The potential series expansion method: application to the asteroid (87) Sylvia

This study aims to investigate the location and stability of equilibrium points in the potential field of the the asteroid (87) Sylvia. The potential series expansion method is used, which involves decomposing the asteroid into homogeneous tetrahedral elements with a constant rotation speed. The results are compared with those obtained using the classical polyhedral method, and we found good agreement outside the body, even in close to its surface. Our model can be applied to any polyhedral-shaped body as it expresses the potential analytically, which makes it easier to manipulate algebraically for determining acceleration and velocity components. Moreover, it significantly reduces computational costs in terms of CPU time requirements, keeping the accuracy at a very acceptable level.