Odd zonal harmonics in the geopotential, from analysis of 28 satellite orbits

The geopotential is usually expressed as an infinite series of spherical harmonics, and the odd zonal harmonics are the terms independent of longitude and antisymmetric about the equator: they define the ‘pear-shape’ effect. The coefficients J3, J5, J7, … of these harmonics have been evaluated by analysing the variations in eccentricity of 28 satellite orbits from near-equatorial to polar. Most of the orbits from our previous determination in 1974 are used again, but three new orbits are added, including two at inclinations between 62° and 63°, which have been specially observed for more than five years by the Hewitt cameras. With the help of the new orbits and revised theory, we have obtained sets of J-coefficients with standard deviations about 40 per cent lower than before. A 9-coefficient set is chosen as representative, and is as follows (all × 109): J3 = - 2530 ± 4, J5 = -245 ± 5, J7 = -336 ± 6, J9 = -90 ± 7, J11 = 159 ± 9, J13 = -158 ± 15, J15 = -20 ± 15, J17 = -236 ± 14, J19 = -27 ± 19. With this set of values, the pear-shape asymmetry of the geoid (north polar minus south polar radius) amounts to 45.1 m instead of the previous 44.7 m. The accuracy of the longitude-averaged geoid profile is estimated as 50 cm, except at latitudes above 86°. The geoid profile and predicted amplitude of the oscillation in eccentricity are compared with those from other sources.