi-Sphere Method

To develop the robust relative position and orientation control algorithms for Coulomb charge control of spacecraft, accurate but computationally efficient electrostatic models are necessary. The multi-sphere method (MSM) predicts the interactions of a charged spacecraft using multiple conducting spheres. To improve the accuracy of this model further, a new method is proposed whereby equal radius spheres are placed uniformly on the surface of the spacecraft. The radius is chosen such that the MSM predicts the same self-capacitance for the conducting geometry as a numerical solution does. While similarities are identified between the new method and the established boundary element method, several key distinctions between the models are established. The accuracy of the new approach is verified using a simple system with two spheres, whereby its ability to capture-induced charge effects is highlighted. Then, a cylinder-sphere system is analyzed using 105 spheres on the cylinder and 30 spheres on the sphere, providing comparison with a previous three-sphere volume populated model for the cylinder. The surface populated model provides much higher accuracy in forces and torques when the separation distances are within 10 craft radii, but there is a little improvement outside this range. While the cylinder MSM with three spheres provides force solutions an order of magnitude quicker than the surface MSM method, the setup time for the surface populated MSM is two orders of magnitude faster.