The elimination of short and intermediate period terms from the problem of a high altitude earth satellite

Abstract

The Delaunay-Similar elements of Scheifele are applied to the problem of an Earth satellite that is perturbed by the Sun, Moon andJ ₂. All three effects are assumed to be the same order of magnitude. Since the external body terms depend explicitly on time, the time element appears as an additional angle variable. Also, the eccentric anomaly is used as a noncanonical auxiliary variable. A solution to the first Von Zeipel equation allows simultaneous elimination of short and intermediate period terms. The canonical transformation to mean elements is defined by a generating function that is a series involving Bessel coefficients.