Quasi-satellite orbits (QSOs) are orbits around the smaller primary in three-body systems. The MMX mission (developed by JAXA, to be launched in 2024) will use QSOs to orbit Phobos, before landing on its surface. This work studies the feasibility of using the invariant manifolds of three-dimensional QSOs for designing landing trajectories, using the Mars-Phobos system as a case study. Applying continuation and bifurcation-analysis techniques, different families of QSOs were computed and their invariant manifolds propagated. Using a set of favorable manifolds as a reference, multiple maneuvers were designed via multiple-shooting and optimization techniques, producing feasible landing trajectories. The robustness of these trajectories was analyzed using a stability index and Monte Carlo simulations. It was found that using the invariant manifolds of QSOs to land is only possible for some families of QSOs. However, for these, the manifolds allow generating robust and propellant-efficient landing trajectories that are able to reach most of Phobos' surface.

Apophis, an Aten-type asteroid, was considered a significant threat to Earth upon its discovery due to its potential impact with Earth in 2029. Although the collision has now been ruled out, Apophis will still perform an exceptionally close flyby of Earth that same year at a distance of 32,000 km from the surface. This event presents a unique opportunity for the investigation of rotational changes due to tidal forces and post-encounter ephemerides for planetary defence purposes. In fact, the upcoming OSIRIS-APEX mission will enter orbit around Apophis shortly after the 2029 flyby. Even though orbits around near-Earth asteroids like Apophis face challenges due to the asteroid's low gravity and the strong perturbations induced by solar radiation pressure, frozen orbits - a specialised orbit with constant eccentricity and argument of periapsis on average - can achieve orbital stability in such a complex dynamical environment. Frozen orbits were successfully employed for some of the mission phases of the OSIRIS-REx mission, and past research has greatly focused on the investigation of frozen orbits around Apophis and other small bodies through the use of analytical and numerical methods. However, no prior research has addressed the design of frozen orbits that can survive the close approach in 2029 without orbital correction manoeuvres. The aim of this research is thus to investigate the stability of control-free frozen orbits around Apophis during the 2029 Earth flyby. To fulfil this goal, both analytical and numerical methods are employed. The analytical analysis involves averaging of Lagrange's Planetary Equations including perturbations from solar radiation pressure and Apophis' zonal gravity up to degree four in combination with a Lyapunov stability analysis and a comparison to numerical simulations. Assuming an argument of periapsis and longitude of the ascending node of +-90 degrees, the analytical method identifies two main solution families: near-equatorial heliotropic/anti-heliotropic orbits and near-polar Sun-terminator orbits. However, the stability analysis predicts only half of the sampled solutions to be stable. The comparison to numerical simulations shows that both analytical techniques fail to identify stable, frozen orbits. The stability index correctly identifies stability for 66.67% of the results that reach the end of a numerical propagation without surface impact or orbital escape. More significantly, 42% of the results are identified as false positives. The variations in eccentricity and argument of periapsis for the solutions that reach the end of a 28-day simulation are approximately 0.69 and 600 degrees respectively for the near-equatorial solutions and, at best, 0.89 and 215 degrees for the near-polar solutions, which are too large to be considered frozen orbits. In the numerical analysis, the frozen orbit problem is defined as a multi-objective optimisation problem with two objectives: minimisation of the maximum variation in eccentricity and argument of periapsis. Trajectories with different orbital injection parameters are simulated to find the optimal initial state leading to a frozen orbit. First, the results are focused exclusively on the pre-flyby period with no constraint on surviving the flyby. The best solutions lead to a maximum variation in eccentricity and argument of periapsis of approximately 0.047 and 66 degrees respectively over a 28-day period. However, these orbits all eventually collide with the asteroid at the time of the flyby. Imposing a constraint on survival increases the maximum variation in eccentricity and argument of periapsis to ranges of 0.08-0.21 and 103-110.5 degrees in the pre-flyby period. The behaviour post-flyby is stable for some of these solutions but no longer corresponds to the frozen configuration. In both cases, the solutions are categorised under the near-circular, near-polar, Sun-terminator frozen orbit family, the same type of orbit employed for the frozen orbit phases of the OSIRIS-REx mission. Despite the limitations of this work, the numerical pre-flyby results exhibit robustness against uncertainties in modelling parameters and orbital injection inaccuracies.

While the space industry expands rapidly and space exploration becomes ever more relevant, this thesis aims to automate the design of Multiple Gravity-Assist (MGA) transfers using low-thrust propulsion. In particular, during the preliminary design phase of space missions, the combinatorial complexity of MGA sequencing is large and current optimisation approaches require extensive experience and can take days to simulate. Therefore, a novel optimisation approach is developed -- called the Recursive Target Body Approach -- that uses the hodographic-shaping low-thrust trajectory representation together with a combination of tree-search methods to automate the optimisation of MGA sequences. The approach gradually constructs the expected optimal MGA sequence by recursively evaluating the optimality of subsequent gravity-assist targets. Moreover, the approach includes novel figures of merit as well as parallelisation concepts to increase the robustness and accelerate the convergence. An Earth-Jupiter transfer with a maximum of three gravity assists is considered as a reference problem. Extensive tuning improved the quality of the MGA trajectory representations substantially and as a result, a robust low-thrust trajectory optimisation could be ensured. A distinct group of highly fit MGA sequences is consistently found that can be passed to a higher-fidelity method. In conclusion, the Recursive Target Body Approach can automatically and reliably be used for the preliminary optimisation of low-thrust MGA trajectories.

This thesis focused on the relevance and feasibility of an uncontrolled cubesat mission in a binary asteroid environment, highlighting the example of the representative Near-Earth Asteroid 1999 KW4, modelled using the TU Delft Astrodynamics Tool (TUDAT). A clear distinction was made between orbits of the cubesat starting in the interior and the exterior ring of the binary for numerical computations. Lifetimes over 100 days were found in the interior ring through a family of so-called pseudo-periodic orbits around the primary asteroid, with some that withstand the introduction of various uncertainties in the model. Reasonable lifetimes in the exterior ring were found to be around 60 days in the exterior ring, but could no longer be guaranteed after the sensitivity analysis. This suggests that targeting pseudo-periodic orbits is the best strategy to adopt. Velocity uncertainties in the initial state of the cubesat were observed to be the driving aspect in both the interior and exterior ring, as managing to lower them could shift a seemingly too risky run into an acceptable one w.r.t. our criteria.

With the increase in the use of Solar Electric Propulsion for Earth-centered applications, comes an additional challenge in the field of low-thrust spacecraft trajectory optimization. This MSc project implements a hybrid optimization approach, using control parametrization to reduce the number of optimization parameters and orbital averaging to decreasing computational speeds. Several improvements are made in comparison to previous works, using co-state scaling, and self-adaptive differential evolution to improve convergence. Additionally, variable-step integration of the orbital state averages improved propagation speed. The implemented optimization tool was applied to the GTO to GEO transfer problem, demonstrating improved convergence compared to the previous authors, with the exception of eclipse conditions, requiring further verification. Additionally, a transfer with significant plane changes to a space debris object in LEO was investigated, including oblateness and aerodynamic perturbations. Without any manual tuning, nor a-priori estimates, the optimization tool is able to find time-optimal trajectories. The tool shows remarkable flexibility, allowing additional perturbations or operational constraints, providing a powerful additional asset to Tudat for the preliminary design of low-thrust transfer trajectories.

Distant Retrograde Orbits (DROs) are special orbits for third bodies in two-body systems. The third body revolves around the secondary – the smaller of the two primaries – in a retrograde way, meaning the direction is opposite to the direction that the primaries revolve around each other. DROs are not close to either of the primaries, making it difficult to model them as perturbed two-body orbits. There is no analytical solution for the initial conditions of DROs. This thesis presents a novel method of calculating an initial velocity guess which is then fed into a differential corrector that is able to calculate the initial conditions. In contrast to the state-of-the-art, this happens without the method of incremental steps in the initial position, which requires to go through all possible DROs for a specific two-body system first. For the calculation of DROs, numerical integration is done. Optimal integrator settings are determined, which is in this case an eighth-order Runge-Kutta method (RK8). By setting the tolerance to the lowest possible value, the accuracy requirements are satisfied. Furthermore, this thesis explores a different method of modeling DROs that makes use of Fourier series and polynomials, which had already been proposed by Hirani in 2006 for a different set of parameters. By exploiting explicit knowledge about the shape of DROs, this approach is made more efficient in terms of accuracy per Fourier/polynomial parameters needed and thus the computation time is enhanced. The second part of this study addresses the stability of DROs. This is analyzed in order to get an idea of what DROs would be suitable for future missions. For mass ratios of primary and secondary that realistically occur in the Solar System, all DROs that are closer to the secondary than the primary turn out to be stable when disregarding perturbations. Perturbations are modeled as a constant external acceleration with a constant direction, which is only a first step towards modeling the Sun's and other planet's point mass gravity (p.m.g.), the solar radiation pressure (s.r.p.), and other perturbations, as they are usually depending on time and position. With this rough estimate, only the Sun's p.m.g. is identified as a possible source of instability for DROs in the Earth-Moon system, as all other perturbations are too small.

The current project investigated the feasibility of aerocapture at Jupiter, and the benefits in terms of payload mass fraction that could be achieved compared to traditional orbital insertion burns. A numerical simulation model has been set up, as well as an analytical formulation of the problem. The numerical verification of the analytical model showed that the analytical model still needs to be refined to produce accurate and useful results. Thermal fluxes, a driving aspect of aerocapture, have been implemented by using correlation laws, as well as corrective terms, all retrieved from literature. The aerocapture problem was numerically modeled and has been then optimized. However, the best trajectories provided a negative mass fraction benefit of −0.37 when compared to a traditional insertion burn. The best available mass fraction for the spacecraft's entry-unrelated subsystems was 0.44. Therefore, apart from some niche applications, aerocapture at Jupiter can be considered unappealing at best in the near future.

When sunlight illuminates a body, a tiny pressure is exerted upon its surface due to the photons impacting on it. Such a principle forms the basis of solar sailing, in which the solar radiation pressure is used to accelerate highly reflective lightweight structures called solar sails. Similarly, a laser-enhanced solar sail is a solar sail in which also an external laser beam pointed towards the sail is exploited to generate thrust. In this way an additional laser radiation pressure is exerted onto the sail, hence conferring higher propulsive and steering capabilities, and leading to an increased maneuverability of the sailcraft. The main purpose of this thesis project is to provide a model of the laser-enhanced solar sail dynamics and to establish the advantages of laser-enhanced solar sailing as compared to "traditional" solar sailing. The analysis has been pursued focusing on interplanetary missions and considering ideal sails, i.e. sails able to perfectly reflect the impinging radiation. Normally, for low-thrust interplanetary missions the propellant consumption and time of flight required for the transfers to take place play a crucial role. However, since solar sails do not exploit any propellant, the traditional and laser-enhanced sailcraft performances have been compared by analyzing their flight-time optimal trajectories, focusing on three different mission scenarios: a Mercury orbit rendezvous, Mars orbit rendezvous and Neptune flyby. These trajectories have been computed by taking advantage of an evolutionary neurocontrol optimizer, in which newly added functionalities have been implemented with the purpose of optimizing laser-enhanced solar sail trajectories. The trajectory analysis results have shown that, if laser-enhanced sailcraft are used instead of traditional sailcraft, flight time gains in the order of 8-11% can be achieved for the missions to Mercury and Mars orbits, while a smaller 2.5% gain is achieved for the flyby mission to Neptune.

Temporarily Captured Orbiters (TCOs) - also known as Earth’s mini-moons – are meter-size asteroid fragments temporarily trapped in the Earth-Moon system. TCOs are challenging to identify due to their small size and high speed. While only two TCOs have been confirmed so far, studies suggest a constant presence of at least one TCO at any given moment. This research aims to analyze transfer possibilities to these objects using a spacecraft powered by low-thrust electric propulsion departing from hibernating orbits near Sun-Earth L1. The study focuses on the TCO 2006 RH120, but it intends to develop tools that can be used to analyze other TCOs as they are discovered by advanced survey systems under development. A fast and robust optimization algorithm is developed, which successfully analyzes various departure orbits and identifies low delta-v transfers in the order of 200 m/s.

An analytical low-thrust design tool for orbits around Earth has been developed which takes perturbations into account. The Simplified General Perturbations 4 model (SGP4) is combined with Edelbaum’s analytical low-thrust trajectory model. This resulted in the SGP4-LT tool which required an iterative version of SGP4. To obtain this iterative SGP4, an existing method was corrected and extended. A convergence rate of 99.5% was obtained for 17542 objects of the satellite catalogue. Convergence was not reached for combinations of inclinations smaller than 0.1° and eccentricities lower than 4e-6. SGP4-LT obtained expected results for orbit raising and non-coplanar orbit change. Altitude maintenance was performed which was based on the GOCE mission. SGP4-LT obtained a 14 % higher amount of propellant than GOCE had available. SGP4-LT provides within seconds a first approximation solution for low-thrust transfer trajectories around Earth and is capable of calculating DeltaV budgets for altitude maintenance in low Earth orbits.

Over the past few years, space missions to minor celestial bodies have gained increased attention from the space community. A prime example is the selection of Psyche as NASA’s fourteenth Discovery Program mission. Orbital dynamics in the vicinity of small irregular bodies pose great challenges for trajectory design. In particular, science orbits close to the surface of small bodies are often strongly perturbed by the irregular gravity field. These irregularities can potentially perturb the trajectory of a spacecraft in such a way that it becomes uncontrollable, resulting in impact on the surface of the central body or escape from the system. A less dramatic consequence would be the need for costly orbit maintenance maneuvers to counteract these instabilities, which is undesirable. For uniformly rotating bodies such as the Psyche asteroid, mean motion resonances with the asteroid rotation amplify instabilities even further, warranting the need for a systematic study of orbital stability in such systems. To increase our understanding of these dynamically challenging environments, we carry out an extensive numerical characterization of stability in the uniformly rotating second degree and order gravity field by uniformly sampling the initial condition space and the gravity field harmonic coefficients. In doing so, we consider two conceptually different notions of stability: Bounded-Input, Bounded-Output (BIBO) stability and the regularity/chaoticity of spacecraft trajectories, quantified by the Fast Lyapunov Indicator (FLI). Through this study we have been able to generate stability plots that can be used to quickly inform mission designers on stable and unstable regions in the phase space. Our results show that FLI maps are an effective complementary mission design tool that flag orbit instabilities sooner when compared to BIBO stability constraints. Finally, our numerical results are complemented by analytically derived equations of the semi-major axis and the eccentricity in the uniformly rotating second degree and order gravity field. These equations clearly show the origin and impact of resonant instabilities. This initial work can be developed further into a complementary mission design tool for future small-body missions.

Previous trajectory proposals with the purpose of exploring the Kuiper Belt have been limited to identifying trajectories to fly by a single pre-selected Kuiper Belt Object (KBO). Furthermore, these proposals were often limited to high-velocity flybys that pass through the Kuiper Belt in a limited number of years, or are based on the assumption of significant and uncertain technological advances. This thesis investigates the existence of currently feasible trajectories which position a spacecraft inside the Kuiper Belt for a significantly longer period of time. The feasibility of these trajectories is based on the assumption of current technological capabilities and a launch date between the years 2025 and 2040. To model these unique trajectories the conventional MGA-1DSM trajectory model is adapted in order to optimize trajectory problems that aim to reach the Kuiper Belt. The use of powered flybys is excluded in these problems in order to reduce problem and mission complexity. Optimization of the trajectory problems was done by performing an interactive multi-objective optimization approach with four distinct objectives on a set of twenty planetary sequences. The high complexity of these problems in combination with conflicting multiple objectives was found to necessitate an iterative optimization process using the pooled results of several algorithms in order to obtain satisfactory results. The optimization algorithm performance was further enhanced using various encouragement methods. By using the established optimization method multiple routes were identified that all culminate in a long-duration flight through the Kuiper Belt. The best results were found with planetary flyby sequences VVEJS, EVEEJN, and JN. The required launch energy (C3) for these trajectories ranges from 16 km² /s² , for sequences utilizing multiple inner planet flybys, to 75.5 km²/s² , for solutions utilizing adirect Jupiter-Neptune route. The maximum onboard delta V capability required for these solutions is 400 m/s. The flight time to the inner boundary of the Kuiper Belt ranges from 14.6 to 24 years. All thesetrajectories feature a flight time through the Kuiper Belt of well over or close to 100 years. In addition, it was found that trajectories that conclude their planetary flyby sequence with a Jupiter-Neptune leg are found to be especially well suited for long-duration Kuiper Belt flight.

With current technology, it has been found that the feasibility of long-term adaptable exploration missions at the far reaches of the Solar System and beyond is limited, due to shortcomings in conventional propulsion systems. Electrodynamic tether (EDT) propulsion methods may provide a viable alternative, utilising either the interplanetary magnetic field generated by the Sun, or even the interstellar magnetic field, to provide propellantless yet continuous thrust. The objective of this research is to assess the feasibility of an EDT propulsion system, applied to such deep space missions; this was done by creating a simulation environment using the Tudat toolbox, testing various EDT configurations and mission profiles, over a series of decades-long simulation periods. The results of this analysis found the EDT performance to be limited, providing spacecraft accelerations in the 1 nm/s2 range at 1 AU with recommendations made on alternative applications and analyses to be done.

Electric low-thrust propulsion has nowadays found wide application in space dynamics as it entails considerable savings in spacecraft propellant mass, thanks to the very high specific impulse that this kind of engine is able to generate. However, continuous thrust opens new extensive sets of feasible trajectories, and optimization algorithms are needed to mine the admissible search space and find optimal transfers. Practical methods to solve complex optimal control problems as low-thrust trajectory optimization typically involve high computational times, the major bottleneck of these techniques. The objective of this work is the development of a novel multiple-shooting optimization tool, employing a variational approach for quick derivative computation, and the assessment of its performance against a variety of test cases. Indeed, after a first analysis of practical optimization methods, the derivative estimation by finite-difference approximations has been found as the major contributor to the computational burden, and the propagation of the variational dynamics has been selected as an accurate approach to speed-up their computation. The theory of variational dynamics for multiple-shooting application has been analyzed in detail, and further developed for what concerns the second-order equations. After practical considerations on the method implementation (scaling procedures, sparsity patterns, et cetera) and its interface with WORHP, the selected non-linear programming solver, the tool has been applied to a broad range of test cases, spanning from elementary problems to practical applications. For what concerns the latter cases, two complex problems were analyzed and optimized: a CubeSat rendezvous departing from Earth-Moon L2 and arriving at asteroid 2000SG334, resulting in a propellant mass convenient trajectory suitable for asteroid reconnaissance well before a proposed NASA manned mission in 2069; The Kessler Run, i.e. the 9th Global Trajectory Optimization Competition (GTOC9), in which the developed tool, employed as last step of the optimization cascade of Strathclyde++ team, managed to make the solution constraint-feasible, valid and further mass-optimal.

Low-thrust propulsion has gained more popularity over the past few decades because of its high efficiency. Interplanetary transfer trajectories in particular benefit from low-thrust propulsion, considering the typically high Delta V to be achieved. In order to allow a fast design of such missions, first-order, efficient representations of transfer orbits are usually used before a more detailed and exact numerical model is applied. The finite Fourier series method is one of these so-called shape-based methods that are suited for this. In this thesis, the focus is twofold: it lies on the implementation and validation of the method in TUDAT, and on improving this first-order method through a different initialisation strategy with the goal of improving its convergence speed and its three-dimensional stability. During implementation, some inconsistencies have been encountered that were not clearly, or even incorrectly addressed or documented by the inventors of this method. These include the calculation of the initial guess, the definition of the decision vector, the performance of the two-dimensional unconstrained finite Fourier series, the two-dimensional reference results and the interpretation of the reference frame. After these problems have been overcome, the method has been validated successfully against three case studies. The original strategy is based on the approximation of the trajectory by means of a third-order power function. In the search of a better strategy, four different function types have been analysed: (the original) power function, an exponential function, a trigonometric function and a logarithmic function. The functions were tested on two transfer trajectories, both in two and three dimensions: from the Earth to Jupiter and from the Earth to Dionysus. It has been concluded that the use of the proper initialisation strategy can considerably boost the effectiveness of the finite Fourier series method. However, a clear contrast between the two-dimensional and three-dimensional version was observed: the two-dimensional version of the algorithm greatly benefits from an exponential function to generate a priori values and shows an increase in convergence speed of up to 42.6%. On the other hand, there has not been a single approach that decreases the convergence time of the solver nor improves the stability for the three-dimensional version. This also led to the conclusion that the finite Fourier series method is rather sensitive regarding a priori values for the axial candidate.

The number of objects in space is increasing over time, and therefore it is desired to find more efficient propagation models in terms of accuracy and computational speed. This thesis project focuses on the propagation of the state and uncertainties of Potential Hazardous Asteroids, to predict potential Earth impacts. A machine learning technique is proposed to reduce the computational expensiveness of current propagation techniques. The PHA position and the error made by the uncertainties are predicted using a neural network, which uses data from currently known PHAs. Several options are considered regarding the input and output variables and the networks are also tuned. The aim for the best model is to find a reasonable accuracy for the prediction of the position and the uncertainty of newly discovered PHAs.

KNO3-Sugar propellants, also known as rocket candy, form a group of simple, cheap and safe solid propellants that are used extensively in student and amateur rocketry communities. One of the most frequently used compositions is KNO3-sorbitol (KNSB) with a typical 65/35 ratio by mass. This composition is used extensively by Delft Aerospace Rocket Engineering (DARE) for small experimental launches including the record-breaking flight of Stratos I in 2009 to 12.3 km altitude. However, KNSB propellant quality has been inconsistent: propellant density is occasionally below 85% in combination with large surface defects. Besides a very high grain rejection rate this has resulted in several explosive failures of new experimental motors in recent years.

The Kuiper belt is one of the last mostly unexplored regions in the Solar System. Exploration of the Kuiper belt can greatly increase humanity's understanding of the Solar System's formation and evolution. The use of low-thrust propulsion for Kuiper belt missions has the potential to improve the payload mass of the mission due to the high efficiency of its propellant. This research looks at the required methodology to optimize low-thrust trajectories with Kuiper belt object flybys. The trajectory is modelled using Tudat with spherical shaping as the trajectory parameterization method. A methodology is constructed which switches between high-thrust and low-thrust legs to constrain the input space for the low-thrust optimization problem. By using close-approach graphs and optimizing multiple flybys at the same time a trajectory with two Kuiper belt object flybys is found. The result is a robust method to find Kuiper belt object flyby trajectories with low-thrust propulsion.