The Primer Vector History of Low Energy Earth-Moon Transfers
- Paper number
IAC-07-C1.3.05
- Author
Mr. Paul Griesemer, University of Texas at Austin, United States
- Coauthor
Dr. Cesar Ocampo, The University of Texas at Austin, United States
- Year
2007
- Abstract
A set of necessary conditions for establishing the local optimality of low energy transfers is developed for the Earth-to-Moon transfer. In this method, a spacecraft is considered captured at the Moon if its Jacobi energy associated with the Earth-Moon restricted three body problem is such a value that bounds the spacecraft’s motion to the Moon. Transfers from low Earth orbit to a state captured with respect to the Moon using multiple impulsive maneuvers are considered. Necessary conditions for an optimal impulsive orbit transfer are derived by applying primer vector theory to the four body Sun-Earth-Moon gravitational system. This gravitational system is chosen to enable the necessary dynamics in ballistic Lunar capture trajectories. The optimal control problem is formulated with the following free variables: the location and the time of departure from low Earth Orbit, the transfer time, and the final state. A constraint is placed on the final state to ensure the spacecraft’s capture with respect to the Moon. Optimal transfers in this system are shown to meet certain conditions placed on the magnitude primer vector and its derivative. With the necessary conditions for optimality formalized, a ballistic Lunar capture transfer is examined. These transfers have been shown to demonstrate fuel savings over Hohmann transfers. However, their optimality has not been established. The primer vector is numerically propagated along a reference trajectory according to the adjoint equations of the optimal control problem. A two point boundary value problem is solved for the initial values of the primer vector and its derivative. The resulting primer vector history is used to demonstrate whether the transfer meets the optimality conditions. The analysis can be seen as a tool for possible improvement in Earth-Moon transfer performance. Earth-Moon transfers are analyzed as an example, but the method is general and can be extended to analyze any multiple gravitational body system.
- Abstract document
- Manuscript document
IAC-07-C1.3.05.pdf (🔒 authorized access only).
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