The renewed academic interest in using solar sails as a source of spacecraft propulsion has been accompanied by a recent fervor of investigations into non-ideal and off-nominal sail performance considerations. One of the most influential considerations, uncertain optical degradation, has been shown to present significant trajectory design difficulties. This paper investigates the potential of using a mid-course degradation model update to mitigate the risk of missing the target destination in a sample 300 day Earth-Venus trajectory. Using a range of potential degradation profiles, it is shown that correcting in the first half of the mission is highly likely to result in a trajectory that arrives sufficiently close to Venus at the end of the mission timeframe. Depending on the exact extent of the uncertainty, the data suggests that the latest a correction should take place ranges from 150 to 240 days into the mission. The influence of two different parameters, the extent and rate of degradation, are compared to show that the former of the two is more impactful on correcting timing than the latter.

The purpose of this thesis is to create a search strategy to find orbital debris when the object fails to appear in the sky at its predicted location. This project is for NASA Johnson Space Center Orbital Debris Program Office through the MODEST (Michigan Orbital Debris Survey Telescope) program. This thesis will build upon the research already done by James Biehl in “Formulation of a Search Strategy for Space Debris at GEO.” MODEST tracks objects at a specific right ascension and declination. A circular orbit assumption is then used to predict the location of the object at a later time. Another telescope performs a follow-up to the original observation to provide a more accurate orbit predication. This thesis develops a search strategy when the follow-up is not successful. A general search strategy for finding space debris was developed based on previous observations. A GUI was also generated to find a search strategy in real-time for a specific object based upon previous observations of that object. Search strategies were found by adding a 2% mean random error to the position and velocity vectors. Adding a random error allows for finding the most likely location of space debris when the orbital elements are slightly incorrect. A bivariate kernel density estimator was used to find the probability density function. The probability density function was used to find the most probable location of an object. A correlation between error in the orbital elements and error in right ascension and declination root mean square (RMS) error was investigated. It was found that the orbital elements affect the RMS error nonlinearly, but the relation between orbital element and error depended on the object and no general pattern was found. It was found that how long after the original object was found until the follow-up was attempted did not have a large impact on the probability density function or the search strategy.

A universal time of flight equation for any orbit is developed as a function of the initial and final radius, the change in true anomaly and the initial flight path angle. Lambert's theorem, a new corollary to this theorem, a trigonometric variable substitution and a continuing fraction expression are used in this development. The resulting equation is not explicitly dependent upon eccentricity and is determinate for -2n < (change in true anomaly) < 2n. A method to make the continuing fraction converge rapidly is evaluated using a top down algorithm. Finally, the accuracy of the universal time of flight equation is examined for a representative set of orbits including near parabolic and near rectilinear orbits. / Master of Science

<p>    </p> <p>Space has become ever more crowded since the launch of Sputnik. The need for predictions of possible collisions between space objects has only ever grown. The development of space, particularly around Earth, increases the density of space objects and skyrockets the number of close approaches between these objects, called conjunctions. This investigation is conducted in the context of probability dilution, a phenomenon leading to a false negative collision prediction where increasing positional uncertainty decreases the predicted likelihood of a collision. Dilution is investigated along two avenues: how to generate accurate collision predictions in an efficient manner and how to obtain better input data with which to make these predictions. Along the first avenue, this research presents a novel analytical rectan- gular probability of collision expression as well as a variety of new covariance scale factor formulations for maximum collision probability that indicate the maximum possible collision risk for any conjunction. Along the second avenue, this research tests new sensor tasking regimes to mitigate dilution, ultimately showing that while dilution can be reduced, shrink- ing the positional covariance through optimal measurement updates may not be enough to avoid false negatives in orbital conjunctions. </p>

<p dir="ltr">With the increase in planned space missions in cislunar space, it is necessary to study the ability of observers to observe and track objects in this regime. This thesis focuses on creating a sensor tasking algorithm for constellations of optical observers to efficiently observe cislunar objects. The circular restricted three body problem is used for the dynamics of the objects while the bi-circular restricted four body problem is used to approximate the position of the sun.</p><p dir="ltr">A new way of discretizing the field of regard is proposed that respects the observers field of view on the unit sphere. A method for providing feedback to the observer in a delayed feedback environment is applied to mean state, single Gaussian, and particle representations of uncertainty. The method of determining a scaling coefficient for Sanson’s probability of detection is recorded. Sanson’s probability of detection is studied for determining the correct effective aperture dimensions of an optical observer. An approximation is presented for expediting calculations of Sanson’s probability of detection. An uncertainty propagation analysis shows there is an efficient number of particles to use for particle uncertainty far below the required number for a full Monte Carlo particle uncertainty representation. </p><p dir="ltr">Mean state, single Gaussian and particle methods of uncertainty characterization are compared in a cislunar simulation showing the benefits of the particles solution over other forms of uncertainty characterization. Particles are not only an effective uncertainty representation in a delayed feedback environment, they are computationally feasible for the sensor tasking problem. The performance of the particle algorithm for a constellation of observers is evaluated in a simulated small satellite breakup in a Lyapunov orbit and a simulated breakup of the proposed Lunar Gateway. The performance of observers in direct retrograde, low lunar, geosynchronous, and northern Halo orbits are evaluated in the breakup simulations. Results from these simulations show that observers in low lunar and Halo orbits can be valuable observation standpoints in breakups around the near-Moon region of cislunar space.</p>

<p>Ballistic and chemical trajectory options to Uranus are investigated for launch dates spanning 50 years. Trajectory solutions are found using STOUR, a patched conic propagator with an analytical ephemeris model. STOUR is heritage software developed by JPL and Purdue, written in FORTRAN. A total of 89 distinct gravity-assist paths to Uranus are considered, most of which will allow for a deep space maneuver (DSM) at some point along the path. For each launch year, the most desirable trajectory is identified and cataloged based on time of flight (up to 15 years), total $\Delta$V cost (DSM and capture maneuver), arrival $V_\infty$, and delivered payload. The Falcon Heavy (Recoverable), Vulcan VC6, Falcon Heavy (Expendable) and SLS Block 1B are considered to provide a range of low- to high-performance launch vehicle capabilities. A rough approximation of Starship's performance capabilities is also computed and applied to select years of launch dates. A flagship mission that delivers both a probe and an orbiter at Uranus is considered, which is approximated as a trajectory capable of delivering 2000 kg. Jupiter is unavailable as a gravity-assist body until the end of the 2020s but alternative gravity-assist paths exist, providing feasible trajectories even in years when Jupiter is not available. A rare Saturn-Uranus alignment in the late 2020's is identified which provides some such trajectory opportunities. A probe-and-orbiter mission to Uranus is feasible for a Vulcan VC6 with approximately 13 year flight times and for a Recoverable Falcon Heavy with approximately 14.5 year flight times. An Expendable Falcon Heavy reduces the time of flight to around 12.5 years and opens up `0E0U' as a gravity-assist path, while the SLS Block 1B typically offers trajectories with 10 to 11 year flight times and opens up more direct `JU' and `U' solutions. With the SLS, flight times as low as 7.5 years are possible.</p> <p>  </p> <p>A new, rapid grid search tool called GREMLINS is also outlined. This new software is capable of solving the same problems as STOUR, but improves on it in three crucial ways: an improved user-experience, more maneuver capabilities, and a more easily maintained and modified code base. GREMLINS takes a different approach to the broad search problem, forgoing $C_3$ matching in favor of using maneuvers to patch together tables of pre-computed Lambert arcs. This approach allows for vectorized computations across data frames of Lambert solutions, which can be computed much more efficiently than the for-loop style approach of past tools. Through the use of SQL tables and a two-step trajectory solving approach, this tool is able to run very quickly while still being able to handle any amount of data required for a broad search. Every line of code in GREMLINS is written in Python in an effort to make it more approachable and easier to develop for a wide community of users, as GREMLINS will be the only only grid search tool available as free and open source software. Multiple example missions and trajectory searches are explored to verify the output from GREMLINS and to compare its performance against STOUR. Despite using a slower coding language, GREMLINS is capable of performing the same trajectory searches in approximately 1/5 the runtime of STOUR, a FORTRAN-coded tool, thanks to its vectorized computations.</p>

Since the discovery of Ceres, asteroids have been of immense scientific interest and intrigue. They hold answers to many of the fundamental questionsabout the formation and evolution of the Solar System. Therefore, a missionsurveying the asteroid belt with close encounter of carefully chosen asteroidswould be of immense scientific benefit. The trajectory of such an asteroidtour mission needs to be designed such that asteroids of a wide range ofcompositions and sizes are encountered; all with an extremely limited ∆Vbudget.This thesis presents a novel heuristic algorithm to optimize trajectoriesfor an asteroid tour mission with close range flybys (≤ 1000 km). The coresearch algorithm efficiently decouples combinatorial (i.e. choosing the asteroids to flyby)and continuous optimization (i.e. optimizing critical maneuversand events) of what is essentially a mixed integer programming problem.Additionally, different methods to generate a healthy initial population forthe combinatorial optimization are presented.The algorithm is used to generate a set of 1800 feasible trajectories withina 2029+ launch frame. A statistical analysis of these set of trajectories isperformed and important metrics for the search are set based on the statistics.Trajectories allowing flybys to prominent families of asteroids like Flora andNysa with ∆V as low as 4.99 km/s are obtained.Two modified implementations of the algorithm are presented. In a firstiteration, a large sample of trajectories is generated with a limited numberof encounters to the most scientifically interesting targets. While, a posteriori, trajectories are filled in with as many small targets as possible. Thisis achieved in two different ways, namely single step extension and multiplestep extension. The former fills in the trajectories with small targets in onestep, while the latter optimizes the trajectory by filling in with one asteroid per step. The thesis also presents detection of asteroids for successfullyperforming flybys. A photometric filter is developed which prunes out badlyilluminated asteroids. The best trajectory is found to perform well againstthis filter such that nine out of the ten planned flybys are feasible.

Orientador: Ernesto Vieira Neto / Banca: Othon Cabo Winter / Banca: Helio Koiti Kuga / Resumo: Com o lançamento do primeiro satélite artificial da Terra, Sputnik I, surgiu a necessidade do desenvolvimento de satélites mais eficientes e mais econômicos. Um dos mecanismos utilizados para economizar combustível numa transferência completa de um veículo espacial em órbita da Terra para uma órbita em torno da Lua, é o fenômeno de captura gravitacional temporária. Nesse trabalho é feita a análise numérica de diversas trajetórias em torno da Lua, considerando-se as dinâmicas de três e quatro corpos, com o objetivo de estudar o fenômeno da captura gravitacional temporária, através do monitoramento do sinal da energia relativa de dois corpos partícula-Lua e das componentes radiais das forças gravitacionais da Terra, da Lua e do Sol. Através desses estudos também foram obtidos diversos mapas de escape e colisão, considerando-se os movimentos prógrado e retrógrado. / Abstract: With the launch of the first artificial satellite of the Earth, Sputnik I, arose the necessity of the development of the satellites more efficient and more economic. One of the mechanisms used to save fuel in a complete transference of one spacecraft in orbit of the Earth to an orbit around the Moon, is the phenomena of the temporary gravitational capture. In this paper is made the numerical analysis of the several trajectories around the Moon, considering the dynamics of the three and four-bodies, with the objective of studying the phenomena of temporary gravitational capture, through monitoring the sign of the relative two-body energy particle-Moon and the radial component of the force of attraction, gravitational of the Earth, of the Moon and of the Sun. Though of these studies also were obtained several maps of the escape and collision, considering the prograde and retrograde movements. / Mestre

This paper is predicated on determining the effectiveness of angles-only initial orbit determination (IOD) methods when limited observational data is available for low-Earth orbit (LEO) rocket body debris. The analysis will be conducted with data obtained from Lockheed Martin Space’s Space Object Tracking (SpOT) facility, focusing on their observational data from 2018 that contains tracking of rocket body debris for less than one minute per overhead pass. After the IOD accuracies are better understood, a feasibility study will follow that investigates the possibility of cataloguing LEO orbital debris from a single optical observation facility with similar observational capabilities as that of the SpOT facility. The IOD accuracy analysis will investigate nine different rocket bodies, with a total of 50 orbital passes of data included in the research. Three main IOD approaches will be tested for each data set to determine the best method in achieving high levels of IOD accuracy: a traditional three-point method, an iterative method, and an assumed-circular orbit method. Application of the iterative approach results in increased accuracy for the resultant initial orbit determination as compared to the three-point IOD method, and an assumed-circular orbit assumption allows for a further increase in accuracy, especially for observed objects in near-circular orbits. The feasibility of cataloguing debris from a singular optical facility shows promise, as subsequent target acquisition after an object’s initial observation is determined to be achievable under the correct circumstances. By choosing a correct telescope pointing angle based on the IOD results from one pass of data, an observed rocket body debris object would pass through the field of view of SpOT’s spotter scope (0.7-degrees) during its next overhead pass for two different test cases. An increase field of view would increase both the likelihood of acquiring the target object and the amount of time the object is visible by the telescope.

Low Earth orbit represents a valuable limited natural resource. Of particular interest are sun-synchronous orbits; it is estimated that approximately 44% of low Earth satellites are sun-synchronous. A previously developed sun-synchronous orbit slot architecture is considered. An in-depth analysis of the relative motion between satellites and their corresponding slots is performed. The long-term evolution of Earth's orbital environment is modeled by a set of coupled ordinary differential equations. A metric for quantifying the benefit, if any, of implementing a sun-synchronous architecture is developed. The results indicate that the proposed slot architecture would reduce the frequency of collisions between satellites in sun-synchronous orbits.