Ballistic capture is a transfer method which was first applied in 1990. It allows a spacecraft to approach a target celestial body and enter a (temporary) orbit around it without requiring manoeuvres in between. Ballistic capture is a promising concept, as it is expected to be safer, cheaper, and more flexible in terms of launch windows than a traditional Hohmann transfer. Currently, a computationally efficient method which simulateneously allows for an inisghtful description of the dynamics of the ballistic capture problem remains to be found. A potential solution lies within the field of Lagrangian Coherent Structures (LCS). LCS is defined as a separatrix of regions in a flow with distinct dynamics. It may be possible that LCS around a planet have some correspondence to results found using stable set manipulation, a classic technique for obtaining capture trajectories. In this research three new areas within the field relating LCS to ballistic capture are explored. Firstly, it has not yet been shown what LCS can be found in an area around a planet, without making use of a priori stable set information. Furthermore, it is unclear what the effect is of changing the integration time in the procedure of extracting LCS. Finally, there has not yet been an analysis to show how the LCS relate to stable sets with different number of revolutions n. In this work two algorithms for extracting LCS have been developed. One is based on the simple but efficient computation of the Finite Time Lyapunov Exponent (FTLE). Another is based on the more involved Variational Theory. Both algorithms are validated on a toy problem used frequently in LCS extraction studies, and are then applied to the Elliptic Restricted Three Body Problem (ERTBP). It is shown that LCS around a planet yield resemblance with stable set results. The FTLE-based algorithm is able to quickly and efficiently identify the shape of the stable set. The Weak Stability Boundary, however, can not be extracted distinctly. The Variational Theory-based algorithm yields more distinguishable results for the Weak Stability Boundary. It is shown that large and constant integration times are beneficial. It is shown that extracted LCS form an approximation of the average resulting WSB for all stable sets. ... Read more

Ballistic capture is a relatively novel concept in interplanetary mission design with the potential to make Mars and other targets in the Solar System more accessible. A complete end-to-end interplanetary mission from an Earth-bound orbit to a stable science orbit around Mars (in this case, an areostationary orbit) has been conducted using this concept. Sets of initial conditions leading to ballistic capture are generated for different epochs. The influence of the dynamical model on the capture is also explored briefly. Specific capture trajectories are then selected based on a study of their stabilization into an areostationary orbit. This stabilization uses a combination of a brief high-thrust maneuver at periapsis and a low-thrust control law that spirals down to the final orbit. The captures selected are then targeted from the sphere of influence of the Earth with a low-thrust heliocentric transfer that is optimized using direct transcription and non-linear programming theory. An arrival-departure date grid is constructed with fuel-optimal transfers obtained for all epochs considered.
Finally, a simple study of the escape from Earth is performed for completion. A strategy to quickly escape Earth and avoid radiation damage in the Van Allen belts is defined using high-thrust chemical propulsion, including the computation of gravity losses due to the use of finite burn maneuvers. The result is the preliminary mission design of a mission concept to Mars using a 16-Unit CubeSat that employs ballistic capture and dual chemical-electric propulsion to reach an areostationary orbit. Estimations of the time of flight and fuel consumption for each stage of the mission are obtained. ... Read more

In interplanetary mission design, ballistic capture is the phenomenon by which a spacecraft approaches its target body, and performs a number of revolutions around it, without requiring manoeuvres in between. For a spacecraft to be captured, its gravitational interaction with at least two celestial bodies has to be taken into account. Because of their fail-safe nature (eliminating the possibility of single point failures), their fuel efficiency and their wider launch windows, ballistic capture trajectories are of particular scientific and engineering interest. Capture orbits are characterized by a specific qualitative dynamics, defining almost-invariant regions in a given space, guiding transport phenomena; the introduction of structures, defining and bounding such domains, naturally follows. Traditionally, the set of initial conditions leading to capture, the Capture Set, has been computed by sampling the domain of interest, and hence analysing the forward and backward behaviour of the orbit associated to each sample. The main limitations of this approach reside in its large computational cost and, even for a dense grid, in the non-smooth approximation of the aforementioned boundary regions; the theory of Lagrangian Coherent Structures (LCS) has the potential of overcoming both limitations, allowing at the same time for a more insightful description of the phenomenon. In fact, Lagrangian Coherent Structures identify transport barriers in dynamical systems, separating regions with qualitatively different dynamics. The development of heuristics applicable to ballistic capture trajectory design and informed by such theory (i.e. flow-informed) appears desirable. In this research, different flow-informed approaches are presented and their relations with ballistic capture are discussed: following, a new heuristic, the Stroboscopic Strainline, is introduced. This new tool is therefore applied to different case studies at Mars, in order to approximate the capture sets associated to different numbers of revolutions and geometries. While a real-ephemerides model has been used to model the dynamical environments, different levels of fidelity have been investigated: perturbing forces have been introduced not only to obtain more accurate results, but also to test the robustness of the proposed technique with respect to different features of the underlying dynamical model. Finally, it is shown how Stroboscopic Strainlines are a good candidate for characterizing the qualitative behaviour of ballistic trajectories, both forward and backward in time. ... Read more

The search for life in other celestial bodies has always been a topic of great interest within the scientific community. The curiosity to know if we are the only ones in the universe or not has driven the development of many engineering projects. This Master Thesis is meant to do its bit in this research field. Europa, a moon of Jupiter, is thought to have an ocean made of water underneath its icy surface. This ocean could be the perfect environment to find life. The hypotheses of the existence of an ocean gained more strength with the discovery of a water vapour plume in the southern hemisphere of Europa. This plume could be expelling particles from the underneath ocean. The main idea of the project is to design a mission of a pseudo-orbiter (a spacecraft orbiting Jupiter and doing flybys of Europa) which could collect particles from this plume during its flyby trajectory.

The objective of this thesis is to determine the maximum number of particles that can be collected with a pseudo-orbiter strategy. To achieve this, first, a plume particle model has been simulated. The outcome of this simulation is a 3D density profile of the water vapour molecules of the plume. The results of this part are needed in order to be able to determine the number of particles that the spacecraft can collect when crossing the plume. After this, the trajectory of the pseudo-orbiter has been designed. The Graphical Method for Same-body Transfers has been used in order to select potential trajectories that could lead to a maximum number of collected particles. This method allows the engineers to identify resonant orbits such that the ground-track of the flyby crosses regions of potential interest. Finally, coupling the two parts of the project has led to the determination of the number of collected particles for the selected trajectories.
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The phenomenon by which a spacecraft can both approach a celestial body and start performing revolutions around it, without needing to manoeuvre in between, is known as ballistic capture. For ballistic capture to take place, the spacecraft must be under the gravitational influence of at least 2 celestial bodies. Therefore, it is possible to design heliocentric transfers to Mars culminating in ballistic capture. With an impulsive-thrust strategy, these have already been studied, but were found to be less fuel-efficient and longer-lasting than Hohmann transfers. The objective of the present thesis is to investigate the characteristics of Earth–Mars low-thrust transfers to ballistic capture.

Small spacecraft are very mass- and power-constrained, so orbit transfers are challenging for them, especially to interplanetary destinations. To try and shift this paradigm, the study was carried out assuming the spacecraft to be a 16-unit CubeSat. In addition, to improve the relevance of the results for the design of a real mission, the decision was made to model the spacecraft's environment with many perturbing forces, including third-body perturbations, solar radiation pressure and non-spherical gravity. Furthermore, the performance of the thruster was modelled as being a function of the spacecraft's distance to the Sun.

Ballistic capture orbits at Mars were found in a systematic way, by investigating the past and future behaviour of candidate states with respect to Mars and collecting the states corresponding to capture into a capture set. The most regular orbits of the capture set were found among those making the closest approaches to Mars, but the opposite appears to be true about the orbits with the longer lifetime, which can reach more than a decade. Furthermore, two groups of capture orbits were identified: one coming from the inside of Mars' orbit, the other from the outside, with the orbits of each group being relatively close to each other.

Some capture orbits were selected, each with a different arrival date at Mars, and targeted from Earth, on multiple departure dates. The spacecraft was assumed to leave Earth's orbit with the planet's velocity and the heliocentric transfers were designed with an interior-point method, after direct transcription and collocation. It was found that if the spacecraft is given enough time, the low-thrust strategy requires roughly the same fuel regardless of Earth departure or Mars arrival dates. In addition, terminating a low-thrust transfer to Mars in ballistic capture does not carry additional costs, when compared to simply rendezvousing with the planet. The revolutions that the spacecraft is guaranteed to perform around Mars are then cost-free. With the assumed spacecraft and departure conditions, only around 5 kg of propellant are required to reach Mars and get ballistically captured. Nevertheless, the spacecraft needs to fly for at least 3.5 years, which can be too long for a CubeSat. ... Read more

Fragments of asteroids and comets constantly encounter the Earth and Moon in their orbits, impacting them as meteoroids. Observations of meteor showers on Earth have been studied for at least 50 years, in order to construct accurate Solar System meteoroid models. More recently, Earth-based telescopic observations of the light flashes produced by lunar meteoroid impacts have revealed useful in the validation and improvement of such meteoroid models. However, Earth-based lunar observations are restricted by weather, geometric and illumination conditions. As such, it has been proposed that a lunar orbiter could improve the detection rate of lunar meteoroid impact flashes. Assessing which orbit a spacecraft should fly in order to detect these flashes and improve current Earth-based observation methods is the aim of this thesis. The study is restricted to spacecraft with the CubeSat format and its inherent limitations, since it is also inserted in the context of the feasibility study of the Lunar Meteoroid Impacts Observer (LUMIO) and ESA’s Lunar CubeSats for Exploration challenge.

A methodology of sequential orbital trade-offs was followed, taking into account acceptance criteria based on the mission requirements and selection criteria based on the research objective. The goal was maximise the number of meteoroid detections, during the mission lifetime, while minimising the mission ∆V budget. Circular Frozen Orbits, Earth–Moon L2 Lyapunov, Halo, Near-Rectilinear, Vertical, Distant-Retrograde and Low-Prograde orbits were selected as candidates, based on a preliminary orbital trade-off. In order to determine the total number of meteoroid detections possible from a certain orbit, the lunar meteoroid environment was modelled and a coverage analysis tool was developed to determine the payload FOV-area in the lunar nightside.

Frozen Orbits were found to allow the detection of meteoroid impacts with kinetic energies too small with respect to the desired, so the design space was restricted to CRTBP orbits. From Lyapunov, Halo, Near-Rectilinear and Vertical Orbits it would be possible to detect between 1000 and 10000 impacts during the mission lifetime, but detections from some DROs could be one order of magnitude larger. Nonetheless, since transfer costs to DROs are known to be high, a Near-Rectilinear Orbit, with a minimal ∆V budget, was chosen as the operational orbit. ... Read more

Many interplanetary missions massively leverage the lunar gravitational pull in the so-called low-energy regime to converge to their aim, saving consistent amount of fuel. Among these, two future Japanese spacecraft are expected to repeatedly encounter the Moon along their trajectories to either facilitate the escape from the Earth–Moon system or opportunely target a specific region in its neighbourhood. Although never actively employed for preliminary trajectory design, lunar collision orbits have shown a rich dynamical structure and an applicability for both medium- and low-energy regimes. These characteristics, together with their intrinsic nature of being close to trajectories experiencing lunar fly-by, have encouraged this research. In this work, lunar collision orbits are employed to delineate a method for obtaining ballistic transfers between two successive lunar encounters, briefly addressed as Moon-to-Moon. This study is first carried out with the assumptions of the autonomous Circular Restricted Three-Body Problem, subsequently extended to the nonautonomous Bi-circular Restricted Four-Body Problem, including the solar gravitational influence.
Poincaré cuts are extensively used as a dimensionality reductant for lunar collision orbits: this allows to ascertain their similar behaviour with trajectories flybying the Moon, whose characteristics are partly foreseen by determining the associated intersection with the same cut. A patching is performed at the cut to obtain both single and multiple ballistic Moon-to-Moon transfers. The strict bond of lunar collision orbits with the invariant manifolds of simple periodic orbits about Lagrangian points is confirmed and exploited to design ballistic itineraries connecting highly elliptic orbits about the Earth to horizontal Lyapunov orbits of the Earth–Moon system, via a single Moon-to-Moon transfer. With the usage of the lunar collision orbits and the Poincaré cut, a simple optimization technique is implemented to retrieve a properly defined Moon-to-Moon transfer from a trajectory missing a second fly-by with the Moon. Including the presence of the Sun, a similar method for obtaining single and multiple Moon-to-Moon transfers is developed. A classification of lunar double-collision transfers is then performed within the same framework, highlighting their similarity with other studies in past literature, eventually leading to the construction of a database of Moon-to-Moon transfers. The latter, conceived as an improvement with respect to the former version by adding the lunar gravitational influence, shows its applicability in real preliminary trajectory design. ... Read more