Investigation of transfer trajectories to periodic horseshoe orbits

Jayme M Howsman, Purdue University

Abstract

Horseshoe orbits are both an intriguing natural occurrence in the solar system and a viable option for spacecraft mission design. Several asteroids, as well as a pair of Saturnian moons, are known to occupy horseshoe orbits. Since horseshoe orbits encompass three libration points, L3, L4, and L 5, they offer a unique scientific exploration opportunity, as well as the potential for extended-mission options for a spacecraft. Therefore, in this preliminary investigation into transfer trajectories to horseshoe orbits, planar, periodic horseshoe orbits are computed and analyzed in both the Saturn-Titan and Sun-Jupiter systems. Several techniques for computing transfer trajectories between libration point orbits and horseshoe orbits are investigated. Significant variation in maneuver cost and time-of-flight is observed in the various types of transfer trajectories. One of the methods investigated for computing transfers incorporates dynamical systems techniques, and achieves extremely low maneuver costs. This technique utilizes Poincar´e maps that reflect the unstable manifolds corresponding to a departure orbit and the stable manifolds computed for an arrival horseshoe trajectory to logically uncover low-cost transfers. For examples in both the Saturn-Titan and Sun-Jupiter systems, cost-free (theoretical) heteroclinic connections are determined between Lyapunov orbits and horseshoe trajectories. The results compiled in this preliminary investigation demonstrate that a transfer to a horseshoe orbit is a feasible option for low-cost mission applications.

Degree

M.S.A.A.

Advisors

Howell, Purdue University.

Subject Area

Aerospace engineering

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