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# Characterization of Quasi-Periodic Orbits for Applications in the Sun-Earth and Earth-Moon Systems

As destinations of missions in both human and robotic spaceﬂight become more exotic, a foundational understanding the dynamical structures in the gravitational environments enable more informed mission trajectory designs. One particular type of structure, quasi-periodic orbits, are examined in this investigation. Speciﬁcally, eﬃcient computation of quasi-periodic orbits and leveraging quasi-periodic orbits as trajectory design alternatives in the Earth-Moon and Sun-Earth systems. First, periodic orbits and their associated center manifold are discussed to provide the background for the existence of quasi-periodic motion on n-dimensional invariant tori, where n corresponds to the number of fundamental frequencies that deﬁne the motion. Single and multiple shooting diﬀerential corrections strategies are summarized to compute families 2-dimensional tori in the Circular Restricted Three-Body Problem (CR3BP) using a stroboscopic mapping technique, originally developed by Howell and Olikara. Three types of quasi-periodic orbit families are presented: constant energy, constant frequency ratio, and constant mapping time families. Stability of quasi-periodic orbits is summarized and characterized with a single stability index quantity. For unstable quasi-periodic orbits, hyperbolic manifolds are computed from the diﬀerential of a discretized invariant curve. The use of quasi-periodic orbits is also demonstrated for destination orbits and transfer trajectories. Quasi-DROs are examined in the CR3BP and the Sun-Earth-Moon ephemeris model to achieve constant line of sight with Earth and avoid lunar eclipsing by exploiting orbital resonance. Arcs from quasi-periodic orbits are leveraged to provide an initial guess for transfer trajectory design between a planar Lyapunov orbit and an unstable halo orbit in the Earth-Moon system. Additionally, quasi-periodic trajectory arcs are exploited for transfer trajectory initial guesses between nearly stable periodic orbits in the Earth-Moon system. Lastly, stable hyperbolic manifolds from a Sun-Earth L

_{1}quasi-vertical orbit are employed to design maneuver-free transfer from the LEO vicinity to a quasi-vertical orbit.## History

## Degree Type

- Master of Science

## Department

- Aeronautics and Astronautics

## Campus location

- West Lafayette

## Advisor/Supervisor/Committee Chair

Kathleen C. Howell## Additional Committee Member 2

David A.Spencer## Additional Committee Member 3

Diane C. Davis## Usage metrics

## Keywords

aerospaceengineeringtrajectorytrajectory designastrodynamicsthree bodythree body mechanicscircular restricted three body problemCR3BPquasi-periodic orbitsperiodic orbitsorbit mechanicscelestial mechanicsdynamical systemsdynamical systems theorydynamicsapplicationsorbitsastronauticsdifferential correctionsinvarianceinvariant circleinvariant torustorusinvariant toristroboscopic mappingmanifoldsSun-Earth systemEarth-Moon systemstabilitymultiple shootingstroboscopic mapeclipse avoidancevertical orbithalo orbitdistant retrograde orbitquasi-haloquasi-verticallissajousquasi-DRODRONRHOquasi-NRHOsynodic resonancetrajectory arcsmission designastromechanicsspaceflight mechanicsdynamical structuresAerospace Engineering

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