Summary: Coefficients of the odd zonal harmonics in the Earth’s gravitational potential \(J_ 3, J_ 5, J_ 7,\dots\), have been evaluated by analysing the variations in eccentricity of 29 satellite orbits from near-equatorial to polar. The evaluation includes data recently derived from the analysis of two extremely sensitive orbits, those of Cosmos 373 and Cosmos 185 rocket at inclinations to the Equator of \(62.9^ \circ\) and \(64.1^ \circ\), respectively.
The amplitude of the oscillation in perigee height arising from the influence of the odd zonal harmonics on each of these satellites is extremely large, amounting to approximately 60 km for Cosmos 373 and 30 km for Cosmos 185 rocket. Next 8-, 14- and 18-coefficient sets have been obtained with standard deviations up to 50% lower than before.
The geoid profile and predicted amplitude of the oscillation in eccentricity are compared with those given by the two most recent models from other sources.