Keplerian representation of a nonKeplerian orbit
Abstract
The properties of a mean reference orbit are developed through the introduction of an augmented radial potential proportional to c/(r squared). The arbitrary constant c is chosen to satisfy the perturbed energy level over an oblate earth. This produces a mean orbit with not only the correct first order anomalistic period, but one which is also functionally identical to a Kepler orbit. Explicit formulas are obtained for the mean elements in terms of the osculating initial values. A comparison of the solution with a numerically integrated 12 h highly eccentric orbit shows that most of the error in the mean orbit is contained within the neglected periodic terms.
 Publication:

Journal of Guidance and Control
 Pub Date:
 April 1980
 Bibcode:
 1980JGC.....3..151B
 Keywords:

 Celestial Mechanics;
 Kepler Laws;
 Orbit Perturbation;
 Orbital Mechanics;
 Astrodynamics;
 Earth Orbits;
 Eccentric Orbits;
 Equations Of Motion;
 Perturbation Theory;
 Astrodynamics