Evaluation of geopotential and lunisolar perturbations by a recursive algorithm
Abstract
The disturbing functions due to the geopotential and Lunisolar attractions are linear and bilinear forms in spherical harmonics. Making use of recurrence relations for the solid spherical harmonics and their derivatives, recurrence formulas are obtained for high degree terms as function of lower degree for any term of those disturbing functions and their derivative with respect to any element. The equations obtained are effective when a numerical integration of the equations of motion is appropriate. In analytical theories, they provide a fast way of obtaining high degree terms starting from initial very simple functions.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 August 1975
 Bibcode:
 1975STIN...7531978G
 Keywords:

 Geopotential;
 Gravitational Fields;
 Recursive Functions;
 Solar Activity;
 EulerLagrange Equation;
 Legendre Functions;
 Numerical Integration;
 Spherical Harmonics;
 Astrophysics