Gaussian variational equations for osculating elements of an arbitrary separable reference orbit.

Abstract

Lagrange-type equations are often used in planetary theory and sometimes in satellite theory. The equations express the variation of osculating Keplerian elements in terms of derivatives of a disturbing function or a perturbing potential. When the perturbing force is derivable from a potential, it is possible to convert the Lagrange-type equations to another form. This form, usually, attributed to Gauss, contains the perturbing forces instead of the derivatives of the potential. The case of an arbitrary separable reference orbit is discussed together with a lemma, a Keplerian check, and questions of the applicability of the equations to the spheroidal method.