<div>Over the past twenty years, ridesharing opportunities for smallsats, i.e., secondary payloads, has increased with the introduction of Evolved Expendable Launch Vehicle (EELV) Secondary Payload Adapter (ESPA) rings. However, the orbits available for these secondary payloads is limited to Low Earth Orbits (LEO) or Geostationary Orbits (GEO). By incorporating a propulsion system, propulsive ESPA rings offer the capability to transport a secondary payload, or a collection of payloads, to regions beyond GEO. In this investigation, the ridesharing scenario includes a secondary payload in a dropped-off Geosynchronous Transfer Orbit (GTO) and the region of interest is the vicinity near the Sun-Earth Lagrange points. However, mission design for secondary payloads faces certain challenges. A significant mission constraint for a secondary payload is the drop-off orbit orientation, as it is dependent on the primary mission. To address this mission constraint, strategies leveraging dynamical structures within the Circular Restricted Three-Body Problem (CRTBP) are implemented to construct efficient and flexible transfers from GTO to orbits near Sun-Earth Lagrange points. First, single-maneuver ballistic transfers are constructed from a range of GTO departure orientations. The ballistic transfer utilize trajectories within the stable manifold structure associated with periodic and quasi-periodic orbits near the Sun-Earth L1 and L2 points. Numerical differential corrections and continuation methods are leveraged to create families of ballistic transfers. A collection of direct ballistic transfers are generated that correspond to a region of GTO departure locations. Additional communications constraints, based on the Solar Exclusion Zone and the Earth’s penumbra shadow region, are included in the catalog of ballistic transfers. An integral-type path condition is derived and included throughout the differential corrections process to maintain transfers outside the required communications restrictions. The ballistic transfers computed in the CRTBP are easily transitioned to the higher-fidelity ephemeris model and validated, i.e., their geometries persist in the ephemeris model. To construct transfers to specific orbits near Sun-Earth L1 or L2, families of two-maneuver transfers are generated over a range of GTO departure locations. The two-maneuver transfers consist of a maneuver at the GTO departure location and a Deep Space Maneuver (DSM) along the trajectory. Families of two-maneuver transfers are created via a multiple- shooting differential corrections method and a continuation process. The generated families of transfers aid in the rapid generation of initial guesses for optimized transfer solutions over a range of GTO departure locations. Optimized multiple-maneuver transfers into halo and Lissajous orbits near Sun-Earth L1 and L2 are included in this analysis in both the CRTBP model and the higher-fidelity ephemeris model. Furthermore, the two-maneuver transfer strategy employed in this analysis are easily extended to other Three-Body systems. </div>

This concept of calculating, optimizing, and utilizing a trajectory known as a ``Free Return Trajectory" to facilitate spacecraft rendezvous with Near-Earth Asteroids is presented in this dissertation. A Free Return Trajectory may be defined as a trajectory that begins and ends near the same point, relative to some central body, without performing any deterministic velocity maneuvers (i.e., no maneuvers are planned in a theoretical sense for the nominal mission to proceed). Free Return Trajectories have been utilized previously for other purposes in astrodynamics, but they have not been previously applied to the problem of Near-Earth Asteroid rendezvous. Presented here is a series of descriptions, algorithms, and results related to trajectory initial guess calculation and optimal trajectory convergence. First, Earth-centered Free Return Trajectories are described in a general manner, and these trajectories are classified into several families based on common characteristics. Next, these trajectories are used to automatically generate initial conditions in the three-body problem for the purpose of Near-Earth Asteroid rendezvous. For several bodies of interest, example initial conditions are automatically generated, and are subsequently converged, resulting in feasible, locally-optimal, round-trip trajectories to Near-Earth Asteroids utilizing Free Return Trajectories. Subsequently, a study is performed on using an unpowered flyby of the Moon to lower the overall DV cost for a nominal round-trip voyage to a Near-Earth Asteroid. Using the Moon is shown to appreciably decrease the overall mission cost. In creating the formulation and algorithms for the Lunar flyby problem, an initial guess routine for generic planetary and lunar flyby tours was developed. This continuation algorithm is presented next, and details a novel process by which ballistic trajectories in a simplistic two-body force model may be iteratively converged in progressively more realistic dynamical models until a final converged ballistic trajectory is found in a full-ephemeris, full-dynamics model. This procedure is useful for constructing interplanetary transfers and moon tours in a realistic dynamical framework; an interplanetary and an inter-moon example are both shown. To summarize, the material in this dissertation consists of: novel algorithms to compute Free Return Trajectories, and application of the concept to Near-Earth Asteroid rendezvous; demonstration of cost-savings by using a Lunar flyby; and a novel routine to transfer trajectories from a simplistic model to a more realistic dynamical representation. / text

An integral part of NASA's vision for the coming years is a sustained infrastructure in cislunar space. The current baseline trajectory for this facility is a Near Rectilinear Halo Orbit (NRHO), a periodic orbit in the Circular Restricted Three-Body Problem. One of the goals of the facility is to serve as a proving ground for human spaceflight operations in deep space. Thus, this investigation focuses on transfers between the baseline NRHO and a family of periodic orbits that originate from a period-doubling bifurcation along the halo family. This new family of orbits has been termed the ``butterfly" family. This investigation also provides an overview of the evolution for a large subset of the butterfly family. Transfers to multiple subsets of the family are found by leveraging different design strategies and techniques from dynamical systems theory. The different design strategies are discussed in detail, and the transfers to each of these regions are compared in terms of propellant costs and times of flight.