Gravity field due to a homogeneous oblate spheroid: Simple solution form and numerical calculations

Abstract

We present a simple derivation of the interior and exterior gravitational potentials
due to oblate spheroid and also its gravity field components by using the fundamental
solution of the Laplace equation in oblate spheroidal coordinates. Application of
the method of separation of variables provides an expression for the potential in terms of
oblate spheroidal harmonics of degree n = 0, 2. This solution is more concise and suitable
for the numerical calculations in comparison with infinite series in spherical harmonics.
Also presented are the computations in the form of potential isolines inside and outside
the spheroid, as well as for the gravity field components. These reveal some interesting
properties of the gravity field of this fundamental geophysical body useful for the applied
gravimetry.