One of the most important aspects of preliminary interplanetary mission planning entails designing a trajectory that delivers a spacecraft to the required destinations and accomplishes all the objectives. The design tool described in this thesis allows an investigator to explore various interplanetary trajectories quickly and easily. The design tool employs the patched conic method to determine heliocentric and planetocentric trajectory information. An existing Lambert Targeting routine and other common algorithms are utilized in conjunction with the design tool's specialized code to formulate an entire trajectory from Earth departure to arrival at the destination. The tool includes many options for the investigator to accurately configure the desired trajectory, including planetary gravity assists, deep space maneuvers, and various departure and arrival conditions. The trajectory design tool is coded in MATLAB, which provides access to three dimensional plotting options and user adaptability. The design tool also incorporates powerful MATLAB optimization functions that adjust trajectory characteristics to find a configuration that yields the minimum spacecraft propellant in the form of change in velocity.
Interplanetary travel is a difficult task due to the high fuel mass required to reach other planets. Minimizing the cost of the manoeuvres (and, in turn, the fuel mass) is the objective preliminary mission design. During this phase, a large number of potential solutions must be evaluated quickly in search of feasible trajectories. This means computationally fast but simple models are preferred over accurate but slow models. Additionally, the process demands for an automatic execution due to the vast amount of solutions that must be evaluated. One of the major improvements regarding space travel was the discovery of the gravity assist, where a spacecraft uses the gravitational pull of a flyby planet to change its velocity with respect to the Sun. This allows reducing the amount of fuel mass, which in turn increases the science payload available for the mission. This thesis deals with the optimization of interplanetary trajectories with gravity assist. From an engineering approach, the thesis aims at producing an automatic optimizer of interplanetary trajectories with gravity assist manoeuvres aimed to preliminary mission design applications. From a scientific approach, the thesis aims at identifying key issues in the literature that allow for improvement and presenting novel implementations. Finally, the thesis has a strong educational component: the code and tools are specially focused towards an easy understanding and analysis of the underlying methods rather than producing a computationally efficient code. The result from this work is an automatic optimizer of multi gravity-assist interplanetary trajectories. The tool is fully modular and works with a double-loop approach: an outer loop obtains feasible sequences of planets using the Tisserand graph and an inner loop finds the best trajectory for each sequence using a hybrid heuristic optimizer and a patched conics method. Five key issues have been investigated and improved upon during the thesis: we provide an improved solution method for the Kepler equation, we have conducted an extensive bibliographic research of Lambert's problem and analyzed the representative methods to select the best for our application, we have recovered and improved the Lambert's problem method by Simó , we present two different models for the patched conics method, we have developed an automatic method to traverse the Tisserand graph and finally we have implemented several heuristic optimization methods and coupled them with an islands model. The resulting tool has already proved to work in operational mission design scenarios. However, it lends itself to many improvements and upgrades, in particular increasing the level of automation, improving the physical model and the patched conics method robustness, improving the visualization capabilities during the optimization stage and translating the code into compiled language to increase the computational performance with complex missions and intensive simulations.
This textbook introduces the theories and practical procedures used in planetary spacecraft navigation. Written by a former member of NASA's Jet Propulsion Laboratory (JPL) navigation team, it delves into the mathematics behind modern digital navigation programs, as well as the numerous technological resources used by JPL as a key player in the field. In addition, the text offers an analysis of navigation theory application in recent missions, with the goal of showing students the relationship between navigation theory and the real-world orchestration of mission operations.
Explores the history and significance of interplanetary space missions. Features detailed explanations and mathematical methods for trajectory optimization. Includes detailed explanations and mathematical methods for mission analysis for interplanetary missions. Covers the introduction, mathematical methods, and applications of the N-body problem (N>2). Discusses navigation and targeting for interplanetary mission.
Trajectory design is traditionally performed under very strict constraints or simplifications. This is because full-force models have thus far eluded analytical solution. One common simplification is the two-body assumption, where the only bodies considered are the spacecraft and a central mass. This simplification yields fairly accurate results for a small number of specific cases (binary stars, low-Earth orbit). However, once the orbital regime enters the interplanetary range, where multiple gravitational bodies are relevant, simple two-body calculations prove inadequate. In response, the patched-conic approach was used, where multiple two-body trajectories would be "patched" together to form an approximate path for the spacecraft. This approach, however, still employed the two-body simplification and so the hidden constraints of the two-body problem are carried over. Consequently, while this method produces useful trajectories, it does not yield the most efficient ones. While the n-body problem had not been explicitly solved, numerical methods with modern computational software programs can be used to identify extremely efficient trajectories by taking into account a greater number of bodies. It was recently discovered that gravitational pathways linking the Solar System's Lagrange points can provide extremely cheap interplanetary travel. While only a handful of missions have flown these so-called "Weak Stability Boundary" (WSB) trajectories in the past, they have the potential to gain widespread use for their extremely low fuel costs. This document will discuss the construction of these WSB trajectories through the use of a Dead-Reckoning numerical simulation tool, called PATHOS, which accounts for at least 3-body gravitational effects. The simulation will be used to generate a group of sample trajectories as validation, as well as compared against similar software tools.
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
