A numerical study of powered Swing-Bys around the Moon

•Find geometry for a powered Swing-By in the Moon.•Explore maximum and minimum variations of energy.•Show the best impulse location.•Analytical empirical equations are derived to express the results.

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 rprp (periapsis distance), δVδV (magnitude of the impulse), ΨΨ (angle of approach) and αα (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 αα near 20° gives the best solution to maximize the energy gains for the situation where the periapsis distance is 1.1 Moon’s radius and Ψ=90°Ψ=90°. This value goes to near -20°-20° when Ψ=270°Ψ=270°. 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.