The Gravitational Potential

Abstract

The gravitational attraction force is a conservative force, i.e. it can be represented by a potential. A potential surrounds the source mass of the gravitational attraction force. We shall refer to this source as the master. If a second mass, which we shall refer to as the satellite, is located in the potential of the master, it will be attracted by the master with an attraction force, whose magnitude and direction is defined by the potential at the location of the satellite. The gravitational potential surrounding a point master is

$$U =-\frac{{\mu m}}{r}$$

for a point satellite in the gravitational field of the point master. On the following pages, we will establish the gravitational potential surrounding a spheroid master; have a look at a general expression for the potential surrounding a master of arbitrary shape, which is then reduced to the case of a master of rotational symmetry. The results can be found in Table 5.1. Eventually we will introduce the concepts of flattening and perturbation force.