Analysis of 27 satellite orbits to determine odd zonal harmonics in the geopotential

The odd zonal harmonics in the geopotential are the terms independent of longitude and antisymmetric about the equator which define the 'pear-shape' effect. The coefficients of these harmonics were evaluated by analyzing the variations in eccentricity of 27 orbits covering a wide range of inclinations. This included 3 accurate orbits at inclinations between 60 deg and 66 deg, where the variations in eccentricity become large, and 3 near-equatorial orbits, at inclinations between 3 deg and 15 deg, whereas previously there were none at inclinations lower than 28 deg. The new data lead to much more accurate and reliable values for the coefficients. With this set of values, the pear-shape tendency of the earth amounts to 44.7 m at the poles, instead of the previous 40 m, though the new geoid is within 1 m of the old at latitudes away from the poles.