The geopotential in nonsingular orbital elements

Details The geopotential in nonsingular orbital elements The geopotential in nonsingular orbital elements

Aug 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977cemec..15..453n&link_type=abstract

Celestial Mechanics, vol. 15, Aug. 1977, p. 453-466. NSF-NASA-supported research.

Mathematics

8

Earth Orbits, Geopotential, Orbital Elements, Singularity (Mathematics), Eccentricity, Equations Of Motion, Inclination, Partial Differential Equations

Scientific paper

Singularities are eliminated from the geopotential and its partial derivatives for zero eccentricity and inclination, and an expression for the geopotential expansion based entirely on nonsingular orbital elements is developed. The argument relies on the treatments of the geopotential function given by Izsak (1964), Allan (1965) and Kaula (1966); the geopotential expansion developed does not involve mixed variables, and therefore does not require the chain rule to formulate the Lagrange planetary equations. The need for recursion relations to be used in conjunction with the nonsingular version of the geopotential expansion is also mentioned.

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