Critical inclinations in satellite theory

Abstract

The main problem of satellite theory is described in polar coordinates by a Hamiltonian function. It is proposed to find a solution of the Hamiltonian function with the following properties: (1) the reference orbit is Keplerian; (2) no restriction is imposed on the eccentricity; in particular, it is exempt of singularities - real or apparent - for small eccentricities; and (3) no restriction is imposed on the inclination; in particular, it is exempt of singularities - real or apparent - for small inclinations; also it is valid even in the neighborhood of inclinations at which the perigee is stationary.