Analytical methods for gravity-assist tour design
This dissertation develops analytical methods for the design of gravity-assist space- craft trajectories. Such trajectories are commonly employed by planetary science missions to reach Mercury or the Outer Planets. They may also be used at the Outer Planets for the design of science tours with multiple flybys of those planets’ moons. Recent work has also shown applicability to new missions concepts such as NASA’s Asteroid Redirect Mission. This work is based in the theory of patched conics. This document applies rigor to the concept of pumping (i.e. using gravity assists to change orbital energy) and cranking (i.e. using gravity assists to change inclination) to develop several analytic relations with pump and crank angles. In addition, transformations are developed between pump angle, crank angle, and v-infinity magnitude to classical orbit elements. These transformations are then used to describe the limits on orbits achievable via gravity assists of a planet or moon. This is then extended to develop analytic relations for all possible ballistic gravity-assist transfers and one type of propulsive transfer, v-infinity leveraging transfers. The results in this dissertation complement existing numerical methods for the design of these trajectories by providing methods that can guide numerical searches to find promising trajectories and even, in some cases, replace numerical searches altogether. In addition, results from new techniques presented in this dissertation such as Tisserand Graphs, the V-Infinity Globe, and Non-Tangent V-Infinty Leveraging provide additional insight into the structure of the gravity-assist trajectory design problem.
Longuski, Purdue University.
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