The satellite 1971–54A entered a near-circular orbit with period 95.9 min and inclination 90.2°. Between 1972 and 1978 the orbit passed slowly through 15th-order resonance, when the track over the Earth repeats after 15 revolutions, and the 15th- and 30th-order harmonics in the geopotential may produce substantial orbital perturbations. The values of orbital inclination and eccentricity from 269 weekly U. S. Navy orbits between November 1972 and January 1978 have been analysed to determine 12 lumped harmonic coefficients of order 15 and 30. The analysis of inclination yields 15th-order coefficients accurate to 1.5 and 2.8%, and 30th-order coefficients accurate to 7 %. The analysis of eccentricity gives two 15th-order coefficients accurate to 3 and 4 %. These lumped harmonic coefficients are used to test the accuracy of the Goddard Earth Model 10B, which is complete to order and degree 36. The agreement with GEM 10B is excellent, for both 15th and 30th order, and shows that GEM 10B is more accurate than was expected. The 12 values of lumped harmonics obtained give 12 linear equations between individual coefficients of order 15 and 30, which will be used in a future solution for the individual coefficients.
Extended analytical formulae for the perturbed Keplerian motion under low-thrust acceleration and orbital perturbations
