General Dynamics in the Restricted Full Three-Body Problem
- Paper number
IAC-06-C1.5.05
- Author
Ms. Julie Bellerose, University of Michigan, United States
- Coauthor
Dr. Daniel J. Scheeres, University of Michigan, United States
- Year
2006
- Abstract
The study of asteroids can provide answers to fundamental questions concerning the formation and evolution of our solar system. The motion of spacecraft in binary systems is of interest as at least sixteen percent of Near-Earth Asteroids are known to be binaries.
The problem formulation of the binary system itself and a spacecraft in such a system have been posed in earlier work, and are referred to as the Full Two Body Problem (F2BP) and the Restricted Full Three Body Problem (RF3BP), respectively. The conditions for relative equilibria and their stability in the F2BP were derived for a system with one of the bodies being a sphere. An ellipsoid-sphere system was further investigated and equilibrium solutions and their stability for a spacecraft in this gravitational field have also been studied.
As the non-equilibrium problem is more common in nature, whereas the F2BP may not be in equilibrium, our recent studies have looked at periodic orbits in both the F2BP and the RF3BP for an ellipsoid-sphere system. For the RF3BP, only periodic orbits close to the Lagrange Points L 4 were computed and analyzed. As a first approximation, the motion of the binary system was modeled as a uniform rotation, where the ratio of the angular spin of the general body to their system orbit rate was a free parameter. In a separate work, periodic orbits in the F2BP were also computed.
The current paper will combine these approaches into a single model. We will investigate the dynamics of a spacecraft in a gravity field defined by the solution to the F2BP.
It was found to be more convenient to express the dynamics of the RF3BP in a frame fixed to the general body. In this frame, we solve for the F2BP dynamics and substitute into the RF3BP model. We provide a general description of the system dynamics and we compute periodic and non-periodic orbits using a Poincaré Map Reduction Method. We show results for a range of free parameters and we investigate the stability of the periodic orbits. We also relate these results to the practical mission design of orbits in these systems.
- Abstract document
- Manuscript document
IAC-06-C1.5.05.pdf (🔒 authorized access only).
To get the manuscript, please contact IAF Secretariat.