Spacecraft trajectory design in the context of a coherent restricted four -body problem

Jose Javier Guzman, Purdue University

Abstract

Consider the design of transfer trajectories to the vicinity of the Sun-Earth collinear libration points. First, note that the equilibrium points actually exist only in the circular restricted three-body problem (CROP). Second, conic solutions are generally not useful (even as initial guesses). Therefore, for libration point missions, most of the qualitative analysis must be accomplished from the perspective of a model with, at least, three bodies. Unfortunately, in some cases, the qualitative behavior that is apparent in the CR3BP might be completely lost due to lunar perturbations. Alternatively, a transfer strategy to exploit the potential advantage of the Moon's presence through gravitational encounters is difficult to implement within the context of either the CR3BP or a model that employs ephemeris information for the Sun and Earth locations. Clearly, a formulation of the four-body problem is warranted. To maximize the four-body model as a useful component, special solutions—such as periodic and quasi-periodic trajectories in the restricted four-body problem—are initially isolated and identified. Semi-analytical approximations (for the special solutions) are obtained with the method of spectral balance and refined via differential corrections. Then, an analysis from the perspective of dynamical systems proceeds. Such an approach is employed in the Sun-Earth system to develop transfer options to L2 Lissajous trajectories; subsequent applications include NASA's Microwave Anisotropy Probe (MAP) mission.

Degree

Ph.D.

Advisors

Howell, Purdue University.

Subject Area

Aerospace materials

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