Evaluation of harmonics in the geopotential of order 15 and odd degree

Abstract

When a satellite orbit decaying slowly under the action of air drag experiences 15th-order resonance with the Earth's gravitational field, so that the ground track repeats after 15 rev, the orbital inclination suffers appreciable changes due to the perturbations from the harmonics in the geopotential of order 15 and odd degree (15,17,19 …). In this paper the changes in inclination at resonance of 11 satellites at inclinations between 30° and 90° have been analysed to determine values of the geopotential coefficients of order 15 and degree l, C ̄ l,15 and S ̄ l,15 in the usual notation. The recommended solution, going up to l = 31, is: l 10 9C̄ l,15 10 9S̄ l,15 15 −21.5 ± 0.9 −8.4 ± 0.9 17 4.4 ± 1.6 9.0 ± 1.5 19 −15.6 ± 2.6 −14.1 ± 2.7 21 10.4 ± 3.0 7.3 ± 3.5 23 22.5 ± 2.8 1.2 ± 4.4 25 −0.9 ± 4.7 −3.8 ± 5.3 27 −11.2 ±3.3 9.1 ± 3.2 29 −20.5 ± 5.4 −1.2 ± 6.1 31 17.7 ± 6.6 −1.0 ± 7.1