Orbit structures in the planar circular restricted three-body problem and its applications

Köprücü, Şahin Ulaş
In this thesis, orbit structures in the planar Circular Restricted Three-Body Problem (CRTBP) are studied with a geometrical perspective. Unlike the two-body problem, there is no general analytical solution for the three-body problem due to its chaotic nature. Therefore, qualitative methods provide precious insights for the orbit structures in CRTBP. In this regard, stability analysis of the equilibrium points is performed and the local orbit structures like periodic, transit and non-transit orbits around those points are investigated. Then, the periodic orbits in the planar CRTBP, so called Lyapunov orbits, are studied in more detail in terms of their stability and global connections. The global orbit structures like homoclinic and heteroclinic orbits are calculated by utilizing the invariant manifolds associated to Lyapunov orbits. In addition, the sensitive dependence to the initial conditions of a Lyapunov orbit is investigated with the use of the Lyapunov exponent which is one of the chaos indicators. Lastly, the two possible applications of the CRTBP are demonstrated. The first application is about constructing fuel efficient low-energy spacecraft trajectories from Earth to Moon by using CRTBPs of the Sun-Earth-spacecraft and the Earth-Moon-spacecraft. The second application is about the search for the undiscovered Planet 9 with sub-relativistic spacecrafts in the context of Sun-Planet 9-spacecraft CRTBP to investigate whether considering the Sun yields new prospects for the detection of Planet 9.
Citation Formats
Ş. U. Köprücü, “Orbit structures in the planar circular restricted three-body problem and its applications,” M.S. - Master of Science, Middle East Technical University, 2023.