Spatial potential of a weakly compressed elliptical disk

Abstract

The problem of expanding spatial potential in terms of eccentricity e accurate to e² has been formulated and solved for a homogeneous gravitating (or charged with static electric charge) elliptical disk. An original method that makes it possible to obtain the desired result using the superposition of a perturbation layer and a circular disk has been developed. The potential of such a layer has been derived. The first term of the expansion of the potential (zero power of parameter e) coincides with the potential of a homogeneous circular disk and the coefficient of the first power of the parameter e is zero. The main term of the expansion of the potential proportional to e² is analytically derived. The resulting expression makes it possible to determine the potential in the entire space, including the inner region of the disk.