Odd zonal harmonics in the geopotential, determined from fourteen well-distributed satellite orbits

Abstract

Coefficients of the odd zonal harmonics in the Earth's gravitational potential are evaluated by analysing the oscillations in orbital eccentricity of seventeen satellites, chosen to give the widest and most uniform possible distribution in inclination and semi major axis. Three of the satellites are excluded for various reasons; the other fourteen yield various sets of values for the odd zonal harmonic coefficients J 3, J 5, J 7… The best representations of the odd harmonics in the potential appear to be in terms of either seven or ten coefficients, assuming that higher-degree coefficients are zero. The two sets of values are: 7-Coefficient 10-Coefficient 10 6 J 3 −2.53 ± 0.02 −2.50 ± 0.01 10 6 J 5 −2.22 ± 0.04 −0.26 ± 0.01 10 6 J 7 −0.41 ± 0.06 −0.40 ± 0.02 10 6 J 9 +0.09 ± 0.06 0 ± 0.06 10 6 J 11 −0.14 ± 0.05 −0.27 ± 0.06 10 6 J 13 +0.29 ± 0.06 +0.36 ± 0.08 10 6 J 15 −0.40 ± 0.06 −0.65 ± 0.10 10 6 J 17 +0.30 ± 0.08 10 6 J 19 0 ± 0.11 10 6 J 21 +0.58 ± 0.11 The errors in the last few coefficients of each set may be slightly greater than the standard deviations suggest, because no allowance is made for the neglected higher harmonics. The large magnitudes of J 15 and J 21 are noteworthy: neither of these coefficients has been determined before. Previously accepted values of J 3 to J 9, are in agreement with those in the more complete sets of coefficients above.