While the interest in the Martian moons increases, the low-thrust propulsion technology is expected to enable novel mission scenarios but is associated with unique trajectory design challenges. Accordingly, the current investigation introduces a multi-phase low-thrust design framework. The trajectory of a potential spacecraft that departs from the Earth vicinity to reach both of the Martian moons, is divided into four phases. To describe the motion of the spacecraft under the influence of gravitational bodies, the two-body problem (2BP) and the Circular-Restricted Three Body Problem (CR3BP) are employed as lower-fidelity models, from which the results are validated in a higher-fidelity ephemeris model. For the computation and optimization of low-thrust trajectories, direct collocation algorithm is introduced. Utilizing the dynamical models and the numerical scheme, the low-thrust trajectory design challenge associated each phase is located and tackled separately. For the heliocentric leg, multiple optimal control problems are formulated between the planets in heliocentric space over different departure and arrival epochs. A contour plot is then generated to illustrate the trade-off between the propellant consumption and the time of flight. For the tour of the Martian moons, the science orbits for both moons are defined. Then, a new algorithm that interfaces the Q-law guidance scheme and direct collocation algorithm is introduced to generate low-thrust transfer trajectories between the science orbits. Finally, an end-to-end trajectory is produced by merging the piece-wise solutions from each phase. The validity of the introduced multi-phase formulation is confirmed by converging the trajectories in a higher-fidelity ephemeris model.<br>

<div>In order to answer the most pressing scientific questions about the two Martian moons, Phobos and Deimos, new remote sensing observations are required. The best way to obtain global high resolution observations of Phobos and Deimos is through dedicated missions to each body that utilize close-proximity orbits, however much of the orbital tradespace is too unstable to realistically or safely operate a mission.</div><div><br></div><div>This thesis explores the dynamics and stability characteristics of trajectories near Deimos. The family of distant retrograde orbits that are inclined out of the Deimos equatorial plane, known as quasi-satellite orbits, are explored extensively. To inform future mission design and CONOPS, the sensitivities and stability of distant retrograde and quasi-satellite orbits are examined in the vicinity of Deimos, and strategies for transferring between DROs are demonstrated. Finally, a method for designing quasi-satellite science orbits is demonstrated for a set of notional instruments and science requirements for a Deimos remote sensing mission.<br></div>

<div>Planetary rings are, and have been, a common feature throughout the solar system.</div><div>Rings have been observed orbiting each of the giant planets, several Trans-Neptunian Objects, and debris rings are thought to have orbited both Earth and Mars.</div><div>The bright, massive planetary rings orbiting Saturn have been observed for centuries, and the Cassini Mission has given researchers a recent and extensive closeup view of these rings.</div><div>The Saturn ring system has served as a natural laboratory for scientists to understand the dynamics of planetary ring systems, as well as their influence on satellites orbiting nearby.</div><div>Researchers have shown that planetary ring systems and nearby satellites can be tightly-coupled systems.</div><div><br></div><div>In this work, I discuss the physics which dominate the dynamical evolution of planetary ring systems, as well as the interactions with any nearby satellites.</div><div>Many of these dynamics have been incorporated into a one-dimensional mixed Eulerian-Lagrangian numerical model that I call "RING-MOONS," to simulate the long-term evolution of tightly coupled satellite-ring systems.</div><div>In developing RING-MOONS, I have discovered that there are three evolution regimes for tightly-coupled satellite-ring systems which I designate as the "Boomerang," "Torque-Dependent," and "Slingshot" regimes.</div><div>Each regime may be defined using the rotation period of the primary body and the bulk density of the ring material.</div><div><br></div><div>The slow rotation period of Mars places it in the Boomerang regime.</div><div>I hypothesize that a giant impact with Mars ejected material into orbit, forming a debris ring around the planet.</div><div>Using RING-MOONS, I demonstrate how Lindblad torques cause satellites which form at the edge of the ring to initially migrate away from the ring, but over time as the mass of the ring decreases, tidal torques always cause the satellites to migrate inwards.</div><div>Assuming the satellites rapidly tidally disrupt upon migrating to the rigid Roche limit, a new ring is formed.</div><div>I show that debris material cycles between orbiting Mars as a planetary ring, or as discrete satellites, and that Phobos may be a product of a repeated satellite-ring cycle.</div><div>Uranus, which has a faster rotation rate falls within the Torque-Dependent regime.</div><div>Hypothesizing that a massive ring once orbited Uranus, I use RING-MOONS to demonstrate how the satellite Miranda may have formed from such a ring, and migrated outwards to its current orbit, but that any other satellites would have migrated inwards overtime.</div><div><br></div><div>Lastly, I examine Trans-Neptunian Objects (TNOs) in binary systems.</div><div>Tidal torques exerted on each body can decrease the mutual semi-major axis of the system.</div><div>I outline the conditions for which a fully synchronous system may experience a complete decay of the mutual orbit due to tidal torques.</div><div>As the semi-major axis decreases, it is possible for the smaller of the two bodies to shed mass before coming into contact with the more massive to form a contact binary.</div><div>I hypothesize that Chariklo and Chiron are contact binaries that formed via the tidal collapse of a binary TNOs system, and demonstrate how mass shedding may have occurred to form the rings observed today.</div>

<div>There is an increasing interest in future space missions devoted to the exploration of key moons in the Solar system. These many different missions may involve libration point orbits as well as trajectories that satisfy different endgames in the vicinities of the moons. To this end, an efficient design strategy to produce low-energy transfers between the vicinities of adjacent moons of a planetary system is introduced that leverages the dynamics in these multi-body systems. Such a design strategy is denoted as the moon-to-moon analytical transfer (MMAT) method. It consists of a general methodology for transfer design between the vicinities of the moons in any given system within the context of the circular restricted three-body problem, useful regardless of the orbital planes in which the moons reside. A simplified model enables analytical constraints to efficiently determine the feasibility of a transfer between two different moons moving in the vicinity of a common planet. Subsequently, the strategy builds moon-to-moon transfers based on invariant manifold and transit orbits exploiting some analytical techniques. The strategy is applicable for direct as well as indirect transfers that satisfy the analytical constraints. The transition of the transfers into higher-fidelity ephemeris models confirms the validity of the MMAT method as a fast tool to provide possible transfer options between two consecutive moons. </div><div> </div><div>The current work includes sample applications of transfers between different orbits and planetary systems. The method is efficient and identifies optimal solutions. However, for certain orbital geometries, the direct transfer cannot be constructed because the invariant manifolds do not intersect (due to their mutual inclination, distance, and/or orbital phase). To overcome this difficulty, specific strategies are proposed that introduce intermediate Keplerian arcs and additional impulsive maneuvers to bridge the gaps between trajectories that connect any two moons. The updated techniques are based on the same analytical methods as the original MMAT concept. Therefore, they preserve the optimality of the previous methodology. The basic strategy and the significant additions are demonstrated through a number of applications for transfer scenarios of different types in the Galilean, Uranian, Saturnian and Martian systems. Results are compared with the traditional Lambert arcs. The propellant and time-performance for the transfers are also illustrated and discussed. As far as the exploration of Phobos and Deimos is concerned, a specific design framework that generates transfer trajectories between the Martian moons while leveraging resonant orbits is also introduced. Mars-Deimos resonant orbits that offer repeated flybys of Deimos and arrive at Mars-Phobos libration point orbits are investigated, and a nominal mission scenario with transfer trajectories connecting the two is presented. The MMAT method is used to select the appropriate resonant orbits, and the associated impulsive transfer costs are analyzed. The trajectory concepts are also validated in a higher-fidelity ephemeris model.</div><div> </div><div>Finally, an efficient and general design strategy for transfers between planetary moons that fulfill specific requirements is also included. In particular, the strategy leverages Finite-Time Lyapunov Exponent (FTLE) maps within the context of the MMAT scheme. Incorporating these two techniques enables direct transfers between moons that offer a wide variety of trajectory patterns and endgames designed in the circular restricted three-body problem, such as temporary captures, transits, takeoffs and landings. The technique is applicable to several mission scenarios. Additionally, an efficient strategy that aids in the design of tour missions that involve impulsive transfers between three moons located in their true orbital planes is also included. The result is a computationally efficient technique that allows three-moon tours designed within the context of the circular restricted three-body problem. The method is demonstrated for a Ganymede->Europa->Io tour.</div>