First order semianalytic satellite theory with recovery of the short period terms due to third body and zonal perturbations

Perturbation theory is applied to the satellite orbit problem to recover in an analytic method the short period terms due to perturbations by the sun, moon and the zonal harmonics of the earth. The perturbation analysis is carried out by means of Lie series and is developed through the first order only. The Hamiltonian is obtained, the short period terms are eliminated and the generating function W is found by integration. From W the coordinates are defined from the Lie series by a transformation equation. These coordinates are nonsingular for small eccentricity. Secular, long and medium period effects are treated using the method of averaging. The singly averaged equations are expanded to high order in the parallax factor. Motion of the third body is included in the analysis. The result is a very fast and accurate semianalytic ephemeris generator. Numerical examples are given.