The dynamics of rendezvous of spacecraft in circular orbits is a problem that is well-understood and that is regularly taught in orbital mechanics majors, as are the techniques of linearization and the applications of the state transition matrix. The design of strategies for rendezvous and formation flying often makes use of standard building blocks in the form of specific manoeuvres and trajectories. Typical rendezvous manoeuvres include the Hohmann transfer and the radial hop, a manoeuvre that can change the along-track separation but that does not change the semi-major axis. Typical rendezvous and formation flying trajectories include drift orbits, safe orbits and hold points on V-bar. In this study, the Hohmann transfer, the radial hop and the useful relative trajectories were generalized to elliptical orbits, and this has enabled the application of the insights gained from circular orbit rendezvous and formation flying to elliptical orbits. The insights gained from the theoretical developments have been applied to the mission analysis for Proba-3, a formation flying mission in a highly elliptical orbit.@en

The first mission proposals to visit the Alpha Centauri system use photon-sail acceleration as a mode of propulsion to reach this stellar system closest to our own Solar System. To prepare for a future mission, the photon-sail dynamics in the system is investigated. Planar Lyapunov orbits around the colinear classical Lagrange points are designed to explore the Alpha Centauri system. This has been done before in other systems like the Earth-moon and Sun-Earth systems, but not yet in an elliptical binary star system. Starting with an initial guess in the circular restricted three-body problem without photon-sail acceleration, a Multiple Shooting Differential Correction (MSDC) algorithm changes the trajectory to a periodic orbit. A continuation method increases the eccentricity to match e = 0.5208, which is the eccentricity of the inner binary system of Alpha Centauri. The lightness number of the photon sail is increased to add photon-sail acceleration to the model up to a defined maximum of ?ZNe = 2. A set of five constant steering laws is chosen to investigate its effect. Next to that, the moment at which the periodic orbit starts in terms of the true anomaly is varied as well. This results in a set of 40 families of periodic orbits with increasing lightness numbers. Depending on the orientation, the augmented Lyapunov orbit either shrinks into smaller orbits or expands into larger orbits when increasing the lightness number. If the orbit shrinks, it can either converge into an artificial equilibrium point or the photon-radiation pressure on the sail can become minimal. In that case, the Lyapunov orbit becomes (almost) independent on the lightness number and reaches ?ZNe = 2. If the orbit expands, the maximum velocity will eventually go to infinity. At this vertical asymptote, the maximum lightness number is found. The initial true anomaly of Alpha Centauri 0 has a great effect on the Lyapunov orbits around L2 and L3 in the classical ER3BP. For 0 = 0, the orbit either converges to an AEP or the maximum velocity goes to infinity. For 0 = , a few orientations can reach ?ZNe = 2. To further explore Alpha Centauri, an adaptive differential evolution algorithm is used to design trajectories between the Lyapunov orbits. The performance of the algorithm is expressed as the Euclidean difference between the states at the end of the departure leg and the beginning of the arrival leg. Three different lightness number of ? = 0.1, 0.5 and 2 are used for these trajectories. With a lightness number of 0.1, the dimensionless Euclidean error is in the range of 1E-1 to 1E-3, depending on the Lyapunov orbits. With this lightness number, the stars are also used as a gravity assist. For larger lightness numbers, the Euclidean error becomes negligible in the range 1E-7. With a lightness number of 2, the time of flight during the trajectory is significantly lower. In future research, this can be further decreased using an MSDC algorithm.

To be able to understand and predict space weather better, global in-situ satellite measurements are needed at an altitude of 100-150 km. However, due to the high density, space weather induced winds and the lack of data, it is a challenge to design a satellite mission to that region. Therefore, in this thesis, the influence of horizontal wind on satellite aerodynamics in the lower thermosphere is analyzed. The impact of the choice in satellite geometry design and orbital parameters on the satellite's aerodynamics and wind sensitivity is tested. To model satellite aerodynamics in this high-density region, a method of using the Stochastic PArallel Rarefied-gas Time-accurate Analyzer, SPARTA, is proposed. It is proven that the worst-case horizontal wind can have a negligible influence on the satellite’s drag coefficient depending on its attitude and satellite geometry. Based on the obtained conclusions, recommendations are given to simplify the design process and reduce aerodynamic drag.

Many contemporary interplanetary missions use efficient low-thrust engines to reach the far corners of our Solar System. Their trajectories, however, have proven to be complicated to optimise due to the non-impulsive manoeuvres involved in low-thrust spaceflight. Even though shaping methods have been used extensively to reduce the computational burden, multiple-gravity assists and the presence of constraints create significant computational hurdles. Reducing the number of fitness evaluations during optimisation is one way of speeding up the search and can be done by `pruning away' regions of infeasible trajectories. In this research, we approach this by applying clustering, an unsupervised machine learning approach, to single leg trajectory optimisation problems based on a hodographic shaping trajectory model in combination with restricted two-body dynamics. Through clustering, groups of promising trajectories can be isolated so that unwanted regions can be discarded. Earth --- Mars, Earth --- Venus, and Earth --- 9P/Tempel 1 trajectories are used as test cases and are shown to exhibit periodic behaviour (related to the synodic periods of the departure and target bodies), which enables clustering on grid search-generated datasets. Different clustering algorithms were compared using the Silhouette, Davies-Bouldin, and Calinski-Harabasz internal validation indices. However, traditional clustering algorithms such as (H)DBSCAN, OPTICS, KMeans, and Gaussian Mixture Models, failed to robustly provide clusterings that can be used for pruning, because of the oblong shape of the clusters and the absence of data/noise density differences due to the artificial nature of the problem. Instead, a multimodality-based clustering model called SkinnyDip was found to be much more promising for this task. This algorithm comes with the additional advantage of having very few hyperparameters, eliminating the need for extensive parameter tuning.

The gravity assist (GA) plays an important role in space missions since itwas first applied by the Luna 3 vehicle in 1959. For preliminary trajectory design, the so-called patchedconics model provides a simple model for a gravity assist. This approach, based on twobody formulations, splits amulti-body probleminto a succession of two-body problems. This model has a fundamental assumption: the trajectory of the spacecraft is driven by one celestial body only. A boundary for switching the driving bodies is defined by the Sphere of Influence (SoI) of the GA body. The patched conics model cannot be used to study low-energy trajectories. Moreover, it fails to describe special dynamics existing in the multi-body regime, such as the invariant manifolds. The three-body formulation is a logical choice to study the dynamics in the multi-body problem. In order to reduce its inherent difficulty, the circular restricted three-body problem (CR3BP) formulation is developed to study the behavior of the motion of a particle influenced by two massive bodies simultaneously. Flybys in the CR3BP have been studied by many researchers, using a numerical or semi-analytical approach, e.g. the Flyby map (FM) and Keplerianmap (KM), respectively. Inspired by these approaches and the idea of artificial intelligence, this thesis focuses on the investigation of flybys froma machine-learning perspective. @en

In the field of radio astronomy the Ultra-Long Wavelength (f < 30MHz) band is unique, it has been studied for nearly a century yet it is still almost completely uncharted. Due to the reflective properties of Earth's ionosphere this band is nearly completely inaccessible for ground-based observatories, which can only receive frequencies down to 8 MHz in ideal conditions. This band may only be explored from space, but the creation of space based observatoriesis problematic due to the large telescope sizes associated with these frequencies. The only viable solution to space-based radio observation is the use of radio interferometry, a process which combines measurements of multipleradio receivers to act as a single instrument with a larger aperture. Plans to establish these constellations have existed for some time, but have always been too expensive. With the rise of micro-satellites the concept of a radiointerferometry constellation has become economically viable. The OLFAR mission is one among the many recent radio interferometry concepts, which stands out among its peers through the application of a swarm design philosophy.The most important instrumental property of a radio interferometer is the number of available instrument pairs (baselines), and the distribution of their relative orientation in uvw space. To facilitate radio interferometry at 10MHz and lower frequencies the OLFAR swarm requires orbits which offer relative velocities below 1 m/s, while also being sufficiently stable to keep the baseline between its members below a maximum of 100 km. A minimal separationof 500 meters between satellites is used for collision safety. Early concepts for the OLFAR mission made use of Lunar orbits, where the Moon would act as a radiation shield against Earth's interference. Previous studies have shown thatsuch orbits expose the swarm to unacceptably large relative velocities, which is why alternative deployment locations are still being studied. This thesis studies the applicability of swarm orbit designs around the fourth Lagrangianpoint, denoted as L4. This point offers very promising orbital properties, but it has not been studied in detail due to the swarm's exposure to interference. As a basis for this work it is assumed that the 9dB of interference mightbe worked around through the dynamic range of hardware and longer integration times, making L4-centric orbits aviable deployment location.Particular attention is paid to developing an accurate numerical model for a perturbed orbital environment, which is necessary to provide long-term orbits of good quality. The inclusion of perturbations in this model is based on theirmaximum demonstrable effect on baselines and overall satellite positions over a year in orbit. After establishing the numerical simulation environment the satellite swarm design problem around L4 is posed as an optimisation problemfor heuristic algorithms. Based on small-scale experiments the efficiency of different algorithms and architectures is evaluated, and the best-suited solution is used to optimise swarm designs for the OLFAR missions. The resultingmethod of choice maximises the potential of multi-threading, using 32 connected differential evolution algorithms with 48 population members to perform as a single algorithm with a population of 1536 individuals.Using this method satellite swarm designs and orbits of up to 35 elements are found, which demonstrably meet all interferometry-related mission requirements for over a year in orbit while only relying on passive formation flight. These swarm designs rely on a process which is described as swarm folding to achieve this result. By distributing the swarm as a column mirrored in the barycentric z direction with uniform velocities, the swarm initially folds overitself. This folding motion is periodically repeated throughout the designed orbit after the initial fold as a result of the swarms natural orbits. The folding motion greatly enhanced long-term cohesion of the swarm, and it creates avery dynamic baseline distribution pattern for radio interferometry. It is demonstrated that these orbit designs have near-ideal baseline distributions, wherein they are only limited by the natural limitations of the Lunar orbital plane.Though the application of swarm folding these designs remain compact for long time periods, even in a perturbed environment. The demonstrated designs have feasible mission lifetimes up to 3 years in-orbit, requiring only a fewmanoeuvres during this time to enforce the 500 meter separation for collision safety. Through the application of active formation control it is expected that this can be extended to 5 years in-orbit with the right swarm orbit design. Itis also expected that using the methods in this thesis larger swarm designs might also be found, potentially ranging into 50 satellites. The largest hindrance to further extending the size of the swarm is the risk of near-collision events,which are inherent to the folding motion.

The number of Moon missions is increasing, but to facilitate these missions, an improved approach for lunar navigation is required. The proposed strategy is to deploy a constellation in Polar or Equatorial Medium Earth Orbits (PECMEO) based on GNSS technology, which can be utilised as universal lunar navigation system: the Lunar Positioning System (LPS). The system will provide navigation for lunar missions on a more autonomous base and without limitations on the number of receivers. However, for the nine LPS navigation satellites to provide accurate positioning for lunar objects, it is crucial that the positions of the satellites themselves are estimated with high accuracy. This is because the ephemeris error of navigation satellites is a dominant factor in the position error of lunar objects. This thesis investigates the achievable position estimation accuracy for the LPS. The estimation is based on observations provided by GNSS constellations, but also by precise inter-satellite ranging within the constellation to enhance the position knowledge of the satellites significantly. This research focuses on the feasible position estimation of the LPS satellites and, specifically, what improvements can be achieved by including ISL. In order to correctly perform the estimation for the ISL systems, modified least-squares algorithms have been developed suitable for observations linked to multiple satellites and the simultaneous position estimation. The average 3-dimensional position error is 7.84 cm if no ISL is used. When ISL is added to the estimation, the average 3-dimensional position error reduces to 1.80 cm. Therefore, it is shown that significant improvements can be achieved for the positioning of the LPS satellites by using ISL. With the achieved accuracy and the prospected improvements in the solution, LPS is shown to be a viable system for lunar navigation.

Many low earth satellites use GNSS for orbit determination, both for operational purposes and post-facto scientific orbits. Using GNSS systems for Lunar navigation proves difficult, however, due to the signals being weak and having limited coverage. This thesis investigates, through numerical simulation, the usage of a constellation of Polar or Equatorial Medium Earth Orbit (PECMEO) satellites for Lunar navigation. The system is proposed as alternative for orbit determination using ground-based observations, making navigation of the spacecraft more autonomous, without limitations on the number of receivers. A navigation constellation of 9 satellites at an orbital radius of 14 000 km is designed by minimizing the Geometric Dilution of Precision (GDOP). The resulting Pareto front of optimum solutions consists of two distinct groups of constellations. Firstly, constellation with lower mean GDOP and higher maximum GDOP have two orbits approximately orthogonal to the ecliptic plane, while the third orbit is in the ecliptic plane. Meanwhile, a second group of solutions with slightly higher mean GDOP, but significantly lower maximum GDOP are found for constellation with one plane approximately orthogonal to the ecliptic plane, while the remaining two planes have an inclination of near 45 degrees. One of the latter group of solutions has been chosen for the system for its lower maximum GDOP. The effect of omitting observations passing through the ionosphere is investigated to determine if there is a need to obtain observations at multiple frequencies to allow for ionospheric corrections. Omitting those observations results in a slightly increased GDOP right before and after a satellite passes behind Earth, of up to 56.4%. However, only 13.9% of the samples are effected, making the overall effect rather small. The positioning accuracy of the system is assessed by simulating pseudorange and carrier phase observations, and solving these with point position and kinematic least squares methods. Two main error contributions on the solutions are caused by observation noise and navigation satellite ephemerides errors. A solution for observations without ephemeris error, a mean 3-dimensional position error of 3.3m is obtained. A solution for noiseless observations yields a mean 3-dimensional position error of 26.8m. Finally, the solution obtained from observations with all simulated errors results in a mean 3-dimensional position error of 27.0m, to which the ephemeris errors are thus the main contributors, despite optimistic assumptions on their magnitude. The observed accuracy shows that the system is a viable navigation method for Lunar spacecraft.

The Laser Interferometer Space Antenna (LISA) is a European mission for the detection of gravitational waves in space set to be launched in 2034. The mission will see the deployment of 3 spacecraft in heliocentric orbit keeping a triangular formation with side length of 2.5 million km. Laser beams are exchanged between the spacecraft by means of suitably mounted telescopes (2 per spacecraft), with the objective of synthesizing a very-large baseline interferometer. The interferometric measurements are taken between free-floating test-masses placed inside the spacecraft. Due to the nature of the scientific objectives, the mission requirements on spacecraft-spacecraft pointing precision are exceptionally strict. Moreover, the formation needs to operate in almost perfect free-fall, therefore the solar radiation pressure needs to be continuously compensated for by the on-board thrusters. Gravitational wave signals are measured in the frequency bandwidth of 20 μHz to 1 Hz, requiring the vibrations in that domain to also be eliminated both for the attitude and the displacement. The task is made possible by the gravitational reference system, a complex device that keeps the test-masses from touching the walls of the spacecraft by applying on the latter an external force through μNewton thrusters. This mode of operation is called Drag-Free and Attitude Control System (DFACS). In this thesis we attempt to study and design a DFACS for LISA using a technique called Quantitative Feedback Theory (QFT). The design process starts from the definition of the orbits, the goal orientation of the spacecraft, the sizing of the solar radiation pressure induced disturbances and the derivation of the dynamics of the 19 degrees of freedom to be controlled. Using QFT, the design process is carried out on the DFACS using separation of the dynamics. As a result, analytical equations for the calculation of the LISA commands are derived and the methods to design a control system compliant to the scientific requirements imposed on the sensitivity are shown.

A detailed modeling of non-gravitational forces is an area that has been left unexplored in the past for orbit modeling of Magellan, primarily due to imperfect knowledge about its attitude and physical properties (optical properties and drag coefficient). As a result, past orbit analyses have restricted the non-gravitational force modeling by implementing a simple cannon-ball model for Magellan. Given that the Venusian surroundings can have significant impact on the spacecraft trajectory, the main objective of this project is to develop a reasonable macro-model for Magellan and investigate its impact on the modeled non-gravitational forces, and consequently on the orbit solution of the spacecraft. Presence of good non-gravitational force models can improve the dynamic orbit modeling of spacecraft, that can eventually enhance the gravity recovery capability of a mission.

In multi-stage launch vehicles, the adjacent stage re-enters the Earth atmosphere. Once the stage is re-entering the atmosphere, the low-melting-point materials melt and the inner parts will be exposed to excessive heat. With heat increasing, the parts will break into debris. Some of the fragments will burn in the atmosphere, others will crash into the Earth’s surface. Since there is a lack of knowledge about the re-entering physics, Demise Observation Capsule (DOC) project is started. The DOC collects information about the re-entry progress of launch vehicle stage, where it is mounted on. Several launchers and stages are considered to investigate the effect of the location on the DOC’s configuration. In an ideal situation, the DOC can be placed on all stages/parts of launch vehicles and at the same time it is optimized for that location. A generalized design concept that fits on several locations and stages, will reduce the cost and effort. Therefore, the thesis objective is to determine whether it is feasible to have a generalized DOC or an optimized DOC per location and load case. Additionally, the current DOC is designed for four locations and the second objective of this thesis is to optimize the current DOC and shift its center of gravity to the nose of the DOC. For this reason, the main research questions are as follows: Is it feasible to generalize the DOC concept design so that it will fit on every ESA launcher and stage and meet the predefined requirements and will withstand environmental loads while general operability of the DOC is guaranteed? How can the center of gravity be shifted on the DOC to its nose under the current designed loads such that the DOC can be made more stable?

Even though several orbit visualization tools exist, the ability to compare multiple satellite orbits or manipulate time are not readily available with the current tools. Furthermore, most other visualization tools require additional effort or installations to work properly. To address these issues with other tools an interactive, web-based, near-Earth orbit visualization tool was developed. This was done to answer the question: What are the uses of another interactive, web-based, near-Earth orbit visualization tool? After the development of the tool was completed, several use cases were examined. These use cases included visualizing constellations and space debris, reproducing the Iridium 33 and Cosmos 2251 collision, visualizing special orbits for educational purposes, and the reproduction of an aurora event which involved SWARM and EPOP satellites. The tool provides its users with a wide range of functionality, while keeping it easy to use. The tool can be accessed on orbits.tudelft.nl and the source code can be found on https://gitlab.com/SvenKardol/OrbitVisualization-Tool.

This thesis aims to assess how different convex penalty functions can be used in orbit determination methods and to design an algorithm to test them under different conditions.
Most traditional Precise Orbit Determination (POD) algorithms use the Least-Squares (LSQ) method to minimise the misfit between a set of modelled and actual measurements. The approach followed in this research is to investigate other convex penalty functions for this purpose in order to achieve better results than the traditional LSQ method, while maintaining the overall quality and robustness of the former.
To simplify the application of convex optimisation methods, an external toolbox was used to implement the different convex cost functions. The testing environment included a Precise Orbit Propagator (POP), measurement generating and processing functions, the POD algorithm itself, and data processing functionalities for the representation of the results. All the different components integrated in the final algorithm were validated before their application.
Tests to assess different aspects of the implemented penalty functions were run, regarding both computational aspects and solution performance. The traditional method was observed to present suboptimal results when the noise present in the observations included unprocessed outliers. In addition, cases where the observations were highly sparse yielded a suboptimal estimation of the trajectory.
After that, the L1-Norm was implemented as penalty function, alongside with Huber’s penalty function, which represents a combination of both LSQ and L1-Norm.
The use of the L1-Norm in the orbit determination algorithm outperformed the traditional method in the cases where it lacked performance, such as in the presence of unprocessed outliers or sparse observation sets. However, in other tests run, the LSQ algorithm was able to reach higher accuracy levels than the L1-Norm. Huber’s penalty function, conversely, proved to be a great candidate for both purposes, closely resembling the results obtained by the best penalty function for each test and even improving it on occasions, at the cost of a higher computational effort.
Finally, the designed algorithms were applied to a real-world study-case making use of GOCE data provided by TU Delft. These applications demonstrated satisfactory performance for each of the methods that were implemented and provided an important validation of the work.