Challenging science requirements and complex space missions are driving the need for fast and robust space trajectory design and simulation tools. The main aim of this thesis is to develop new and improved high performance algorithms and solution techniques for commonly encountered problems in astrodynamics. Five major problems are considered and their state-of-the art algorithms are systematically improved. Theoretical and methodological improvements are combined with modern computational techniques, resulting in increased algorithm robustness and faster runtime performance. The five selected problems are 1) Multiple revolution Lambert problem, 2) High-fidelity geopotential (gravity field) computation, 3) Ephemeris computation, 4) Fast and accurate sensitivity computation, and 5) High-fidelity multiple spacecraft simulation. The work being presented enjoys applications in a variety of fields like preliminary mission design, high-fidelity trajectory simulation, orbit estimation and numerical optimization. Other fields like space and environmental science to chemical and electrical engineering also stand to benefit.

On-orbit servicing (OOS) of space systems provides immense benefits by extending their lifetime, by reducing overall cost of space operations, and by adding flexibility to space missions. Refueling is an important aspect of OOS operations. The problem of determining the optimal strategy of refueling multiple satellites in a constellation, by expending minimum fuel during the orbital transfers, is challenging, and requires the solution of a large-scale optimization problem. The conventional notion about a refueling mission is to have a service vehicle visit all fuel-deficient satellites one by one and deliver fuel to them. A recently emerged concept, known as the peer-to-peer (P2P) strategy, is a distributed method of replenishing satellites with fuel. P2P strategy is an integral part of a mixed refueling strategy, in which a service vehicle delivers fuel to part (perhaps half) of the satellites in the constellation, and these satellites, in turn, engage in P2P maneuvers with the remaining satellites. During a P2P maneuver between a fuel-sufficient and a fuel-deficient satellite, one of them performs an orbital transfer to rendezvous with the other, exchanges fuel, and then returns back to its original orbital position. In terms of fuel expended during the refueling process, the mixed strategy outperforms the single service vehicle strategy, particularly with increasing number of satellites in the constellation. This dissertation looks at the problem of P2P refueling problem and proposes new extensions like the Cooperative P2P and Egalitarian P2P strategies. It presents an overview of the methodologies developed to determine the optimal set of orbital transfers required for cooperative and non-cooperative P2P refueling strategies. Results demonstrate that the proposed strategies help in reducing fuel expenditure during the refueling process.

This study investigates methods for assessing threats in space. Space services are crucial to both civilian and military capabilities, and a loss of such systems could have severe consequences. Space systems are exposed to various types of threats. To ensure the benefits of space-based applications, protect space assets, improve security, and maintain the space environment, it is crucial to assess threats in space. This thesis focuses on co-orbital antagonistic threats arising from satellites that are capable of performing precision manoeuvres. These satellites could either perform physical attacks or perform operations such as inspection, eavesdropping, or disruption on other satellites. Lambert's problem can be utilised for calculating orbital transfers. By solving the problem iteratively over a range of values of when the transfer is executed and the transfer time, it is possible to detect when a transfer is feasible. This can be used to assess when a satellite can pose a threat to a target. The calculations of orbital transfers are improved by the implementation of a genetic algorithm. The algorithm can solve for both direct transfers to the target and transfers using multiple impulses. Furthermore, a genetic algorithm, called NSGA-II, which can handle multiple objective functions is also analysed. The implemented methods show the potential of being employed to assess threats, especially for direct transfers where a single impulse is executed to transfer to a target. In this case, it is possible to identify threats based on the satellite's $\Delta v$ budget. However, when additional impulses are introduced it becomes more complicated. It is more difficult to estimate when an attack is more likely to commence. The implemented methods show potential, but further research is required in order to develop a robust method to assess co-orbital threats.  The conducted analysis has highlighted a few aspects that are crucial for assessing co-orbital threats. Information about the $\Delta v$ budget of the satellite that potentially could pose a threat must be available. Furthermore, space surveillance and tracking capabilities are essential to detect orbital changes, which can be vital to perform counter-operations in the event of an attack / Denna studie undersöker metoder för hotbedöming i rymden. Rymdtjänster är av avgörande betydelse för både civila och militära förmågor och förlusten av sådana system kan leda till allvarliga konsekvenser. Rymdsystem är utsatta för olika typer av hot. För att säkerställa fördelarna med rymdbaserade tillämpningar, skydda rymdresurser, förbättra säkerheten och bevara rymdmiljön är det viktigt att bedöma hot i rymden. Detta examensarbete fokuserar på hot från precisionsmanövrerande satelliter som antingen kan genomföra fysiska attacker eller utföra operationer såsom inspektion, avlyssning eller störning av en annan satellit. Lamberts problem kan användas för att beräkna banmanövrar. Genom att lösa problemet iterativt över olika värden för när manöverna utförs och flygtiden är det möjligt att fastställa när en manöver är genomförbar. Detta kan användas för att bedöma när en satellit kan utgöra ett hot mot en målsatellit. Beräkningarna av banmanövrar förbättras genom implementeringen av en genetisk algoritm. Algoritmen kan lösa både direkta manövrar till målet och manövrar med flera impulser. Dessutom analyseras en genetisk algoritm, kallad NSGA-II, som kan hantera flera målfunktioner. De implementerade metoderna visar potential för att kunna användas för hotbedömning, särskilt för direkta manövrar där en enda impuls används för att ändra banan till målet. I detta fall är det möjligt att identifiera hot baserat på satellitens $\Delta v$-budget. Däremot blir det mer komplicerat när ytterligare impulser introduceras. Det blir svårare att bedöma när en attack sannolikt inleds. De implementerade metoderna visar potential, men ytterligare forskning krävs för att utveckla en robust metod för att bedöma hot från precisionsmanövrerande satelliter. Den genomförda analysen har framhävt några aspekter som är av avgörande betydelse för att utföra en hotbedömning. Information om satellitens $\Delta v$-budget som potentiellt kan utgöra ett hot måste vara tillgänglig. Dessutom är inmätning och övervakningsförmåga av satelliter avgörande för att upptäcka banförändringar, vilket kan vara kritiskt vid genomförande av motåtgärder i händelse av en attack.