Trajectory design in the sun-earth-moon four-body problem

Roby Scott Wilson, Purdue University

Abstract

The objective of this work is the development of efficient techniques for the preliminary design of trajectories in the Sun-Earth-Moon four body problem that may involve lunar gravity assists and must satisfy specific trajectory requirements, such as apogee placement, launch constraints, or end state targeting. These types of trajectories are highly applicable to mission design in the restricted three and four body problems. The general solution approach proceeds in three steps. In the initial analysis, conic arcs and/or other types of trajectory segments are connected at patch points to construct a first approximation. Next, multi-conic methods are used to incorporate any additional force models that may have been neglected in the initial analysis. An optimization procedure is then employed to reduce the effective velocity discontinuities, while satisfying any constraints. Finally, a numerical differential corrections process results in a fully continuous trajectory that satisfies the design constraints, and includes appropriate lunar and solar gravitational models. The methodology is applicable to a wide range of trajectory solutions. Examples are presented for multiple lunar swing by trajectories, transfers to libration point orbits, and achieving escape velocity using lunar gravity assists. Additionally, the specific application of the methodology to the GENESIS trajectory is detailed. The three step process is also presented as a method to perform error analysis, and for the determination of effective recoveries from injection or other maneuver errors. Finally, a parametric study and a targeting scheme are presented in a preliminary investigation into optimizing the cost of transfer trajectories to libration point orbits.

Degree

Ph.D.

Advisors

Howell, Purdue University.

Subject Area

Aerospace materials|Mechanics

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