The origin of the Martian dichotomy is subject to question and no substantial evidence exists. Some surface and interior features that are not visible in, e.g., topography data, can show up in gravity data. Therefore, this research inverts gravity data to find a crustal and mantle global density model. Previous research performed a one-layer inversion, assuming equal mass in all columns. Also, missions like InSight do not provide global interior information, but only at the landing site. The aim of this research is to provide a global density model of both the Martian crust and upper mantle. The inversion is performed using a weighted, regularized least-squares algorithm. The gravity input consists of the residual between the MRO120F data set and the state-of-the-art gravity field model of the TU Delft. The design matrix is built using Green’s functions, which define the influence of a mass element in all different directions on a measurement point. Using this least-squares algorithm, three different methods for inversion are used. The separate two-layer inversion, the combined independent two-layer inversion and the combined dependent two-layer inversion. All three inversion methods are performed on synthetic planets as well, for verification purposes. By performing all inversions on the synthetic planets, it was found that the combined independent two-layer inversion results in a strong decoupling of short and long wavelength signals, but is not able to attribute gravity signals to different features in the crust and mantle. The combined dependent two-layer inversion does lead to a result that shows decoupling of crust and mantle features. The hypothesis is that adding different gravity components to the combined dependent two-layer inversion will further increase its accuracy. The results of the inversion methods applied to Mars are in agreement with existing research in terms of standard deviations of the crust and mantle density anomalies. The maps were also analysed geologically, where the most important conclusion is the evidence of potential impact basins in the north polar region. These can be evidence to accept the several impact theory for the origination of the Martian dichotomy. Increasing the resolution and refining the third inversion method with multiple gravity components will increase the potential of gravity inversion to define geological features of Mars.

The number of space objects has largely increased in the recent years, becoming a considerable threat to the present and future of satellite operations and human spaceflight. This introduces a need to accurately compute the risk of collision between satellites and space debris. Current methodologies are limited by the type of encounter and the vehicle shape, usually simplified by a sphere. These assumptions rely mainly on linearization of the dynamics and simplification of the uncertainty distribution as a Gaussian function. Developing a collision probability calculation method that overcomes these limitations and provides high-accuracy results is the topic of this work. The methodology developed follows a hybrid combination of trajectory propagation and statistical methods for uncertainty propagation. With the propagation method covariance information of the satellite position and velocity will be available. Finally, the method is adapted to any satellite geometry by developing a numerical quadrature technique based on a combination of spheres to model the real body shape. The combination of these methodologies to compute the collision probability has been verified with a set of test cases by means of a Monte Carlo simulation and compared to alternative algorithms. It is found that the method improves the accuracy in calculating the collision probability by more than 70% with respect to conventional alternatives. Regarding real-life scenarios, the Cosmos-2251/Iridium-33 and the Chang Zheng-4C/Cosmos-2004 encounters are simulated. In both cases, the time of encounter and collision risk have been correctly estimated with the developed method. Finally, in view of the recent destruction of satellite Cosmos-1408 as a result of an anti-satellite missile test, a screening of its resulting debris threatening the International Space Station (ISS) is performed. During a two-week period, ten close encounters were detected, one of which posed a significant risk to the ISS. When applying the method considering the real shape of the ISS, the collision probability decreases by two orders of magnitude, proving the significance of this approach to correctly estimate the risk and guide space operations.

We have developed, from scratch, a 3D radiative transfer code based on the Monte Carlo method, that fully takes into account the spherical shape of a planetary atmosphere, multiple scattering, and the polarized nature of light. Accounting for the sphericity of an atmosphere is important for the analysis of observations near the planetary limb and the twilight zone, i.e. the regions on a planet where the parent star and/or the observer are low or even below the local horizon. In such regions, the widely used radiative transfer models that are based on the locally plane-parallel atmosphere approximation can lead to significant errors, especially for planets that have extended atmospheres. With our code, we simulate total flux and polarization signals of light that is reflected by spatially resolved and spatially unresolved planets with extended atmospheres. We discuss the effects due to the atmosphere’s sphericity and compare against computations with a locally plane-parallel code. Our results are relevant both for the interpretation of observations of various Solar System planets and moons (with atmospheres) and for the investigation of total flux and polarization signals of exoplanets at all phase angles, including during transits. Especially hot Jupiters are likely to have extended atmospheres and to be detected in edge-on orbits with transits. During a transit, an extended atmosphere can strongly increase the amount of starlight that is measured, thus leading to a smaller derived planet size. We also specifically simulate the polarimetric signal of Titan, Saturn’s largest moon that is known to have an extended atmosphere. We find that at small phase angles, as observed from Earth, Titan’s limb is strongly affected by the sphericity of its atmosphere and that at large phase angles, as observed by a spacecraft like Cassini, Titan’s brightness increases strongly due to forward scattered light.

The first close-up image of a black hole has been taken recently by means of a network of high-resolution telescopes situated all around the globe, also known as Event Horizon Telescope (EHT). In that regard, this Master Thesis reviews the feasibility of establishing accurate inter-satellite baselines in a two-satellite constellation of satellites placed in co-planar Medium Earth Orbits (MEO) equipped with telescopes to, amongst other applications, allow performing Very Long Baseline Interferometry (VLBI) on celestial bodies such as the supermassive black hole in the centre of our galaxy.

Regarding the workflow of this study, first a thorough analysis of the visibility conditions from the GPS and Galileo constellations has been performed for the pair of MEO-placed satellites. The results have shown that the receiver antennas need to adapt a nadir orientation to maximize the number of visibility contacts from mentioned GNSS constellations. Second, an assessment on the impact of different error sources in the absolute orbit accuracy has been conducted for the pair of satellites. The sensitivity analysis comprises errors that derive from realistic uncertainties in the geopotential model, GNSS orbits and clocks, satellites’ solar radiation pressure model, centre of mass and antenna reference point. The results have shown that the error sources that most affect the accuracy of the absolute orbit solution are disturbance aligned with the velocity component in both centre of mass of the satellites and reference point of the receiver antennas.

Furthermore, to achieve the high standards of relative navigation, optical ISL observations with micro-meter precision level were employed. This precision level was determined by the limits of the employed software tool, as the state-of-the-art precision of these measurements is at the nano-metre level. Due to the 1D nature of the ISL observation, it has been found that they cannot be processed alone and require the GNSS code and phase observations to be processed along with them. In these processes, the system architecture of the inter-satellite ranging system has been assumed to be two-way to rule out the errors that derive from the non-synchronization of the satellites’ clocks. The relative POD results have shown that the shorter the distance between the satellites, the higher the precision of the relative orbit solution in radial and along-track components, ultimately being limited by the precision of the ISL observations. The fact that the satellites are placed in co-planar orbits makes the cross-track component not be visible and probably yield conditioning problems to the LSQ matrix. Therefore, the impact of angular separations ranging from 1 to 10 degrees on the relative POD accuracy is also investigated. The most promising results come from the case in which the relative distance between the MEO-placed satellites is low (1,000km) and an angular separation in the orbital planes of 10 degrees has been induced. In that case, the relative orbit solution is improved in all components (radial, along-track and cross-track) and placed in the few millimetre level.

Though NanoSats are becoming increasingly capable of featuring active payloads, and acquiring inertial data at arcsec level precision; the payload operational duty-cycle largely remains limited by its data downlink capabilities. NanoSat laser communication terminal (LCT) promises 1 Gbps data downlink capabilities. However, LEO to ground free space optical data transmission requires precision attitude knowledge under agile ground target tracking conditions. Under such stringent operational conditions, the calibration of gyro-stellar misalignment and scale factors is a well-established practice for traditional satellites. Nevertheless, the impact of such non-idealities in the context of MEMS gyro-stellar based NanoSat precision pose estimation is unclear. Furthermore, the gyro-stellar calibration performance that can be achieved with NanoSat ADCS system requires further investigation. Under agile operational conditions, slew rate induced star tracker drop-out is common for NanoSats, which limits the operational envelope of agile precision tracking missions. To increase our understanding of attitude knowledge estimation capability of today's NanoSats, this thesis work is extended at Hyperion Technologies. In collaboration with Hyperion Technologies, gyro-stellar sensors are characterised; and CubeCAT LCT is used to laydown the reference payload and mission requirements of an agile precision terrestrial target tracking NanoSat mission. Based on state steady noise PSD properties, and attitude knowledge requirements set by the LCT, gyro-stellar configurations are selected, and characterised. A rigid body attitude simulator is developed, considering the characterised sensor suite, to generate representative nominal and non-ideal sensor outputs under four different mission phases: 1.) Inertial pointing with no angular rate, 2.) Non-harmonic sinusoidal manoeuvres 3.) Agile precision ground target tracking and 4.) Inertial target tracking with non-zero angular rate. Reaction-wheel time delay and torque limits are evaluated to analyse the feasibility of attitude pointing requirements under agile target tracking conditions. Due to favourable properties of robustness to large initialisation errors, fast convergence, and preservation of attitude quaternion unity norm constraint; UnScented QUaternion Estimator (USQUE) variant of UKF based filter is synthesised for attitude estimation. The USQUE filter is further extended to facilitate the calibration of gyro-stellar misalignment and scale factors. It is demonstrated that the presence of gyro-stellar misalignment and scale factor, and star tracker occultation under agile slew rates significantly deteriorates the attitude estimation performance of USQUE based attitude estimator. Star tracker misalignments and dropouts are observed to have a significantly larger impact on the attitude knowledge estimation performance, when compared against MEMS rate-gyro scale factor and misalignment. Degraded MEMS rate gyro sensors are observed to have little impact on the attitude knowledge estimation performance of 6/7 state USQUE filter. However, it has a considerable impact on the convergence performance of star tracker misalignment calibration. More persistent calibration manoeuvres are observed to improve the star tracker misalignment parameter estimation performance. Gyro misalignment and scale factor calibration objectives were not met. A root-cause analysis showed that the signal distortions introduced by such non-idealities are below the gyro-stellar noise floor. Calibration filter synthesised has the potential to improve autonomy, reduce commissioning and ground calibration times, and enhance NanoSat pose estimation performance.

In the Krafla region in North East Iceland, a change in the deformation pattern was observed in 2018. Since the 1975-1984 rifting event, there was subsidence seen in the Krafla caldera and along the fissure swarm. This subsidence was explained by deflation which decreased exponentially along the years. In 2018, this deformation pattern reversed, and for the first time since 1989, uplift was observed in the region. Therefore, this work concentrates on examining the change in deformation pattern in the region that occurred in 2018. Four geodetic techniques, a combination of ground and space geodetic techniques, are used to study this change in deformation pattern noted in the Krafla region. Data from 2016 to 2019 are considered as they span the time of interest when the change took place. In levelling, InSAR and GPS, the uplift observed is located to the North of the Krafla power plant. Similarly, there is an increase in net gravity seen to the North of the power plant. This suggests there is an increase in mass/density. A possible reason could be movement of magma from the deep to the shallow magma chamber. The reason behind this start of the magma movement is not known. On the other hand, there is continued subsidence and an increase in net gravity seen in the fissure swarms present to the south of the power plant. This result agrees with the fact that the uplift is concentrated (a local phenomena) in the northern region and there is still subsidence seen in the south. A simple Mogi model is fitted to InSAR and GPS data to understand the cause for this change in deformation. But, the fitted model provided very few insights in this work. The results from modelling mainly concentrated on the subsidence in the southern region and corresponding model parameters were obtained. The location of the source responsible for the modelled deformation (subsidence) is found to be near the power plant. The depth and volume however are not properly constrained. But since the model tries to constrain at deeper depths, correspondingly larger volume is also seen. This outcome strengthens the hypothesis that the source for the deformation could lie at deeper depths. Based on the overall results, the following recommendations are made to enhance the results: i) Maintaining the continuity in the data ii) To increase the number of benchmarks measured near the deformation area (especially in gravity and levelling) iii) Use of multiple source modelling for the better understanding of the sub-surface processes.

Saturn’s moon Enceladus harbours a global subsurface ocean beneath its icy crust. Tidal dissipation within the moon’s core generates a substantial amount of heat which leads to ocean convection. Observations of the moon indicate ocean thickness variations of up to 20 km from equator to pole and heterogeneous heat generation within the core likely results in latitude-dependent temperature gradients. The effects of meridional thickness variations and heterogeneous temperature gradients on rotating thermal convection have not been simulated in previous studies. Here we simulate a non-uniform spherical shell employing a degree-2 zonal thickness profile. Using direct numerical simulations, we analysed various properties associated with heat transfer behaviour for flows in a uniform and non- uniform spherical shell domain driven by thermal convection with the Rayleigh number in the range 1.6×10⁵ ≤ Ra ≤ 5.0×10⁶ and constant Ekman number of Ek = 3×10^-4 and Prandtl number of Pr = 1. Our results demonstrate that different regimes of convection exist, which depend on the relative influence of rotation. With increasing thermal forcing, convection moves from being restricted to equatorial regions to filling the whole fluid domain. Global scaling behaviour for both domains was found to be consistent with literature, although weaker polar convection in non-uniform shells caused a decrease in heat transfer efficiency and thus a diminished heat transfer scaling behaviour. The diminishing transport of heat at the poles in the non-uniform shell deviates from the predicted heat flux profile at Enceladus, suggesting that stronger thermal heterogeneities are required to enhance polar heat transfer.

The objective of this master thesis research project is to determine the overall polarisation sensitivity of the Near Infrared Spectograph (NIRSpec) on board the JamesWebb Space Telescope (JWST). Understanding the polarisation sensitivity is important to correctly interpret the output data and accurately calibrate the instrument during operational lifetime. As experimental research on this topic for NIRSpec was limited, a numerical code has been built to simulate the light following the optical path of NIRSpec. This numerical code is effectively a ray tracer with polarisation state analysis functions. They ray tracer is designed to be modular, making it straightforward to add new functions or optical elements, either for future work on NIRSpec or application to other instruments. The analyses regarding the polarisation sensitivity were performed in three main categories: the induced polarisation through reflections by mirrors, the grating efficiencies and overall throughput, and the effect on the calibration process. The JWST is a large space telescope that aims to help better understand every time period of the universe from the Big Bang till the present. The launch is currently scheduled in March 2021. The JWST shall provide new data by observing thermal radiation from various celestial objects. It houses four main science instruments, one of which is NIRSpec developed by the European Space Agency. The optical design of NIRSpec is based on three three-mirror anastigmats and six main opto-mechanical assemblies. Two of those assemblies are the grating wheel assembly which houses dispersive reflection gratings and the calibration assemblywhich is used to internally calibrate the instrument. These optical elements introduce a polarisation sensitivity, meaning that the instrument output data will depend on the polarisation state of the incoming radiation. Even though NIRSpec will mainly observe unpolarised light sources, a degree of polarisation will always be induced via reflections by themirrors. The optical path of the calibration beam differs from the nominal science path, so a different degree of polarisation will be induced via the calibration path compared to the nominal science path. Application of the calibration measurements to the science measurements can thus lead to errors on the deduced signals. The induced degree of polarisation for the nominal science path will likely remain below 2%. This degree of polarisation is slightly dependent on both wavelength and initial incidence angle, but not significantly. The analysis of the grating efficiencies clearly indicates a polarisation sensitivity up to 20% for the medium resolution gratings and up to 40% for the high resolution gratings. Due to the low estimated induced polarisation below 2%, the maximumuncertainty in the output data for unpolarised incoming light would be lower than 1%. Observing celestial objects with an inherent degree of polarisation, however, could introduce a significant uncertainty in the measurements. Finally, the calibration process has also been examined and it can be concluded that the induced degree of polarisation by the calibrationmirrors before the light reaches the grating will be 1 to 2% higher compared the nominal science path. Whether or not this difference should be taken into account will depend on the application. Recommendations for future work can be divided into four categories. First, the reflection grating efficiencies should be analysed in more details as the accuracy of the presented results is uncertain. Second, the filters and detector are modelled as single layer Fresnel surfaces, while in reality they consist of multiple layers of different materials. It should be researched how this assumption affects the presented results. Third, configurations using the long-slit spectroscopy and integral field spectroscopy have not been analysed while the microshutter assembly is modelled as ideal transmitter. Analysing these configurations would provide a more complete understanding ofNIRSpec’s polarisation sensitivity. Fourth, validation through measurement data would help determine the accuracy of the ray tracer presented in this master thesis research. This data could come from eithermeasurements of NIRSpec during operational lifetime or comparable instruments of which measurement data is available.

In 2022, ESA plans to launch the JUICE (JUpiter ICy moons Explorer) mission which will spend at least three years making detailed observations of Jupiter and three of its largest moons, Ganymede, Callisto and Europa. These moons are currently a hot topic within the science community as their interiors might include oceans consisting of liquid water. These oceans could provide life, but at the moment little is known about the exact composition and structure of these interiors. Only Earth based observations and a few fly-by’s have been performed to measure the characteristics of these moons. The JUICE mission will provide more detailed information on the moons through fly-by’s. This thesis research will focus on Ganymede as JUICE will be the first human-developed satellite to orbit thismoon. Ganymede stands out as a potential scientific target due to several specific reasons; the most remarkable being it’s intrinsic magnetic field. Only two other solid bodies within the Solar System generate such a magnetic dipole field (Earth andMercury). The complex interactions of this magnetic fieldwith Jupiter’smagnetic field are unique and could provide a lot of new knowledge when studied. Measurements from Galileo and the Hubble space telescope suggest that a subsurface layer of (saline) water is present within the moons interior. Saline water could be a good conductor of electricity, generating the magnetic field. The magnetic field of Ganymede could also point towards a complex core, which is another possibility for the generation of this field. It could be that the core of Ganymede consists of liquid, iron rich elements which generate and maintain this magnetic field. Unfortunately, current models of the gravitational potential field and the interior of Ganymede are still uncertain. A precise gravitationalmodel of Ganymede could provide a lot of information about this interior. An orbiter or in-situ probes are required to achieve high precision gravitational potential field models. JUICE is expected to obtain a model of Ganymede’s gravitational potential field of at least degree and order 15. This thesis will provide insight in how different possible internal density distributions of Ganymede influence the gravitational potential field of the moon. Thisway,when JUICE obtains more information on the gravitational potential field of Ganymede, variations within this field can directly be utilized to determine what interior aspects could cause these variations. From 44 billion 1D homogeneous models considered during this research, only 260 adhered to current known characteristics of Ganymede. Certain elements and water phases are present in all models: a pure iron or iron-sulfide core, a silicon mantle, an ice VI layer together with an liquid ocean and a outer crust consisting of Ice Ih. Dependent on the exact layer thicknesses within a model, intermediate ice phases, ice III and V, can also be present. Layer correlations between the 260 models were analyzed and fourteen models where selected for further research. These models were combined with different boundary and density variations to obtain different 3D heterogeneous models. Gravitational potential simulations for spherical harmonics coefficients up to order/degree 48 were performed. It was found that several relations exist between gravitational potential field data and internal density distributions within Ganymede. If one can effectively correct gravitational potential field signals for measurable components within Ganymede’s interior, several sets of internal structures emerge. Furthermore, taking into account the established limitations and correlations between layers, the gradient of the gravitational signal power over spherical harmonics degree can be directly related to the thickness of an interiors ocean. Several distinguishable models show that the presence of ice III, and to a lesser extent ice V, increase the gravitational signal power of a model. When combined with the correlations found between internal layers during this research, one could even establish an accurate first order approximate of Ganymede’s internal composition. These results, together with measurements performed by JUICE, will provide numerous new insights on Ganymede’s frozen enigma.

Large Low Shear-Velocity Provinces (LLSVPs) in Earth have been recognized in seismic data for several decades. The anomalies are however still poorly understood for reasons including their inconvenient location in the deep mantle, inhibiting progress in our understanding. Comprehension of these structures is important, because of their speculated major role in the formation and evolution of the Earth, and her residents. The gravity anomaly associated with the LLSVPs, the C22-lobs, are roughly observed in the gravity field of Mercury too. Therefore, the gravity and topography data about Mercury is assessed for indications of similar deep mantle features as observed in Earth. The advantage of Mercury is its thin mantle, that allows for a relatively shallow location of the core-mantle boundary (CMB), hence shallow deep mantle anomalies. The cause of the thin mantle is yet unknown, currently suggested explanations include vaporization of the mantle due to the immense heat of the solar nebula or a hit-and-run collision scenario that ripped off the mantle of Mercury. In this research it is investigated how deep mantle structures like LLSVPs and CMB topography could account for the gravity field of Mercury. It is concluded that deep mantle structures with comparable size and density characteristics as the LLSVPs in Earth could exist. Compensation by CMB topography would require a rough CMB. The results are highly affected by the limited knowledge about crustal compensation in Mercury and the truncation of the gravity field. Better crustal models of Mercury could be obtained by investigating local gravity anomalies in relation to topographic features, considering flexural isostasy and using normal modes. In addition to that, BepiColombo is currently en route to Mercury to gather more global data of Mercury, that would highly aid in our understanding of the crust and mantle of Mercury. A relation comparable to the hypothesised relation between hotspot volcanism and LLSVPs on Earth is also investigated for Mercury. A relation was not necessarily observed, however it was also not ruled out and requires more attention as soon as the crustal models have improved and more global coverage of volcanic features on Mercury is available.

The gravity field changes associated with the earthquake are analysed using the GRACE (Gravity Recovery and Climate Experiment) data. GRACE data can track the temporal variations in the gravity field and therefore information on mass redistribution can be achieved. There have been many studies already carried out using the GRACE data to analyse the coseismic and postseismic effects of the earthquakes. The previous studies mainly concentrated on the separation of the earthquake signals from various other signals and noises to understand the internal mass redistribution. In this work two recent past earthquakes have been considered. Sumatra-Andaman earthquake that occurred on 26th December 2004 with a magnitude of Mw 9.1. The other major earthquake that has been taken into account is the off coast Northern Sumatra earthquake (also called as Indian Ocean earthquake) which occurred on 11th April 2012 with a magnitude of Mw 8.6. A new initiative has been taken to separate the long term postseismic term (2004 earthquake) from the coseismic term and the effects of the 2012 earthquake (both the postseismic and coseismic effect). This decoupling process was done using the GRACE monthly solutions of spherical harmonics. Gravity disturbances were calculated from GRACE monthly solutions to understand the internal mass redistribution.

Autonomously landing a spacecraft on the surface of a planetary body with a degree of precision in the order of meters is highly challenging. Over the course of time, the landing ellipse, defined as the region with a 99% likelihood of where a space vehicle will land, has improved steadily but currently still has dimensions in the order of kilometers. The first and single Martian spacecraft that has performed a guided atmospheric entry and utilized precision landing technologies is the Mars Science Laboratory (MSL). The MSL probe and its focal point, the Curiosity rover, has thus been the most advanced mission yet to have flown to Mars. Nonetheless, space missions to the Red Planet have thus-far never landed following fuel optimal paths. Similarly, dispersions for landing on Titan with current technologies expand to hundreds of kilometers. The only reference mission to Titan is the Huygens probe, which has not utilized precision landing technologies nor optimal path planning. Besides, the goal of the Cassini-Huygens mission was to maximize descent time to augment scientific data retrieval of Titan's atmosphere. As part of the NASA Space Exploration Technology Directorate, a parafoil is proposed for landing on Titan due to its cost effectiveness, ease of deployment, relatively low mass compared to the prospective payload and capabilities of precise autonomous delivery. While considering all phases of Entry, Descent and Landing (EDL) and all elements of Guidance, Navigation and Control (GNC), the central focus of the research was put on the (powered and parafoil) terminal descent phase. The research core concerns a convex optimization programming approach to guarantee soft-landing. The algorithm has been verified based on the extensive Mars powered descent guidance literature. As part of the research conducted at NASA/JPL/Caltech, the algorithm has been extended to become compatible with landing a parafoil on Saturn's moon Titan. Throughout the discussion a distinction is made between lossless and successive convexification for optimal guidance. Both types have been simulated to either compute fuel optimal paths for powered Mars landing or pull-power optimal paths for parafoil Titan landing. The soft-landing is guaranteed while adhering to imposed mission constraints. By using the full capability of the spacecraft unprecedented precision may be achieved. This will enable engineers and scientists to reach the most alluring places on planetary bodies, thereby providing humanity a deeper understanding of the Universe.

The Rotation and Interior Structure Experiment (RISE) on the InSight lander and the LaRa experiment on the ExoMars platform will provide precise measurements (accuracies of a few mas) of the rotation of Mars, in terms of the Mars rotation and orientation parameters (MOP). These parameters include the rate of precession and the amplitudes of the nutations, of the length-of-day (LOD) variations, and of the polar motion components. The MOP are sensitive to the interior properties of Mars, particularly to the presence and size of a liquid core. However, uncertainties of current interior models in other physical parameters describing the internal structure of Mars, such as the temperature distribution, the composition, and the elasticity, limit the information on the interior obtainable from the MOP. Current estimates of the core radius have uncertainties of about 100 km, and suggest a fully liquid core. The improvement of the accuracy of the MOP solution from the landers coming from the inclusion of radio-tracking data from Trace Gas Orbiter (TGO) was studied in this project. Both numerical (through the orbit determination software GINS and Tudat) and analytical (through the ORB software developed at the Royal Observatory of Belgium) methods were employed to asses the sensitivity of the TGO orbit and radio-tracking data to the MOP of interest. In particular, an analytical method based on Kaula’s equations was developed to predict the effect of the MOP on a wide range of orbits. The satellites most affected by CW were found to be those in near-circular orbits at about 40∘ of inclination. The orbiters most sensitive to LOD variations were those in near-equatorial, highly-eccentric orbits. As for the improvements on the MOP estimation due to TGO data, a covariance analysis was performed with different assumptions on the dynamical and observation models, and on the estimated parameters. The improvement with respect to a lander-only solution is of up to 6 % for the CW components, up to 8 % in the LOD variations components, and up to 20% and 12% on the nutations amplification factor and the FCN frequency (the latter two judged excessively optimistic). However, no definite inference on the resulting core radius accuracy improvement could be made.

Satellite-derived gravity models have been used in modelling of several subduction zones, but not yet for the Sumatra subduction zone. There, gravity models can shed light on the geometry and density of the plate, and whether a slab tear is present under northern Sumatra, as seismic and tomographic studies present contradicting conclusions.

Ten different gravity sensitivity tests were carried out. Those tests investigated the sensitivities of the radial gravity (g_R) and the second gravity gradient tensor invariant (I₁) to different slab parameters (depth, thickness, density), three isostatic scenarios, and the inclusion of subduction-specific characteristics, e.g. a slab tear, and subducting crust. An innovative approach was implemented to determine slab thickness estimates based on oceanic lithospheric age, subduction direction, and a weighted half-space cooling model. Thereafter, a numerical model for the Sumatra subduction zone was developed which approximates the XGM2016 satellite-terrestrial gravity observations and supports a slab tear.

The gravity sensitivity test results together with the numerical model for the Sumatra subduction zone provide a valuable and universal foundation for future gravity-based subduction zone research.

In this work interval analysis is applied to the thirteen control effector Innovative Control Effectors model to find its trim set. The method to find trim states is based on interval box consistency. At low speed the method is capable of finding interval enclosures of single trim points with a high accuracy if the minimum number of required control effectors is used. At higher speeds the found accelerations are larger. When looking for a full trim set the method finds continuous bounds on the control effectors for the entire input range in one run. This is a good demonstration of the advantages that interval analysis has over conventional methods that generally can only find one trim point at a time. The found bounds are a maximum of 1 deg wide for each control effector, but despite this the remaining accelerations can be up to 0.5 m/s^2 for linear accelerations and up to 10 deg/s^2 for rotational accelerations. Because of these large accelerations the found solutions are not acceptable as trim conditions. On the other hand the potential that interval analysis has as a trimming method is demonstrated, since continuous bounds on trim sets have been found in a single run. This is a feat that no other trimming method has yet accomplished. Further research is needed to exploit the full potential of interval trim methods so that the results can be used for other purposes such as flight envelope prediction.