Analysis of Low-Energy Lunar Transfers in a High-Fidelity Dynamics Model

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Virginia Tech


Renewed interest in returning to the Moon, emboldened by recent directives and missions by NASA, has necessitated the establishment of lunar infrastructure to support continuous human presence. With that, the objective of making this return more cost effective has gained significant importance. Low energy lunar transfers are more efficient ways to reach the Moon than the traditional Hohmann-type transfer. These trajectories leverage the multi-body gravitational effects to reduce overall delta-v requirements, in some cases removing the capture delta-v completely. While the time of flight for these transfers can be much longer than a Hohmann-type transfer, the chaotic design space of these transfers can enable large changes in arrival conditions at the Moon for small changes in initial conditions. Many investigations of these transfers take place in simplified dynamical models, such as the Planar Circular Restricted Three Body Problem, with very few higher-fidelity models being implemented. This approach is good to understand the dynamics of these trajectories as well as provide initial guesses for higher-fidelity models; but approximating the dynamics heavily make these models less applicable to mission design. This thesis aims to investigate the application of a higher-order model to simulate these trajectories. STK Astrogator was used to recreate the NASA GRAIL trajectory; and from the recreated trajectory, a nominal trajectory absent of mid-course corrections was established. This nominal trajectory was used to perform parametric and variational studies of departure and arrival conditions as well as compare to a nominal trajectory in a reduced-fidelity model. An investigation into the post launch correction burn requirements following launch vehicle under-performance was completed. Utilizing low energy transfers proved beneficial to adjusting arrival conditions for low delta-v requirements. All arrival inclinations are reasonably achievable for around 255 m/s. Using 255 m/s as a baseline, right ascension of the ascending node could be reached in a 40 degree range and argument of periapsis in a 50 degree range. Lunar insertion arrival can be varied by 7 hours on either side for less than 80 m/s. Trans-lunar injection epoch can be varied by 7 hours on either side of nominal departure for less than 4 m/s. Orbit radius and initial velocity are the most expensive errors to correct. These trajectories can be tuned to reduce the overall mid-course correction delta-v requirement for differing arrival inclinations if other orbital elements are relaxed. A relationship between placement of post-launch correction maneuver for velocity or radius errors was found. Comparing the trajectory in STK to the Inclined Bi-Elliptic Restricted Four Body problem, revealed that timing of the trajectory is variable while keeping the same arrival and departure conditions. However, solar radiation pressure cannot be ignored for more accurate simulation of these trajectories. This investigation has shown that low energy lunar transfers are a viable method to reach the Moon and their chaotic nature can be leveraged to relax restrictions in the design space.



STK, NASA GRAIL, Low-Energy Lunar Transfer, High-Fidelity, Simulation