In this chapter we discuss the gravitational potential whose gradient enters the momentum equation. The potential is the sum of two terms, the potential of the Earth and the tidal potential caused by the Moon and Sun. For many problems, the gradient of the Earth's potential can be assumed to be a constant gravitational acceleration g0. However, the actual equipotential surfaces (the geoid) have a fairly complicated shape. The gravitational potential is determined by the mass distribution, as the solution of a Poisson equation. For a prescribed mass distribution this solution can be expressed in terms of the Green's function of the Poisson equation. The determination of the gravitational potential then becomes a mere matter of integration, with well-known solutions for a sphere and other simple distributions. For a self-attracting rotating body, like the Earth, the mass distribution is not known a priori but needs to be determined simultaneously with the gravitational potential. For a fluid body of constant density, the solution to this implicit problem is MacLaurin's ellipsoid. For the Earth, the geoid needs to be measured.

The basic geometry of the geoid is an oblate ellipsoid. This suggests oblate spheroidal coordinates as the most convenient coordinate system. Since the eccentricity of the geoid is small one can approximate the metric coefficients of this coordinate system such that they look like the metric coefficients of spherical coordinates.