The theory of the gravitational potential applied to orbit prediction
Abstract
A complete derivation of the geopotential function and its gradient is presented. Also included is the transformation of Laplace's equation from Cartesian to spherical coordinates. The analytic solution to Laplace's equation is obtained from the transformed version, in the classical manner of separating the variables. A cursory introduction to the method devised by Pines, using direction cosines to express the orientation of a point in space, is presented together with sample computer program listings for computing the geopotential function and the components of its gradient. The use of the geopotential function is illustrated.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 October 1976
 Bibcode:
 1976STIN...7712092K
 Keywords:

 Geopotential;
 Gravitational Fields;
 Orbit Calculation;
 Computer Programs;
 Laplace Equation;
 Orbit Perturbation;
 Potential Theory;
 Astrodynamics