Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis. VIII - Elliptic expansions in terms of the sectorial variables for the ninth, tenth, eleventh, and twelfth categories

Details Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis. VIII - Elliptic expansions in terms of the sectorial variables for the ninth, tenth, eleventh, and twelfth categories Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis. VIII - Elliptic expansions in terms of the sectorial variables for the ninth, tenth, eleventh, and twelfth categories

Nov 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985ap%26ss.116..251s&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 116, no. 2, Nov. 1985, p. 251-283.

Astronomy and Astrophysics

Astrophysics

7

Eccentric Orbits, Elliptical Orbits, Orbit Calculation, Orbit Perturbation, Orbital Elements, Series Expansion, Orbital Mechanics, Trigonometric Functions

Scientific paper

The elliptic expansions in terms of sectorial variables that were introduced by Sharaf (1982) for the regularization of a highly oscillatory perturbation force in some orbital systems are presently established analytically and computationally, for the ninth, tenth, eleventh and twelfth categories of the scheme proposed by Sharaf (1983). For each of the elliptic expansions belonging to a category, there are established both the literal analytical expressions for the coefficients of its trigonometric series representation, and the recurrence formulas that are satisfied by these coefficients. The numerical results presented furnish test examples for the construction of computational algorithms.

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