A numerical study of powered Swing-Bys around the Moon

The present research studies Swing-By maneuvers combined with the application of an impulse at the spacecraft periapsis passage. The studies were made for different values of r(p) (periapsis distance), delta V (magnitude of the impulse), Psi (angle of approach) and alpha (angle that defines the direction of the impulse). The results show the best direction to apply the impulse for each specific geometry of the passage, maximizing the gains or energy losses. The results show, as an example, that an angle alpha near 20 degrees gives the best solution to maximize the energy gains for the situation where the periapsis distance is 1.1 Moon's radius and Psi = 90 degrees. This value goes to near -20 degrees when Psi = 270 degrees. In the case of maximizing the energy losses, two families with impulses against the direction of the spacecraft motion are found to be the best solutions. Conditions where the impulse generates a capture around the Moon or a collision are also mapped. For values larger than 1.1 Moon's radius for the periapsis distance, the angle that maximizes the energy variation increases. Empirical analytical equations are obtained that express the energy variation as a function of the angle of approach, which replaces well-known equations obtained from the two-body approximation.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