Multi-body trajectory design strategies based on periapsis Poincaré maps

Diane Elizabeth Craig Davis, Purdue University

Abstract

Incorporating multi-body dynamics into preliminary spacecraft trajectory design expands the design space and provides trajectory options that may not otherwise be available. However, multi-body environments are not as well understood as those involving a single gravitational body, and preliminary design in these complicated scenarios is challenging. The current investigation focuses on preliminary design of orbits in the vicinity of the second primary in a 3- or 4-body model, for example, trajectories near a planet in a Sun-planet-moon system. The tidal acceleration due to the distant larger primary (P1) has significant influence on large orbits about the second primary (P 2). The effects on individual orbits are explored before the investigation is expanded to include large groups of orbits. Periapsis Poincaré maps are employed to simplify and organize the design space. By parameterizing trajectories in terms of periapse radius and orientation relative to the P 1-P2 line, the short- and long-term behaviors of many trajectories are predictable based on initial conditions. Trajectories that impact P 2 or escape its vicinity are easily identified. Initial conditions that lead to long-term orbits with particular characteristics, for example, periodic or quasi-periodic orbits, as well as quasi-frozen orbits, are selected from the maps. The existence of various types of trajectories at different spacecraft energy levels and in different P1-P2 systems is explored. The expanded knowledge of the design space in the vicinity of P2 is then applied to various mission design objectives. By employing periapsis Poincaré maps, mission objectives are satisfied in a simple, methodical process. In the same way, an examination of flybys from a multi-body perspective is insightful. Before adding the influence of a gravity assist body to the larger problem, the flyby itself is explored within the context of the 3-body problem. Then, the flyby design is combined with a tidally-influenced orbit to produce a trajectory that takes full advantage of its multi-body environment.

Degree

Ph.D.

Advisors

Howell, Purdue University.

Subject Area

Aerospace engineering

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