The research presented in this dissertation aims at characterizing the relative motion between spacecraft in periodic orbits in the circular restricted three-body problem. Proximity operations maneuvers, such as rendezvous and station-keeping, are approximated using a semi-analytical approach, i.e. by combining the analytical approximation of the nominal periodic orbit of the targeted spacecraft or targeted orbital location with simplified equations of motion that are derived by assuming that the chasing spacecraft and target (or targeted location) are always "close" to each other. The presented method is compared to the "exact" solutions obtained by numerically integrating the non-linear equations of motion of the circular restricted three-body problem. Orbit propagation examples, i.e. control-free trajectories, are shown along with proximity operation maneuvers for which delta-v's are computed. Suitable initial conditions for proximity operations are also computed based on known orbital transfers to specific orbits of interest, including halo orbits and distant retrograde orbits in the Earth-Moon and Mars-Phobos systems. Propellant-optimal results are found and compared to nearby local minima for a given set of time constraints in order to find a maneuver that allows for flexibility regarding departure and arrival time along with contingency plans. This approximation is validated against the use of the more computationally expensive full nonlinear equations of motion of the three-body problem and the "area of applicability" of this method is defined based on a metric that takes into account the initial conditions used when initiating proximity operations and the time-of-flight required to accomplish such maneuvers. Sample results for the Earth-Moon and Mars-Phobos systems are presented for cis-lunar and cis-Martian orbits of interest. The implementation of this method in pre-phase A mission design is also demonstrated in a sample end-to-end Earth-to-Mars mission. The method presented in this dissertation is shown to accurately describe the control-free relative motion between spacecraft in addition to being able to predict the necessary delta-v maneuvers for various proximity operations. Additionally, this method requires less computational time than full numerical methods while being able to assess its accuracy and the validity of the results obtained. Limitations of this method are imposed on the initial relative position between spacecraft as a function of the time required to accomplish proximity operation maneuvers.

Focusing on the orbital mechanics tools and techniques necessary to design, predict, and guide a trajectory of a spacecraft traveling between two or more bodies in a Solar System, this book covers the dynamical theory necessary for describing the motion of bodies in space, examines the N-body problem, and shows applications using this theory for designing interplanetary missions. While most orbital mechanics books focus primarily on Earth-orbiting spacecraft, with a brief discussion of interplanetary missions, this book reverses the focus and emphasizes the interplanetary aspects of space missions. Written for instructors, graduate students, and advanced undergraduate students in Aerospace and Mechanical Engineering, this book provides advanced details of interplanetary trajectory design, navigation, and targeting.

The stability of a satellite near the Lagrange points is studied in a Circular Restricted Three-Body Problem (CR3BP). The Runge Kutta method is used to trace out the orbital path of the satellite over a period of time. Various initial positions near the Lagrange points and velocities are used to produce various paths the satellite can take. The primary paths focused are on horseshoe paths. Horseshoe orbits are shown to be sometimes stable and sometimes chaotic.

Zusammenfassung: This conference attracts GN&C specialists from across the globe. The 2022 Conference was the 44th Annual GN&C conference with more than 230 attendees from six different countries with 44 companies and 28 universities represented. The conference presented more than 100 presentations and 16 posters across 18 topics. This year, the planning committee wanted to continue a focus on networking and collaboration hoping to inspire innovation through the intersection of diverse ideas. These proceedings present the relevant topics of the day while keeping our more popular and well-attended sessions as cornerstones from year to year. Several new topics including "Autonomous Control of Multiple Vehicles" and "Results and Experiences from OSIRIS-REx" were directly influenced by advancements in our industry. In the end, the 44th Annual GN&C conference became a timely reflection of the current state of the GN&C ins the space industry. The annual American Astronautical Society Rocky Mountain Guidance, Navigation and Control (GN&C) Conference began 1977 as an informal exchange of ideas and reports of achievements among guidance and control specialists local to the Colorado area. Bud Gates, Don Parsons, and Bob Culp organized the first conference, and began the annual series of meetings the following winter. In March 1978, the First Annual Rocky Mountain Guidance and Control Conference met at Keystone, Colorado. It met there for eighteen years, moving to Breckenridge in 1996 where it has been for over 25 years

Orbital Mechanics for Engineering Students, Second Edition, provides an introduction to the basic concepts of space mechanics. These include vector kinematics in three dimensions; Newton’s laws of motion and gravitation; relative motion; the vector-based solution of the classical two-body problem; derivation of Kepler’s equations; orbits in three dimensions; preliminary orbit determination; and orbital maneuvers. The book also covers relative motion and the two-impulse rendezvous problem; interplanetary mission design using patched conics; rigid-body dynamics used to characterize the attitude of a space vehicle; satellite attitude dynamics; and the characteristics and design of multi-stage launch vehicles. Each chapter begins with an outline of key concepts and concludes with problems that are based on the material covered. This text is written for undergraduates who are studying orbital mechanics for the first time and have completed courses in physics, dynamics, and mathematics, including differential equations and applied linear algebra. Graduate students, researchers, and experienced practitioners will also find useful review materials in the book. NEW: Reorganized and improved discusions of coordinate systems, new discussion on perturbations and quarternions NEW: Increased coverage of attitude dynamics, including new Matlab algorithms and examples in chapter 10 New examples and homework problems