Venus presents a compelling case study of the greenhouse effect, resulting in the highest surface temperatures of any planet in our solar system. Despite its similarities to Earth in origin and size, Venus has a vastly different atmosphere, dominated by CO2 and thick sulfuric acid clouds undergoing retrograde super-rotation. To better understand Venus’ climate and characterise it, this thesis employs the technique of polarimetry to develop precise computational models of light scattering in its atmosphere. These models are compared with existing observations to investigate dynamic atmospheric phenomena, such as gravity waves and variations in cloud top altitude. Planet-wide gravity waves were observed by the Japanese Akatsuki spacecraft in thermal infrared wavelengths on Venus. These waves were attributed to the underlying mountainous topography and are generated when wind flows over mountains and propagate to themiddle and upper cloud layers. In chapter 2, we explore the possibility of whether orographic gravity waves of similar nature would be observable through polarimetry. As gravity waves propagate, they alter atmospheric density and aerosol distribution, making them observable through various imaging techniques. While direct and thermal imaging have primarily been used to detect these waves, those affecting higher altitudes cause much smaller changes in atmospheric density as compared to the cloud tops. Consequently, these high-altitude waves are challenging to observe with direct imaging and have been detected primarily through in-situ sensors or night-glow measurements. Unlike direct imaging, which captures both polarized and unpolarized light, polarimetry is more sensitive to density variations due to the high degree of polarization imparted by gas molecules, which also varies with solar and viewing geometry.

Planetary rings seem to be a common appearance around large planets because every large planet in the solar system has them. They have, however, not yet definitively been detected around exoplanets. Because the formation of rings might be closely related to planetary formation, as well as the formation of moons, much could be learned from discovering rings around exoplanets. To aid in this search, we developed a radiative transfer model that includes all orders of scattering and polarization and can calculate the reflected and transmitted light for any planetary orbit and ring geometry. Previous studies have analyzed the effect that rings have on a transit as well as on the reflected light but those studies have not included the polarization of light. Using the developed model, the effect that rings have on the reflected flux, polarized flux, and the degree of polarization was characterized by varying the orbit orientation, ring orientation, ring size, the optical thickness of a ring, and the ring particle properties. Our study showed that rings introduce unique features in both the flux and degree of polarization curves. Especially the existence of ring-plane crossings, when the ring is illuminated from the side, causes distinct features in the light curves. Adding polarimetric capabilities to the next generation of telescopes could help with determining the presence of rings due to the different scattering behavior of the ring and planet.
The developed model allows for a fast and easy generation of accurate light curves which allowed for two additional studies to be done. These were a bit smaller in scope and the first involved fitting the transit of a planet with a potential ring. The result of the fit and subsequent analysis is that there is likely no ring. However, because the model was not initially designed to deal with the close proximity of the planet to its star no definitive conclusion can be drawn. In the second study, the reflected flux and polarization of the transiting planet J1407b, which is suspected to have a large circumplanetary disk, were computed to assess the detectability. These generated light curves and values were then compared to unpublished observations made with the SPHERE/ZIMPOL instrument that detected no signal. The computed flux and degree of polarization lie well below the detection limit and are thus in agreement with the SPHERE/ZIMPOL observations.

Neuromorphic architectures are of interest in space application due to their energy efficiency. However, space radiation has been shown to damage computational hardware. Research has been performed on the radiation robustness of (pre-trained) spiking neural networks, and the brain has shown to be able to recover from certain types of lesions. Other work has shown Spiking Neural Networks (SNNs) can obtain advantages for graph algorithms. Such (distributed) SNN graph algorithmsmay become relevant for space applications. For example, SNNs may form a neuromorphic implementation of the Minimum Dominating Set (MDS) algorithm that others have proposed for distributed satellite swarm coordination. This research combines the trend of SNN implementations of distributed graph algorithms with neuromorphic space applications and brain-adaptation induced robustness as inspiration. It shows that brain inspired adaptation mechanisms can increase the simulated radiation robustness of an SNN implementation of an unweighted, distributed Minimum Dominating Set Approximation (MDSA) algorithm. An SNN implementation of the MDSA algorithm by Alipour et al. is created and used for this experiment. That SNN is adapted with a population coding approach, and with a sparse redundancy approach. These three SNNs are exposed to simulated radiation effects in the formof synapticweight increaseswhich occurwith a probability of 0.001% to 20% per synapse per timestep. Separate simulations are performed with a simulated radiation induced permanent neuron death with a probability of 0.01 % to 25 % per neuron per timestep. The SNN performance is measured by comparing its output to the unradiated algorithm output. The sparse redundancy increases the robustness against simulated radiation induced neuron death for radiation probabilities from0.5 % to 25% per neuron per time step, for theMDSA SNN. Belowthese probabilities, the adaptation mechanism is contra productive. Similarly, population coding is contra productive below0.1% and increases radiation robustness for simulated synaptic weight increase probabilities of up to 5%.

Uranus is one of the most intriguing and unexplored bodies of the Solar System. Its mysteries include its active atmospheric dynamics, its low internal energy, its extreme obliquity, its complex magnetic field, and its ring and satellite system containing possible ocean worlds. As of today, none of the current formation and evolution models can explain all its chemical and dynamical aspects. An in-situ mission to study Uranus' atmosphere could provide answers to this planet's mysteries, enabling the measurement of its deeper layers. A 6 DoF flight simulator was designed, with a focus on identifying the specifications and limitations of its Guidance, Navigation, and Control modules, for feasibly flying in Uranus' challenging atmosphere, and providing new science return. The mission architecture consists of two gliders flying near the planet’s equator and north pole until the 100 bar pressure level for around 13 Earth days, supported by an orbiting spacecraft in a circular, equatorial, and synchronous orbit, for continuous trajectory tracking and relay of the scientific data to Earth ground stations. Due to Uranus’ opaque atmosphere, typical optical navigation sensors such as star sensors, Sun sensors, and imagers are avoided. Instead, the modelled navigation sensors are taken from the payload suite.

Missions to small bodies are increasingly gaining interest as they might hold the secrets to our solar system’s origin while some are also posing a threat to life on Earth. The small size and irregular shape result in complex dynamics complicating the close-proximity operations. Furthermore, due to the long round-trip time communication delays of up to 20 minutes can exists, excluding any required computation time on Earth. Currently used approaches either rely on detecting pre-defined landmarks on the target, detecting features and matching them to a database, or tracking craters or unknown features across images (relative navigation). However, these methods rely heavily on a-priori information, suffer from computationally intensive matching steps, or depend on the accuracy of the initial state estimate.

This work investigated the usage of a novel CNN-based pipeline that can be used to autonomously navigate accurately around asteroids. A top-down CNN-based feature detector is developed consisting of an object and keypoint detection network in sequence, which detects n pre-defined keypoints designated on the target’s 3D model using the 3D SIFT algorithm. These 2D detections alongside their 2D-3D correspondences are sent to an Efficient Perspective-n-Point (EPnP) solver that solves the Perspective-n-Points (PnP) problem. The CNN-based feature detector replaces traditional hand-engineered Image Processing (IP) algorithms as it is more robust to illumination conditions and image noise. Furthermore, the use of a CNN facilitates an offline feature selection step and as such avoid the cumbersome and computationally intensive 2D-3D matching step of the detected 2D feature to their location on the 3D model, plaguing traditional approaches. This pose estimation pipeline can be used to navigate around the asteroid up until it covers the full field of view of the camera, and it can be used to(re)-initialize the navigation filter for a relative navigation approach.

The networks have been selected based on their applicability to embedded devices and this resulted in the use of the SSD-MobileNetV2-FPN-Lite as the object detection network and the Lightweight Pose Network (LPN) model as the keypoint detection network. This lightweight CNN-based pipeline has a fraction of the parameters and Floating Point Operations (FLOPs) compared to state-of-the-art deep-learning networks and pipelines. These networks have been trained and evaluated on synthetic datasets created in this work, consisting of 32,352 images with a variety of poses for a distance of 4.5 km to 9 km from the asteroid for different illumination conditions, asteroid orientations, and image corruptions that emulate real sensor artifacts.

The pipeline could achieve a mean and median line-of-sight distance estimate of around 42 m and 30 m, respectively, at a confidence level of 90% for the large relative range, while satisfying the accuracy requirement of a maximum 10% knowledge error for 99.979% of the cases. Furthermore, the pipeline has been proven to be robust against illumination conditions, occlusions, textures, and image corruptions, mimicking effects of real sensors and the space environment. Demonstrating the efficacy of this CNN-based approach for autonomous navigation around asteroids.

Due to the insufficient worldwide efforts to reduce greenhouse gas emissions and related global warming, marine cloud brightening (MCB) is gaining interest as an instrument to artificially lower Earth's temperature. MCB is based on exploiting the aerosol-cloud effects to enhance the albedo of stratocumulus clouds and prolong their lifetime by injecting clouds with sea salt aerosols. As there are still many uncertainties in the expected output of MCB due to the unresolved questions related to cloud processes and feedback mechanisms, this thesis aims to assess the efficacy of MCB to enhance solar radiation reflection of stratocumulus clouds using the turbulence-resolving Dutch Atmospheric Large-Eddy Simulation model. This assessment is made by investigating which cloud properties and processes that determine the cloud's radiative forcing are affected by the aerosol injection for different meteorological conditions and injection strategies in 30-hour simulations. The simulation domain has a horizontal size of 25.2 $\times$ 25.2 km$^2$ and 2 km in the vertical, with a mesh size of 100 m horizontally and 20 m vertically. The two studied cloud cases are based on the measurements of the first and second research flights of the DYCOMS-II field experiment and are characteristic for a shallow stratocumulus-topped boundary layer (STBL). The investigated surface aerosol injection strategies are a horizontally uniform source and a point source that is restricted to a single grid cell. In addition, an assessment is made of the effects of differences in aerosol number concentrations between the STBL and the free troposphere on the cloud's aerosol number concentration and radiative properties. This is done in 6-hour simulations with and without a uniform aerosol source, based on the second research flight of DYCOMS-II. The simulated horizontal domain is 3.2 $\times$ 3.2 km$^2$ and 2 km in the vertical, with a mesh size of 25 m horizontally and 20 m vertically. Our simulations showed that boundary layers with relatively low background aerosol concentrations were most effective in generating a negative radiative forcing, compensating slightly less than half of the forcing related to the CO$_2$ doubling in the atmosphere. For boundary layers with an average background aerosol concentration, the radiative forcing approaches a quarter of this value, which diminishes to negligible effects for boundary layers with relatively high background aerosol concentrations. For precipitating boundary layers, the enhanced radiative forcing is mainly caused by its suppressing effect on precipitation. For non-precipitating boundary layers, the reduction in cloud droplet size showed to be the primary source of the enhancement. No pronounced differences in efficacy were found when using a homogeneously distributed aerosol source or a point source. For the two studied cloud cases, investigation of the contributions to changes in the liquid water path showed that to exploit the effect of aerosol injection on the liquid water path, it is most effective to suppress precipitation and enhance cloud cover. The differences in aerosol number concentration between the STBL and the free troposphere significantly and consistently altered the aerosol number concentration in the cloud layer due to the entrainment of air from just above the cloud-top into the cloud layer. This indicates that these differences in aerosol number concentration need to be considered when modelling MCB, as they change the intended aerosol number concentration enhancement and thereby affect their cloud-modifying effects.

By the late 2020s or early 2030s, the next generation of telescopes will be able to directly observe the reflected starlight of Earth-like exoplanets. Because of the huge distance to other stars, such exoplanets will appear as single unresolved pixels. A single pixel can, however, provide information about what the planet looks like because its brightness varies in time as it rotates about its axis and orbits its star. Several researchers have shown that these changes in brightness can, indeed, be used to retrieve a map of the planet. Their methods use the Lambertian model of diffuse reflection to retrieve albedo maps of the planet's surface. We aim to develop new algorithms that can retrieve maps of non-Lambertian planets with a Rayleigh scattering atmosphere, clouds with water droplets that cause rainbows and oceans that exhibit a glint feature. We also aim to evaluate the validity of the Lambertian assumption for such non-Lambertian planets. We numerically compute reflected light curves with the previously mentioned non-Lambertian effects, including the polarization of the reflected light. Instead of retrieving albedo maps, we classify facets by their surface type and cloud coverage, using convolutional neural networks. We show that a convolutional neural network can classify facets on a non-Lambertian planet with an accuracy of 87% for an ideal geometry and no noise, when the rotation axis is known. Using another neural network architecture, we show that the rotation axis can be constrained with a mean squared error as low as 0.006 for our training data and similar results are seen for a model Earth. Including polarization in the retrieval improves the rotation axis retrieval's mean squared error (MSE) by roughly 15% and the classification accuracies of ocean facets and cloudy facets by 2% and 1%, respectively. We show that a retrieval algorithm that relies on the Lambertian assumption causes concentric artefacts about the poles when applied to light curves of a non-Lambertian planet for all inclinations besides face-on. The MSE of the rotation axis retrievals increases by roughly one order of magnitude for these inclination when making the Lambertian assumption.

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.

Over the last five decades, thermal modelling of airless minor planetary bodies such as asteroids have experienced significant improvements. However, at lower wavelengths of the mid-infrared range, thermal models such as the widely used Near-Earth Asteroid Model (NEATM) are still considered unreliable since reflected light starts contributing significantly towards the observed flux density. Through a controversy related to the Wide-field Infrared Survey Explorer (WISE) mission, which was an infrared survey telescope with four observational bands found at 3.4, 4.6, 12, and 22 microns, Nathan Myhrvold suggested that the thermal modelling carried out did not properly account for reflected light and that the results, especially derived from the first two observation bands, were compromised since Kirchhoff's law of thermal radiation was violated. To date, the WISE mission is considered the highest yielding mission with more than 158,000 asteroids detected, however Myhrvold's findings state that the result derived for about half of those detections are compromised. This controversy motivated this master thesis project to create a numerical code, which properly combines thermal and reflected light modelling, to further investigate the influence of the latter at the four WISE observational bands. The initial aim of this master thesis was the create an advanced thermal model, but due to the time scope of this master thesis, an intermediate thermal model named the Asteroid Thermal and Reflected light Model (ATRM) was achieved. On top of being able to model simple spherical and ellipsoidal shapes, the ATRM can model irregularly-shaped asteroids with precise orbital and rotational properties taken into account as do advanced thermal models, but assumes instantaneous thermal equilibrium as do simple thermal models such as the NEATM. Furthermore, the ATRM caters to mostly convex-shaped asteroids due to the simple shadowing algorithm implemented, and not taking into account multiple scattering. However, the ATRM is able to vary the surface albedo distribution pattern of an asteroid through an octant method, which is typically not the case for simple and advanced thermal models which all assume a homogeneous surface albedo. With the aforementioned capabilities of the ATRM, the percentage of reflected light in the total flux density at the four wavelength bands of WISE were estimated for different albedo values covering the majority of asteroids falling under the three broad Bus-DeMeo taxonomic classification system (C-, S-, X-types). Furthermore, the influence of the heliocentric distance, emissivity, and shape of the asteroid on the contribution of reflected light were investigated. Ultimately, this project is another step-wise progress in the field of physical characterisation of airless planetary bodies, especially asteroids, and has far-reaching consequences in terms of planetary formation, in-situ resource utilisation (ISRU), commercial asteroid mining, and planetary defence.

Despite a large number of in-situ missions, only VeGa-2 provided the high-resolution thermal measurements of the deep atmosphere of Venus below 12 km and they indicated a highly unstable layer below 7 km altitude. Lebonnois and Schubert (2017) tried to explain the VeGa-2 measurements by introducing a theory of a composition gradient in the deep atmosphere of Venus. In our research, we test this theory of composition gradient by making use of the near-infrared observations from Akatsuki and Venus Express missions in combination with the altimetry observations from Magellan Mission. To make use of the highly contaminated Akatsuki dataset, we develop a procedure to sequentially reduce the contamination to an acceptable level. Next, an atmospheric radiative transfer model is built to simulate the thermal emission coming from the surface of Venus, which is then used to generate a temperature vs altitude profile from the observations. Using this temperature profile we investigate the theory of composition gradient.

This research contains the design, modeling, and analysis of the Terrascope. This apparatus intends to use the Earth’s atmosphere as a lens to bend light rays from celestial objects and focus them into a detector placed at a distance from the Earth, for example, the Moon. We develop an independent model from that of David Kipping, on whose Terrascope research this work is based. Our Terrascope model uses gradient-index optics to calculate the light bending through the Earth’s atmosphere. We also model three different atmospheric effects which modify the light passing through the atmosphere: turbulence, Rayleigh scattering, and ozone absorption. Our results show that turbulence has the largest impact on the light, and, consequently, on the functioning of our Terrascope. It causes the light to spread out, decreasing the image resolution and amplification. Without atmospheric effects, our model simulations predict a maximum amplification of about 55,000, the same results as Kipping. This occurs when using a 1m detector aperture, 1.5×10ዃm detector distance, and 1000nm wavelength light. Using the same parameters, when scattering and absorption are considered, the amplification decreases by 14%. When turbulence is considered, the amplification decreases by 99.98% to a total of 10. This is much lower than Kipping’s prediction of 22,500. We conclude that turbulence is the most important aspect of the Terrascope to consider in any future work. The Terrascope continues to be interesting concept for study and may have promise for observing celestial objects if a farther detector distance, longer light wavelength, and different atmosphere are considered.

Human exploration on Mars is nearing actualisation and the space industry is therefore in need of vehicles with the capability of transporting goods and exploring the surrounding area. Current Mars rovers by NASA, such as the Curiosity, provide excellent researching capabilities from a remote location.

However, these land based drones are slower and less manoeuvrable around obstacles than airborne vehicles would be. Due to the need of transportation and exploration, this report aims to get acquainted with current research on Mars flight and provide a preliminary design concept enforced by the following mission goal:
”To aid future Mars colonists by providing a feasibility study of a flying vehicle capable of carrying a predetermined payload.”

To approach this goal, it was decided to determine which flying vehicle concept would be the most optimal in a Martian atmosphere via a trade-off analysis. Four options were considered and a balloon was deemed more optimal for a Martian environment compared to aircraft, rotor craft and flapping wing vehicles. The main reasons for this are that the balloon is the most power efficient and is a design that provides the least amount of risk concerning likelihood of failure and safety of astronauts.Thereafter, the process required to design a hot air balloon and the programming of the code is described. Results indicate that a balloon with a prolate ellipsoid shape is optimal with the ratio between the minor and major axis being 0.41, therefore resulting in a balloon with a major axis radius of 33.8 푚 and a minor axis radius of 13.86 푚. A surface area of 131.58푚² is selected for the flexible solar cells which have been calculated to be able to power a two propeller system ensuring that the balloon can counter headwinds of up to 15푚/푠.

Finally, to ensure altitude control is possible, a venting system is applied on the top of the balloon ensuring a venting volume of 117푚³ is possible. This is enough to ensure the balloon can land, take-off and control its altitude as desired.This thesis is therefore able to provide an initial design for a Mars exploration balloon capable of controlling not only its altitude but also its position. This is achieved by using the solar energy to increase the balloon’s temperature and a vent area of 19.03 푚² to control this temperature. All this provides a design that can be controlled and meets the versatility requirement as it is capable of carrying a variety of heavy payloads and fly past ground obstacles

The Trappist-1 system consists of an M-dwarf star and seven known planets tightly orbiting it, located 39 light years away from Earth. The system is interesting due to how closely the planets are orbiting their parent star, in addition to the likelihood of one of its planets containing surface water, a crucial component for life. The system has been the subject of many studies concerning atmospheric predictions and polarimetric modeling. However, these did not explore phenomena such as the atmospheric composition and its effect on the polarization signals, having a patchy cloud cover, and the eclipse of the planets behind their parent star. In this work, we present the phase curves of the polarized flux and degree of polarization of the individual Trappist-1 exoplanets, as well as the entire system including the star.

Aims: Analysing historical disk-integrated polarization data of Venus with the help of numerical simulations to learn about the time variability in cloud and haze properties, the position of the UV-absorber and the polar cap regions.
Method: With numerical simulations, polarization curves will be calculated for specific input conditions. We compare numerically computed polarization curves to the historical polarization data to derive the microphysical properties of Venus's cloud and haze particles. Results: From our research we obtain values for the imaginary part of the refractive index of the cloud particles of the order 10^(-4). It is most likely that the absorber is mainly located at the equator or in patchy clouds covering 80% of the planet. It is found that in the presence of precise disk-integrated polarization data, it is possible to detect variations in the polar regions. For Venus we found that it is likely that there exist larger particles at higher altitudes at the Venus poles. Unfortunately, it is very hard to say something about the long term variations on the planet. For the Venus case, it can be roughly stated that: the polarization was higher in 1975/1976 than in 1965/1968; the polarization was also higher in 1968/1970 than 1965/1968 but not higher than in 1976; there was a decrease in the polarization of the ultraviolet region in the years 1964/1965. Conclusions: Future observations should be made in a broad range of wavelengths, at as many phase angles as possible and in time frames similar to the orbital period of the (exo)planet. Since Venus can be observed as if it were an exoplanet (broad range of observable phase angles and disk-integrated data), we applied this research to exoplanets as well. We concluded with the help of the Venus data and simple models that it is possible to obtain cloud properties, such as the refractive index and the optical thickness of the cloud, of exoplanets using polarization observations. It was found that those properties are harder to distinguish using flux measurements since the geometric albedo and the distance to the planet are unknown.

Martian mesospheric CO2 ice clouds are formed out of the main constituent of the Martian atmosphere: CO2 gas. The nature of these clouds is poorly understood, characterization of these clouds in terms of particle morphology would give valuable insight into the Martian climate. So far, these CO2 clouds have only been detected from space. In this Master Thesis, feasibility of a surface-based observation strategy has been investigated to predict the flux and polarization signal of the CO2 clouds, using a Monte Carlo radiative transfer code. Simulation results suggest that the CO2 clouds are observable from the surface during twilight. Furthermore, it is concluded that observation from the surface allows for detection of the cloud's degree of polarization at a broad range of scattering angles, which is useful for effective characterization of cloud particle morphology.

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 this thesis we consider the reconstruction of albedo maps of exoplanets. This is done with a new variant of spin-orbit tomography that has been described in [Cowan and Agol, 2008] and more in depth in [Fujii and Kawahara, 2012]. This method reconstructs the albedo map from the reflected-light curve, the total intensity of the light that originates from the host star and is reflected by the planet. In the mentioned papers, the surface map of the planet is modeled as a sum of finite sized surface elements with constant albedo, and the relation between this approximation of the map and the light-curve in the time domain is determined. In this report, we use that the signal is quasi periodic due to diurnal and annual motion, and work with the Fourier peaks of the light-curve. We also approximate the map in a different way, writing it as the sum of spherical harmonics, and neglecting spherical harmonics with high spatial frequencies. This has the advantage that the relation can be worked out analytically (for edge-on and face-on observations) without the use of complex mathematics, and that both the surface map and the light-curve contain a daily frequency. We derive an equation for the reflective light-curve under the assumption that the surface map is not a function of time (no clouds), and that the reflection is Lambertian (equal in magnitude in all directions). This transformation is found to be a linear function of the surface map. This equation is worked out for edge-on and face-on observations with arbitrary axial tilt, which describes the orientation of the spin axis with respect to the observer and the orbital plane. Furthermore, we describe how to invert this relation if the axial tilt is known to the observer. We also aimed at recovering the map if the axial tilt is unknown to the observer, since this would make sure that the reconstruction does not rely on other observations. In contrast to what was found in papers like [Fujii and Kawahara, 2010] and [Fujii and Kawahara, 2012], we did not succeed in this. A number of methods were used for this. The first two looked at the problem from a mathematical perspective: the minimization of the distance between the measured light-curve and the light-curve from the reconstructed map, and Tikhonov regularization. The two failed because both the column space and the singular values respectively are not a function of the axial tilt. The third method that has been treated and tested involved the maximization of the ‘amount’ of positive albedo on the reconstructed map, but a test showed that the distinction that this method makes is in the same order of magnitude as the numerical error, thus proving that this method was not useful as well. Further study might show what causes the results of the two methods to differ in this respect

Satellites that have reached their end-of-life pose a threat to the space environment. An object in orbit that no longer adds value to its user is called space debris. Collisions between objects in Low Earth Orbit (LEO) can have disastrous consequences and have the potential to create thousands of new debris objects, which in their turn can cause collisions. In order to limit the number of potential collisions it is vital to remove space debris from orbit. Removing space debris from orbit can be done via a so-called de-orbit maneuver. Satellites often have an integrated on-board propulsion system, used for stationkeeping. At the end-of-life, these systems can be used to apply a thrust force and guide the satellite into a de-orbit maneuver. This thesis investigates the effect of a controlled low-thrust de-orbit maneuver on the propellant usage, duration and collision risk of the trajectory. This maneuver is conducted for three different objects in LEO: Zenit-2, Tsyklon-3, and Kosmos-3m. These three objects represent a wide range of different debris scenarios that form a potential danger to the space environment. Two different epochs of the debris environment are investigated: October 23, 2013, and November 7, 2014. Each trajectory is shaped by a thrust magnitude and thrust control algorithm that turns the engine of the object either on or off at different time points. The values for the thrust magnitude and thrust activation times are determined by an optimization algorithm that tries to find trajectories with optimal (minimal) values for the propellant usage, trajectory duration and collision risk. The collision risk associated with a de-orbit trajectory is determined by representing the position error of each object as an error covariance matrix. By mapping the error covariance matrix of each object pair during a close conjunction onto a common plane of reference (the B-plane), the collision probability can be described in terms of a probability density function. Integrating this function over the occupied area of the two objects in the B-plane results in a collision probability associated with that close conjunction. The total collision probability associated with a de-orbit trajectory is then the result of the accumulation of the collision probabilities of all close conjunctions. The result of this analysis is a set of different de-orbit trajectories with varying values for the propellant usage, duration and collision probability. Trajectories with a high collision risk have collision probabilities ranging from $10^{-1}$ to $10^{-3}$. The low-risk trajectories have collision probabilities ranging from $10^{-6}$ to $10^{-16}$. A general trend is observed where trajectories with a short duration have relatively low collision probabilities. However, by observing the accumulation of the collision probability over time, it can be seen that the value of the total accumulated collision probability is largely determined by a low number of high-risk conjunctions. A sensitivity analysis is performed to assess the robustness of the obtained trajectories. It is found that a small variation in an initial state vector element results in a difference in the associated collision probability ranging from $10^{-3}$ to $10^{-6}$ for some cases, and $10^{-2}$ to $10^{-48}$ for other cases. This shows that the obtained result are not robust and are highly sensitive to variations in either the initial state vector or the state derivative (i.e. changes in the environment model). Additionally a high thrust is applied in order to further assess the statistical effects of multiple conjunctions on the accumulated collision probability. Again, the associated collision probability was determined by a low number of risk-risk conjunction events. These results lead to the conclusion that no robust method was found for a de-orbit trajectory that limits the collision probability. The accumulated collision probability is not smoothly determined by the number of encountered conjunctions but rather a limited number of high-risk conjunction events. Additionally, the collision probability is highly sensitive to small position offsets of either of two objects in a conjunction. Therefore, a prediction of a de-orbit trajectory that limits the collision probability is unreliable.

Anthropogenic nitrogen dioxide (NO₂) in the troposphere is mainly produced by combustion engines in traffic, industry and energy production, and continues to affect air quality, human health and environment. Daily global measurements of tropospheric NO₂ columns are obtained by satellites with increasing spatial resolution and signal-to-noise levels, to improve monitoring of emission sources and air quality forecasting. The recently launched TROPOMI instrument on-board ESA’s Sentinel-5 Precursor satellite measures tropospheric NO₂ with a spatial resolution of 7.1 km by 3.6 km. During its commissioning phase, the instrument was temporarily operated in ’zoom-mode’ to measure at a resolution of 2.4 km by 1.8 km. This research presents the processed results from this unique data-set, which allows mapping NO₂ pollution sources from space with unprecedented detail. Comparison to measurements at operational resolution shows the improvement in spatial information content, at the cost of increased noise and uncertainty. The benefits and possibilities of measuring tropospheric NO₂ at high resolution are explored with several case studies. Comparisons with chemical transfer model forecasts show the improved ability of these measurements to capture local NO₂ enhancements and possibly improve emission inventories. The found correlations with co-located space-borne CO₂ column observations and the performance of a plume detection algorithm applied to the data-set provide additional support for simultaneous high resolution measurements of co-emitted CO₂ and NO₂, planned for future satellites to improve CO₂ emission monitoring. Finally, test retrievals with the zoom-mode data, using experimental high resolution surface reflectivity and NO₂ profile shape input, demonstrate the potential impact of high resolution a priori databases on the retrieval performance.