The long-period motion of 24-hour satellites

The long-period behavior of the Keplerian elements for an earth-orbiting 24-hour satellite is developed using extended phase-space canonical formalism. The effects of oblateness, equatorial ellipticity, and lunisolar perturbations are included in the developments. Small values of the eccentricity and inclination are assumed. All perturbations are developed through second order in terms of a set of nonsingular variables which are similar to the classical Poincare variables. Lunar motion is described by the second-order approximation of the Hill-Brown lunar theory. Solar motion is assumed to be elliptical about the earth-moon barycenter. Resonance due to equatorial ellipticity is handled by a Bohlin-type expansion of the Hamiltonian with respect to a reference semimajor axis.