Zonal Harmonics of the Gravity Field in Def-Variables

To take advantage of the linear and regular formulation and treatment of Celestial Mechanics problems (Kustaanheimo & Stiefel 1965; Stiefel & Scheifele 1971; Deprit, Elipe & Ferrer 1994), Sharaf & Saad (1997) have given an analytical expansion of the Earth’s gravitational zonal potential in terms of Kustaanheimo-Stiefel (KS) regular elements (Stiefel & Scheifele 1971, §19), with special emphasis on its application to elliptic-type two-body orbits and, consequently, using a generalized (elliptic) eccentric anomaly as the independent variable.Motivated by these and other considerations based on the definition and use of KS elements, and following a treatment similar to that of Stiefel & Scheifele (1971, §19), we develop element equations corresponding to a DEF-formulation of the satellite problem under the effect of the zonal potential.