LAUSR

Abstract This paper deals with the integrations of homogeneous quasi-Keplerian Hamiltonians, that is, perturbed Kepler Hamiltonians which perturbation is of the form ∑ j = 2 N A j ∕ r j with A j constant. Although there are many applications of these Hamiltonians in Physics, Astronomy and Astrodynamics, we focus our interest on a particular case in the core of Artificial Satellite Theory, the Cid’s radial intermediary. For this problem, we integrate the equations of motion in two different ways, by means of the elliptic P -Weierstrass function and by using the Krilov-Bogoliubov averaging method to integrate a perturbed harmonic oscillator. In this case, the resulting solution is given in terms of the classical Kepler’s equation, with no need of introducing more complex generalized Kepler’s equation.