Families of low DeltaV earth-to-moon trajectories in the restricted three-body problem.

摘要

In the search for fuel-efficient trajectories to the Moon, Sweetser used the circular restricted three-body problem (CR3BP) and Jacobi's constant to mathematically compute a theoretical minimum DeltaV bound for Earth-to-Moon trajectories. Efforts documented in this thesis were focused on computing physical trajectories exploiting Sweetser's analysis and its conclusions. Families of trajectories associated with this minimum DeltaV were sought through numerical integration of the restricted three-body problem (R3BP) equations of motion. Strategies were developed through trial-and-error approaches to find various methods to compute families of trajectories with low DeltaVs and/or times of flight for the CR3BP. The lowest DeltaV for an Earth-to-Moon trajectory found was 71 m/sec greater than Sweetser's theoretical minimum and 167 m/sec less than the classic two-body Hohmann transfer. The study also examined the effects of adding the ellipticity of the Earth-Moon orbit to the R3BP. The elliptic restricted three-body problem (ER3BP) was numerically integrated successfully resulting in families of trajectories using the same design methods as the CR3BP. Since the theoretical minimum DeltaV computed by Sweetser was a function of inclination, this study calculated the effects on Earth-to-Moon trajectories when inserted into inclined lunar orbits from 0--90°. Finally, the influence of the solar gravity perturbation on Earth-to-Moon trajectories was evaluated. This effort was successful in computing Earth-to-Moon trajectories and evaluating some perturbation models, however more work is required to further reduce the total DeltaV toward Sweetser's theoretical lower bound minimum DeltaV and to find more "useful" trajectories. Also, the trial-and-error design method requires optimization to further study the gravitational and perturbation effects on the trajectories.