Representation of the gravitational potential of a level ellipsoid by a simple layer

TL;DR

This paper derives a closed-form expression for representing the gravitational potential of a level ellipsoid using a simple layer, enabling new ways to model gravitational fields of oblate spheroids.

Contribution

It introduces a novel closed-form solution for the density of a simple layer that matches the potential of a level ellipsoid of revolution.

Findings

Derived a closed-form expression for the simple layer density.

Established the potential equivalence for any level spheroid of positive mass.

Presented various density function examples for practical applications.

Abstract

A closed-form expression is obtained for the density of a simple layer, equipotential to an oblate level ellipsoid of revolution in an outer space. The potential of any level spheroid of positive mass with the inward direction of attracting force on its surface can be represented in this way. A family of density functions defined on the whole volume of a level ellipsoid of revolution is found. Several density examples are considered.