Spacecraft operating on the Martian surface have used relay satellites as a means of improving communication capabilities, mainly in terms of bandwidth and availability. However, the spacecraft used to achieve this have been large spacecraft (1000s of kilograms) and were not designed with relay capability as the design priority. This thesis explores the possibility of using a CubeSat-based constellation as a communications network for spacecraft operating on the Martian surface. Brute-force techniques are employed to explore the design space of possible constellations. An analysis of constellation configurations that provide complete, continuous coverage of the Martian surface is presented. The stability of these constellations are analyzed, and recommendations are made for stable configurations and the orbital maintenance thereof. Link budget analysis is used to determine the communications capability of each constellation, and recommendations are made for sizing each communication element. The results of these three analyses are synthesized to create an architecture generation tool. This tool is used to identify mission architectures that suit a variety of mission requirements, and these architectures are presented. The primary recommended architecture utilizes 18 CubeSats in three orbital planes with six additional larger relay satellites to provide an average of over one terabit/sol downlink and 100 kbps uplink capability.

This thesis will present the effects of the orbital debris evolution in two key areas: the geosynchronous disposal orbit regime known as “graveyard” and the two geopotential wells found in 105◦ W and 75◦ E longitude bins. After developing a GEO specific orbit propagator for NASA Johnson Space Center’s Orbital Debris Of- fice, collisions were simulated throughout these regimes using a low velocity breakup model. This model considered the effects of perturbations particularly non-spherical Earth effects (specifically sectorial and zonal harmonics), lunar effects, third body effects and solar radiation pressure effects. The results show that CDPROP does well in simulating the presence of the Eastern and Western geopotential wells, as well as catching drifting GEO objects. It does not do as well in catching East-West trapped objects. Three collision test cases were then simulated in graveyard and the East and West geopotential wells.

A dual satellite system in a Low Earth Orbit, LEO, would be beneficial to study the electromagnetic occurrences in the magnetosphere and their contributions to the development of the aurora events in the Earth's lower atmosphere. An orbit configuration is sought that would increase the total time that both satellites are inside the auroral oval. Some additional objectives include minimizing the total fuel cost and the average angle between the satellites' radius vectors. This orbit configuration is developed using a series of instantaneous burns applied at each satellite's perigee. An analysis of the optimal solutions generated by a Particle Swarm Optimization method is completed using a cost function with different weights for the time, fuel, and angle terms. Three different scenarios are presented: a single burn case, a double burn case, and a four burn case. The results are calculated using two different orbital mechanics models: an unperturbed two-body simulation and a two-body simulation with added Earth's equatorial bulge effects. It is shown that the added perturbation reduces the total event time in the optimal solutions generated. Specific weights for the cost function are recommended for further studies. / Master of Science

Orbit propagation is the backbone of many problems in the space domain, such as uncertainty quantification, trajectory optimization, and guidance, navigation, and control of on orbit vehicles. Many of these techniques can rely on millions of orbit propagations, slowing computation, especially evident on low-powered satellite hardware. Past research has relied on the use of lookup tables or data streaming to enable on orbit solutions. These solutions prove inaccurate or ineffective when communication is interrupted. In this work, we introduce the use of physics-informed neural networks (PINNs) for orbit propagation to achieve fast and accurate on-board solutions, accelerated by GPU hardware solutions now available in satellite hardware. Physics-informed neural networks leverage the governing equations of motion in network training, allowing the network to optimize around the physical constraints of the system. This work leverages the use of unsupervised learning and introduces the concept of fundamental integrals of orbits to train PINNs to solve orbit problems with no knowledge of the true solution. Numerical experiments are conducted for both Earth orbits and cislunar space, being the first time a neural network integrator is implemented on flight-like hardware. The results show that the use of PINNs can decrease solution evaluation time by several order of magnitude while retaining accurate solutions to the perturbed two-body problem and the circular restricted three-body problem for deployment on spaceflight-like hardware. Implementation of these neural networks aim to reduce computational time to allow for real-time evaluation of complex algorithms on-board space vehicles.

Thesis (MScEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Stellenbosch University and the Katholieke Universiteit Leuven has a joint undertaking to develop a satellite communications payload. The goals of the project are: to undertake research and expand knowledge in the area of dynamically configurable antenna beam forming, to prove the viability of this research for space purposes and to demonstrate the feasibility of the development in a practical application. The practical application is low Earth orbit satellite communication system for applications in remote monitoring. Sensor data will be uploaded to the satellite, stored and forwarded to a central processing ground station as the satellite passes over these ground stations. The system will utilise many low-cost ground sensor stations to collect data and distribute it to high-end ground stations for processing. Applications of remote monitoring systems are maritime- and climate change monitoring- and tracking. Climate change monitoring allows inter alia, for the monitoring of the effects and causes of global warming. The Katholieke Universiteit Leuven is developing a steerable antenna to be mounted on the satellite. Stellenbosch University is developing the communications payload to steer and use the antenna. The development of the communications protocol stack is part of the project. The focus of this work is to implement the application layer protocol, which handles all file level communications and also implements the communications strategy. The application layer protocol is called the Satellite Communications Software System (SCSS). It handles all high level requests from ground stations, including requests to store data, download data, download log files and upload configuration information. The design is based on a client-server model, with a Station Server and Station Handler. The Station Server schedules ground stations for communication and creates a Station Handler for each ground station to handle all ground station requests. During the design, all file formats were defined for efficient ground station-satellite communications and system administration. All valid ground station requests and handler responses were also defined. It was also found that the system may be made more efficient by scheduling ground stations for communications, rather than polling each ground station until one responds. To be able to schedule ground station communications, the times when ground stations will come into view of the satellite have to be predicted. This is done by calculating the positions of the Satellite and ground stations as functions of time. A simple orbit propagator was developed to predict the satellite distance and to ease testing and integration with the communications system. The times when a ground station will be within range of the satellite were then predicted and a scheduling algorithm developed to minimise the number of ground stations not able to communicate. All systems were implemented and tested. The SCSS executing on the Satellite was developed and tested on the satellite on-board computer. Embedded implementations possess strict resource limitations, which were taken into account during the development process. The SCSS is a multi-threaded system that makes use of thread cancellation to improve responsiveness. / AFRIKAANSE OPSOMMING: Die Universiteit van Stellenbosch ontwerp tans ’n satelliet kommunikasieloonvrag in samewerking met die Katolieke Universiteit van Leuven. Die doel van die projek is om navorsing te doen oor die lewensvatbaarheid van dinamies verstelbare antenna bundelvorming vir ruimte toepassings, asook om die haalbaarheid van hierdie navorsing in die praktyk te demonstreer. Die praktiese toepassing is ’n satellietkommunikasiestelsel vir afstandsmonitering, wat in ’n Lae-Aarde wentelbaan verkeer. Soos die satelliet in sy wentelbaan beweeg, sal sensor data na die satelliet toe gestuur, gestoor en weer aangestuur word. Die stelsel gebruik goedkoop sensorgrondstasies om data te versamel en aan te stuur na kragtiger grondstasies vir verwerking. Afstandsmoniteringstelsels kan gebruik word om klimaatsverandering, sowel as die posisie van skepe en voertuie, te monitor. Deur oa. klimaatsveranderinge te dokumenteer, kan gevolge en oorsake van globale verhitting gemonitor word. Die Katholieke Universiteit van Leuven is verantwoordelik vir die ontwerp en vervaardiging van die satelliet antenna, terwyl die Universiteit van Stellenbosch verantwoordelik is vir die ontwerp en bou van die kommunikasie loonvrag. ’n Gedeelte van hierdie ontwikkeling sluit die ontwerp en implementasie van al die protokolle van die kommunikasieprotokolstapel in. Dit fokus op die toepassingsvlak protokol van die protokolstapel, wat alle leêrvlak kommunikasie hanteer en die kommunikasiestrategie implementeer. Die toepassingsvlaksagteware word die Satellietkommunikasie sagtewarestelsel (SKSS) genoem. Die SKSS is daarvoor verantwoordelik om alle navrae vanaf grondstasies te hanteer. Hierdie navrae sluit die oplaai en stoor van data, die aflaai van data, die aflaai van logs en die oplaai van konfigurasie inligting in. Die ontwerp is op die standaard kliënt-bediener model gebasseer, met ’n stasiebediener en ’n stasiehanteerder. Die stasiebediener skeduleer die tye wanneer grondstasies toegelaat sal word om te kommunikeer en skep stasiehanteerders om alle navrae vanaf die stasies te hanteer. Gedurende die ontwerp is alle leêrformate gedefinieer om doeltreffende adminstrasie van die stelsel, asook kommunikasie tussen grondstasies en die satelliet te ondersteun. Alle geldige boodskappe tussen die satelliet en grondstasies is ook gedefnieer. Daar is gevind dat die doeltreffendheid van die stelsel verhoog kan word deur die grondstasies wat wil kommunikeer te skeduleer, eerder as om alle stasies te pols totdat een reageer. Om so ’n skedule op te stel, moet die tye wanneer grondstasies binne bereik van die satelliet gaan wees voorspel word. Hierdie voorspelling is gedoen deur die posisies van die satelliet en die grondstasies as funksies van tyd te voorspel. ’n Eenvoudige satelliet posisievoorspeller is ontwikkel om toetsing en integrasie met die SKSS te vergemaklik. ’n Skeduleringsalgoritme is toe ontwikkel om die hoeveelheid grondstasies wat nie toegelaat word om te kommunikeer nie, te minimeer. Alle stelsels is geimplementeer en getoets. Die SKSS, wat op die satelliet loop, is ontwikkel en getoets op die satelliet se aanboord rekenaar. Die feit dat ingebedde stelsels oor baie min hulpbronne beskik, is in aanmerking geneem gedurende die ontwikkeling en implementasie van die SKSS. Angesien die SKSS ’n multidraadverwerkingsstelsel is, word daar van draadkansellasie gebruik gemaak om die stelsel se reaksietyd te verbeter.

This study focuses on the Sun's influence on the motion near the triangular libration points of the Earth-Moon system. It is known that there exists a very strong resonant perturbation near those points that produces large deviations from the libration points, with an amplitude of about 250,000 km and a period of 1,500 days. However, it has been shown that it is possible to find initial conditions that negate the effects of that perturbation, even resulting in stable, although very large, periodic orbits. Using two different models, the goal of this research is to determine the initial configurations of the Earth-Moon-Sun system that produce minimal deviations from the libration points, and to provide a better understanding of the dynamics of this highly nonlinear problem. First, the Bicircular Problem (BCP) is considered, which is an idealized model of the Earth-Moon-Sun System. The impact of the initial configuration of the Earth-Moon-Sun system is studied for various propagation times and it is found that there exist two initial configurations that produce minimal deviations from L₄ or L₅. The resulting trajectories are very sensitive to the initial configuration, as the mean deviation from the libration points can decrease by 30,000 km with less than a degree change in the initial configuration. Two critical initial configurations of the system were identified that could allow a particle to remain within 30,000 km of the libration points for as long as desired. A more realistic model, based on JPL ephemerides, is also used, and the influence of the initial epoch on the motion near the triangular points is studied. Through the year 2007, 51 epochs are found that produce apparently stable librational motion near L₄, and 60 near L₅. But the motion observed depends greatly on the initial epoch. Some epochs are even found to significantly reduce the deviation from L₄ and L₅, with the spacecraft remaining within at most 90,000 km from the triangular points for upwards of 3,000 days. Similarly to what was observed in the BCP, these trajectories are found to be extremely sensitive to the initial epoch. / text

<p>The missed-thrust problem is a modern challenge in the field of mission design. While some methods exist to quantify its effects, there still exists room for improvement for algorithms which can fully anticipate and plan for a realistic set of missed-thrust events. The present work investigates the use of machine learning techniques to provide a robust controller for a low-thrust spacecraft. The spacecraft’s thrust vector is provided by a neural network controller which guides the spacecraft to the target along a trajectory that is robust to missed thrust, and the controller does not need to re-optimize any trajectories if it veers off its nominal course. The algorithms used to train the controller to account for missed thrust are supervised learning and neuroevolution. Supervised learning entails showing a neural network many examples of what inputs and outputs should look like, with the network learning over time to duplicate the patterns it has seen. Neuroevolution involves testing many neural networks on a problem, and using the principles of biological evolution and survival of the fittest to produce increasingly competitive networks. Preliminary results show that a controller designed with these methods provides mixed results, but performance can be greatly boosted if the controller’s output is used as an initial guess for an optimizer. With an optimizer, the success rate ranges from around 60% to 96% depending on the problem.</p> <p><br></p> <p>Additionally, this work conducts an analysis of a novel hyperbolic rendezvous strategy which was originally conceived by Dr. Buzz Aldrin. Instead of rendezvousing on the outbound leg of a hyperbolic orbit (traveling away from Earth), the spacecraft performs a rendezvous while on the inbound leg (traveling towards Earth). This allows for a relatively low Delta-v abort option for the spacecraft to return to Earth if a problem arose during rendezvous. Previous work that studied hyperbolic rendezvous has always assumed rendezvous on the outbound leg because the total Delta-v required (total propellant required) for the insertion alone is minimal with this strategy. However, I show that when an abort maneuver is taken into consideration, inserting on the inbound leg is both lower Delta-v overall, and also provides an abort window which is up to a full day longer.</p>

The Turning Point Method (TPM) for the evaluation of ion scattering in a sheath of a biased probe immersed in an unmagnetized plasma is reviewed. The TPM implemented originally in a computer program for spherical probes is expanded to include cylindrical probes as well as the evaluation of the turning angle of the charged particle (repelled or attracted) around the probe. TPM results have the potential to provide a standard against which to compare more complicated current collection simulations. TPM results are validated by comparing with Laframboise's earlier work for current collection in the Orbital Motion Limited regime. Calculations of the turning angle of a charged particle with specific energy and angular momentum revealed that higher plasma shielding limits the range of impact parameters that experience significant scattering, and that attracted particles entering tangent to the sheath experience increased scattering. The TPM results also show that there are significant changes in orbital trajectories between different space charges within the Orbital Motion Limited limit.

<p>An increasing interest in lunar exploration calls for low-cost techniques of reaching the Moon. Ballistic lunar transfers are long duration trajectories that leverage solar perturbations to reduce the multi-body energy of a spacecraft upon arrival into cislunar space. An investigation is conducted to explore methods of constructing ballistic lunar transfers. The techniques employ dynamical systems theory to leverage the underlying dynamical flow of the multi-body regime. Ballistic lunar transfers are governed by the gravitational influence of the Earth-Moon-Sun system; thus, multi-body gravity models are employed, i.e., the circular restricted three-body problem (CR3BP) and the bicircular restricted four-body problem (BCR4BP). The Sun-Earth CR3BP provides insight into the Sun’s effect on transfers near the Earth. The BCR4BP offers a coherent model for constructing end-to-end ballistic lunar transfers. Multiple techniques are employed to uncover ballistic transfers to conic and multi-body orbits in cislunar space. Initial conditions to deliver the spacecraft into various orbits emerge from Periapse Poincaré maps. From a chosen geometry, families of transfers from the Earth to conic orbits about the Moon are developed. Instantaneous equilibrium solutions in the BCR4BP provide an approximate for the theoretical minimum lunar orbit insertion costs, and are leveraged to create low-cost solutions. Trajectories to the <i>L</i>2 2:1 synodic resonant Lyapunov orbit, <i>L</i>2 2:1 synodic resonant Halo orbit, and the 3:1 synodic resonant Distant Retrograde Orbit (DRO) are investigated.</p>

<p>Many future satellite applications in cislunar space require repeating, periodic transfers that shift away from some operational orbit and eventually return. Resonant orbits are investigated in the Earth-Moon Circular Restricted Three Body Problem (CR3BP) as a mechanism to enable these transfers. Numerous resonant orbit families possess a ratio of orbital period to lunar period that is sufficiently close to an integer ratio and can be exploited to uncover period-commensurate transfers due to their predictable periods. Resonant orbits also collectively explore large swaths of space, making it possible to select specific orbits that reach a region of interest. A framework for defining period-commensurate transfers is introduced that leverages the homoclinic connections associated with an unstable operating orbit to permit ballistic transfers that shuttle the spacecraft to a certain region. Resonant orbits are incorporated by locating homoclinic connections that possess resonant structures, and the applicability of these transfers is extended by optionally linking them to resonant orbits. In doing so, transfers are  available for in-orbit refueling/maintenance as well as surveillance/communications applications  that depart and return to the same phase in the operating orbit.</p>