On Broucke's velocity-related series expansions in the two-body problem

Details On Broucke's velocity-related series expansions in the two-body problem On Broucke's velocity-related series expansions in the two-body problem

Dec 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975cemec..12..513j&link_type=abstract

Celestial Mechanics, vol. 12, Dec. 1975, p. 513-518.

Mathematics

1

Aerodynamic Drag, Orbital Velocity, Series (Mathematics), Two Body Problem, Abnormalities, Fourier Series, Kepler Laws, Legendre Functions, Orbital Mechanics

Scientific paper

Broucke (1974) developed velocity-related series expansions in the two body problem, and showed that these expansions in terms of mean and true anomalies are important in the analysis of atmospheric drag perturbation. This paper supplements Broucke's results by using a Poisson series method to derive the Fourier and Legendre expansions of the function of the true anomaly, the square of the function of the true anomaly, and the square of the reciprocal of the function of the true anomaly. Interesting relations involving Legendre polynomials are discussed.

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