Geopotential harmonics of order 15 and odd degree from analysis of resonant orbits

Abstract

We have analysed the variations of inclination in 13 satellite orbits as they pass slowly, under the action of air drag, through 15th-order resonance with the geopotential, when successive equatorial crossings are 24° apart and the ground track repeats after 15 rev. The size and form of the change in inclination are determined mainly by the values of the geopotential harmonics of 15th order and odd degree, C ̄ l,15 and S ̄ l,15 (with l = 15, 17, 19, …) in the usual notation. Our analysis gives values of these coefficients up to l = 33 as follows: l 10 9 C̄ l,15 10 9 S̄ l,15 15 −23.5 ± 0.8 −7.7 ± 0.8 17 6.3 ± 1.5 5.6 ± 1.5 19 −25.1 ± 2.5 −7.3 ± 2.3 21 27.8 ± 3.6 −0.7 ± 3.4 23 17.1 ± 4.1 13.9 ± 4.8 25 −1.1 ± 3.0 8.5 ± 4.2 27 10.0 ± 3.3 6.7 ± 2.7 29 −9.4 ± 3.5 0.1 ± 4.7 31 10.1 ± 5.4 3.8 ± 5.6 33 1.1 ± 5.7 3.1 ± 5.8 Four of the orbits analysed also yield good values for lumped harmonics of 30th order: their mean numerical value is 14 × 10 −9. The evaluation of individual 30th-order coefficients should be possible when results from a few more resonant orbits have accumulated.