Available at: https://digitalcommons.calpoly.edu/theses/1853
Date of Award
MS in Aerospace Engineering
Dr. Kira Jorgensen Abercromby
Throughout the history of interplanetary space travel, the Newtonian dynamics of the two-body problem have been used to design orbital trajectories to traverse the solar system. That is, that a spacecraft orbits only one large celestial body at a time. These dynamics have produced impressive interplanetary trajectories utilizing numerous gravity assists, such as those of Voyager, Cassini, Rosetta and countless others. But these missions required large amounts of delta-v for their maneuvers and therefore large amounts of fuel mass. As we desire to travel farther and more extensively in space, these two-body dynamics lead to impossibly high delta-v values, and missions become infeasible due to the massive amounts of fuel that they would need to carry. In the last few decades a new dynamical system has been researched in order to find new ways of designing mission trajectories: the N-body problem. This utilizes the gravitational acceleration from multiple celestial bodies on a spacecraft, and can lead to unconventional, but very useful trajectories.
The goal of this thesis is to use the dynamics of the Circular Restricted Three-Body Problem (CRTBP) to design interplanetary transfer trajectories. This method of modelling orbital dynamics takes into account the gravitational acceleration of two celestial bodies acting on a spacecraft, rather than just one. The invariant manifolds of halo orbits about Sun-planet Lagrange points are used to aid in the transfer from one planet to another, and can lead into orbital insertion about the destination planet or flyby trajectories to get to another planet. This work uses this method of dynamics to test transfers from Earth to both Jupiter and Saturn, and compares delta-v and time of flight values to traditional transfer methods. Using the CRTBP can lead to reduced delta-v amounts for completing the same missions as two-body dynamics would. The aim of this work is to research if using manifolds for interplanetary transfers could be superior for some high delta-v missions, as it could drastically reduce the required delta-v for maneuvers. With this method it could be possible to visit more distant destinations, or carry more mass of scientific payloads, due to the reduced fuel requirements.
Results of this research showed that using manifolds to aid in interplanetary transfers can reduce the delta-v of both departure from Earth and arrival at a destination planet. For transfers to Jupiter the delta-v for the interplanetary transfer was reduced by 4.12 km/s compared to starting and ending in orbits about the planets. For a transfer to Saturn the delta-v required for the interplanetary transfer was reduced by 6.77 km/s. These delta-v savings are significant and show that utilizing manifolds can lead to lower energy interplanetary transfer trajectories, and have the potential to be useful for high delta-v missions.