Abstract
BY analysing the orbit of Ariel 3, Gooding1 obtained two equations between 15th-order coefficients in the Earth's gravitational potential from the changes in orbital inclination as the satellite passed through 15th-order resonance (when the successive tracks over the Earth are exactly 24° apart). Gooding's equations, simplified by omitting terms which should be small, are:where the quantities C̄ and S̄ are normalized coefficients in the infinite series expansion of the geopotential, as defined, for example, by Gaposchkin and Lambeck2.
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References
Gooding, R. H., Nature Physical Science, 231, 168 (1971).
Gaposchkin, E. M., and Lambeck, K., J. Geophys. Res., 76, 4855 (1971).
Allan, R. R., Royal Aircraft Establishment Technical Report 71245 (1911).
Hiller, H., and King-Hele, D. G., Royal Aircraft Establishment Technical Report 72003 (1972).
King-Hele, D. G., Royal Aircraft Establishment Technical Report 72050 (1912).
Eberst, R. D., Nature Physical Science, 235, 130 (1972).
Higbie, J. W., and Stacey, F. D., Nature Physical Science, 234, 130 (1971).
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KING-HELE, D., HILLER, H. Equations for 15th-Order Harmonics in the Geopotential. Nature Physical Science 235, 130–131 (1972). https://doi.org/10.1038/physci235130b0
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DOI: https://doi.org/10.1038/physci235130b0
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