An improved theory of motion of an artificial satellite
Abstract
The paper deals with the problem of motion in the potential field defined by V =  1/r+J2P2 (sin0)/r3+J4P4(sin0)/r2, where J2 and J4 are small parameters, with J4 =0 (J22). The disposable constants Cl, Cl, and 2 of the author's intermediate orbit (1958) are revised so as to in corporate the known secular variations up to the second order, furnished by the perturbation theory (1959). The revised algorithm provides a more accurate final orbit, incorporating a substantial fraction of the Keplerian secular variations of third order. An internal check of the theory is carried out by a comparison of the natural frequencies of the orbit with those of a perturbed ellipse.
 Publication:

The Astronomical Journal
 Pub Date:
 April 1964
 DOI:
 10.1086/109260
 Bibcode:
 1964AJ.....69..223G