Expansion Theory for the Elliptic Motion of Arbitrary Eccentricity and SemiMajor Axis  Part Seven  Elliptic Expansions in Terms of the Sectorial Variables for the Seventh and Eighth Categories
Abstract
In this paper of the series, elliptic expansions in terms of the sectorial variables θ{_{j}/^{j}} introduced recently in Paper IV (Sharaf, 1982) to regularise highly oscillating perturbations force of some orbital systems will be established analytically and computationally for the seventh and eighth categories. For each of the elliptic expansions belonging to a category, literal analytical expressions for the coefficients of its trigonometric series representation are established. Moreover, some recurrence formulae satisfied by these coefficients are also established to facilitate their computations, numerical results are included to provide test examples for constructing computational algorithms.
 Publication:

Astrophysics and Space Science
 Pub Date:
 May 1985
 DOI:
 10.1007/BF00668408
 Bibcode:
 1985Ap&SS.112...51S
 Keywords:

 Celestial Mechanics;
 Elliptical Orbits;
 Orbital Mechanics;
 Eccentric Orbits;
 Recursive Functions;
 Series Expansion;
 Trigonometric Functions;
 Astronomy