Contribution of zonal harmonics to gravitational moment
Abstract
A celestial body produces a gravitational moment about the mass center of a small orbiting body, which affects the orientation of the smaller body. Each zonal harmonic in the gravitational potential of a celestial body is shown to make a contribution to the gravitational moment which can be expressed in a recursive vectordyadic form. A formal derivation is presented, followed by an example in which the result is employed in obtaining the contribution of the zonal harmonic of 2nd degree. The contribution of the zonal harmonic of 3rd degree is also reported.
 Publication:

Flight Mechanics/Estimation Theory Symposium, 1990
 Pub Date:
 December 1990
 Bibcode:
 1990fmet.symp..417R
 Keywords:

 Axisymmetric Bodies;
 Celestial Bodies;
 Center Of Mass;
 Gravitational Fields;
 Orbits;
 Vectors (Mathematics);
 Zonal Harmonics;
 Moments;
 Polynomials;
 Astrodynamics