Odd zonal harmonics in the geopotential, from analysis of 28 satellite orbits |
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| Authors: | D G King-Hele C J Brookes G E Cook |
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| Institution: | Royal Aircraft Establishment, Farnborough, Hants;University of Aston in Birmingham;Royal Aircraft Establishment, Farnborough, Hants |
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| Abstract: | Summary. 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 J 3, J 5, J 7, … 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): J 3=– 2530 ± 4, J 5=–245 ± 5, J 7=–336 ± 6, J 9=–90 ± 7, J 11= 159 ± 9, J 13=–158 ± 15, J 15=– 20 ± 15, J 17=– 236 ± 14, J 19=– 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. |
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