Semi-Analytical Solutions for Proximity Operations in the Circular Restricted Three-Body Problem
Open Access
- Author:
- Conte, Davide
- Graduate Program:
- Aerospace Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 31, 2019
- Committee Members:
- David Bradley Spencer, Dissertation Advisor/Co-Advisor
David Bradley Spencer, Committee Chair/Co-Chair
Robert Graham Melton, Committee Member
Sven G Bilen, Committee Member
Joseph Paul Cusumano, Outside Member - Keywords:
- Astrodynamics
Moon
Mars
Phobos
Proximity Operations
Relative Motion
Semi-Analytical - Abstract:
- The research presented in this dissertation aims at characterizing the relative motion between spacecraft in periodic orbits in the circular restricted three-body problem. Proximity operations maneuvers, such as rendezvous and station-keeping, are approximated using a semi-analytical approach, i.e. by combining the analytical approximation of the nominal periodic orbit of the targeted spacecraft or targeted orbital location with simplified equations of motion that are derived by assuming that the chasing spacecraft and target (or targeted location) are always "close" to each other. The presented method is compared to the "exact" solutions obtained by numerically integrating the non-linear equations of motion of the circular restricted three-body problem. Orbit propagation examples, i.e. control-free trajectories, are shown along with proximity operation maneuvers for which delta-v's are computed. Suitable initial conditions for proximity operations are also computed based on known orbital transfers to specific orbits of interest, including halo orbits and distant retrograde orbits in the Earth-Moon and Mars-Phobos systems. Propellant-optimal results are found and compared to nearby local minima for a given set of time constraints in order to find a maneuver that allows for flexibility regarding departure and arrival time along with contingency plans. This approximation is validated against the use of the more computationally expensive full nonlinear equations of motion of the three-body problem and the "area of applicability" of this method is defined based on a metric that takes into account the initial conditions used when initiating proximity operations and the time-of-flight required to accomplish such maneuvers. Sample results for the Earth-Moon and Mars-Phobos systems are presented for cis-lunar and cis-Martian orbits of interest. The implementation of this method in pre-phase A mission design is also demonstrated in a sample end-to-end Earth-to-Mars mission. The method presented in this dissertation is shown to accurately describe the control-free relative motion between spacecraft in addition to being able to predict the necessary delta-v maneuvers for various proximity operations. Additionally, this method requires less computational time than full numerical methods while being able to assess its accuracy and the validity of the results obtained. Limitations of this method are imposed on the initial relative position between spacecraft as a function of the time required to accomplish proximity operation maneuvers.