Geopotential harmonics of order 15 and even degree, from changes in orbital eccentricity at resonance

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 eccentricity may suffer appreciable changes due to perturbations from the gravitational harmonics of order 15 and even degree (16, 18, 20…). In this paper the changes in eccentricity at resonance for six satellites in near-circular orbits at inclinations between 56 and 90° have been analysed to derive 11 pairs of equations linking the harmonic coefficients of order 15 and (even) degree l, C l,15 and S l,15 in the usual notation. These equations (together with eight constraint equations) are solved to give: l 10 9 C l,15 10 9 S l,15 16 −13.7 ± 1.3 −18.5 ± 2.7 18 −42.3 ± 1.8 −34.7 ± 3.4 20 10.5 ± 3.1 29.8 ± 5.2 22 −8.6 ± 3.8 −20.2 ± 7.4 To obtain realistic error estimates, including the errors due to neglecting higher-degree harmonics, a 50 per cent increase in the quoted S.D. is suggested.