A Study of Single- and Double-Averaged Second-Order Models to Evaluate Third-Body Perturbation Considering Elliptic Orbits for the Perturbing Body

The equations for the variations of the Keplerian elements of the orbit of a spacecraft perturbed by a third body are developed using a single average over the motion of the spacecraft, considering an elliptic orbit for the disturbing body. A comparison is made between this approach and the more used double averaged technique, as well as with the full elliptic restricted three-body problem. the disturbing function is expanded in Legendre polynomials up to the second order in both cases. the equations of motion are obtained from the planetary equations, and several numerical simulations are made to show the evolution of the orbit of the spacecraft. Some characteristics known from the circular perturbing body are studied: circular, elliptic equatorial, and frozen orbits. Different initial eccentricities for the perturbed body are considered, since the effect of this variable is one of the goals of the present study. the results show the impact of this parameter as well as the differences between both models compared to the full elliptic restricted three-body problem. Regions below, near, and above the critical angle of the third-body perturbation are considered, as well as different altitudes for the orbit of the spacecraft.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Inst Nacl Pesquisas Espaciais, BR-12227010 Sao Jose Dos Campos, SP, BrazilUniversidade Federal de São Paulo UNIFESP, BR-12231280 Sao Jose Dos Campos, SP, BrazilUniversidade Federal de São Paulo UNIFESP, BR-12231280 Sao Jose Dos Campos, SP, BrazilCNPq: 150195/2012-5CNPq: 304700/2009-6FAPESP: 2011/09310-7FAPESP: 2011/08171-3Web of Scienc