Third body perturbation using a single averaged model considering elliptic orbits for the disturbing body
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In the present work, we expanded the study done by Solorzanol(1) including the eccentricity of the perturbing body. The assumptions used to develop the single-averaged analytical model are the same ones of the restricted elliptic three-body problem. The disturbing function was expanded in Legendre polynomials up to fourth-order. After that, the equations of motion are obtained from the planetary equations and we performed a set of numerical simulations. Different initial eccentricities for the perturbing and perturbed body are considered. The results obtained perform an analysis of the stability of a near-circular orbits and investigate under which conditions this orbit remain near-circular.