## AAS 99-160

## The Main Oblateness Perturbation Problem is DEF Regular Elements

#### I. Aparicia, L. Floria

University de Valladolid, Spain
## Abstract

Within the linear and regular formulation and treatment of Celestial Mechanics problems, we apply the so-called "focal method" to derive the analytical expression, in terms of elements attached to the linearizing DEF-variables (introduced by Deprit, Elipe and Ferrer), of the second zonal harmonic of the geopotential, and obtain the corresponding second-order quasi-linear differential equations of motion for any value of the orbital eccentricity. These quasi-linear equations govern a set of four perturbed oscillators. The DEF-elements of the motion are constants of integration involved in the general solution of the unperturbed equations generated by the Kepler problem, whereas for perturbed problems they satisfy systems of first order differential equations (the element equations corresponding to a DEF-formulation). The DEF-element equations for the J2 problem are derived, and integrated analytically in terms of function of a true-like anomaly.