Expansion of the inverse of mutual distance between two bodies raised to any power

Details Expansion of the inverse of mutual distance between two bodies raised to any power Expansion of the inverse of mutual distance between two bodies raised to any power

Aug 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981ap%26ss..78....3k&link_type=abstract

Astrophysics and Space Science, vol. 78, no. 1, Aug. 1981, p. 3-26.

Mathematics

7

Fourier Series, Orbital Elements, Orbital Mechanics, Perturbation Theory, Two Body Problem, Celestial Mechanics, Differential Equations, Disturbing Functions, Eccentric Orbits, Elliptical Orbits, Operators (Mathematics), Series Expansion

Scientific paper

The expression delta to the -s (delta being the mutual distance between two bodies and s being a natural integer taking the values 1, 3, 5, . . .) is calculated in terms of true anomalies and classical orbital elements, referring to a common fixed plane and working up to power four of eccentricities and tangents of inclinations. Two final results are obtained, the first when gamma prime is greater than gamma, the second when gamma is greater than gamma prime.

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