Evaluation of 15th-order harmonics in the geopotential from analysis of resonant orbits

Abstract

Satellite orbits contracting under the influence of air drag experience 15th-order resonance when the track over the Earth repeats after 15 revolutions. If the orbital decay rate is slow enough, an orbit passing through the resonance is appreciably perturbed by the effects of 15th-order harmonics in the geopotential. We have used the observed perturbations in 23 resonant orbits, at various inclinations to the equator, to determine the harmonic coefficients of order 15 and degree 15, 16, 17,... 35. Analysis of the changes in orbital inclination on the 23 orbits gives the harmonics of odd degree, while those of even degree are found from the changes in eccentricity on 16 of the orbits. The values derived are given in tables 6 and 8. The coefficients of degrees 15, 16, 17,... 23, should be more accurate than any previously obtained; their average s. d. is 1.4 x 10 -9 , equivalent to 1 cm in geoid height. Comparisons with comprehensive Earth models show the Goddard Earth Model 10B to be the best, and a standard deviation of about 3 x 10 -9 in the GEM 10B 15th-order coefficients is indicated.