THE INFLUENCE OF TESSERAL HARMONICS ON NEARLY CIRCULAR POLAR AND EQUATORIAL ORBITS,

Effects were determined for some of the tesseral harmonics of the Earths gravity potential on the motion of nearly circular, polar and equatorial satellite orbits. Analytical expressions are derived and results are presented for the radial, in-track, cross-track and nodal period perturbations resulting from the presence of the second sectorial harmonic. The effects of some of the higher order tesseral harmonics on nearly circular polar orbits are assessed by means of numerical digital computer investigations. The influence of tesseral harmonics on the special case of the 24-hour equatorial orbit is determined analytically, and results are presented which illustrate the drifts from the nominal position which occur in this class of orbits as a result of the perturbative forces. Wherever possible, the analytical solutions are compared with results obtained from numerical integration. The high degree of correspondence which is exhibited between the analytical and numerical data serves to substantiate the general results presented. Author