The zonal harmonic perturbations of an artificial satellite

Abstract

The paper extends the known solution of the Main Problem of the artificial satellite theory to include the effects of all the higher zonal harmonics of the geopotential. The method of von Zeipel is used to calculate the secular and the long-periodic variations of orders J and / 2, respectively. The results are exhibited in a compact form, in terms of the associated Legendre polynomials in (1- e2)- and in cosi.