APRÈN. Portal de la producció docent del professorat de la UPC

Star trackers are the most accurate attitude-determination systems for satellites. Its operation is based on the identification of the stars present in the field of view of a small telescope and the determination of the astronomical coordinates of the centre of the image. To allow star identification, the star tracker uses a catalogue of stars whose size and properties primarily depend on the expected accuracy and the field of view. Identifying the stars present in the field is a difficult and time-consuming process for which there exist many different algorithms. It is necessary to benchmark many of these algorithms in terms of accuracy, computational burden, and size of the star catalogue, among other figures of merit. A specially demanding phase of attitude determination is the case in which there is no prior information on the orientation of the satellite, as is the case when it is just released from the rocket. This is referred to as Lost-in-Space (LIS) and requires the identification of the star field from scratch. This Final Degree Thesis is devoted to the exploration of some of the leading algorithms usable with limited computational power expected to be available in small satellites. The codes, which must be valid for LIS and nominal operations, will be written in MatLab and their performance measured through the standard MatLab tools for such purposes. Our project is particularly relevant in the context of the development of attitude determination and control of PhotSat, a 12U CubeSat with astronomical applications currently being developed in the Institute of Space Studies of Catalonia.

En los últimos a ños, las misiones llevadas a cabo con CubeSats se han hecho muy po- pulares tanto en el mundo acad émico como en el comercial, la ambici ón y los complejos requisitos de estas misiones han aumentado, y tambi én la precisi ón del control y la de- terminaci ón de la actitud. Esta tesis se enmarca en el contexto del dise ño de Photsat, un CubeSat de 12 unidades, y pretende comparar diferentes algoritmos de determinaci ón de actitud, de forma que se clarifiquen las ventajas e inconvenientes de los mismos y se pue- da proporcionar una idea general sobre la elecci ón de uno de los algoritmos en funci ón de los requisitos de la misi ón así como de las capacidades del sistema abordo.

The present study explores the complex dynamics of spacecraft in Earth's orbit at altitudes ranging up to a few hundred kilometres. Spacecraft have the challenge of navigating through an atmosphere that consists of gases with extremely low densities, leading to the generation of substantial aerodynamic forces, particularly drag. The long-term impacts of these forces give rise to challenges that cannot be analysed with the assumption of the classical continuous gas model used in fluid dynamics. The primary focus of this study revolves around the thermosphere, a critical atmospheric layer that plays a significant role in the operation of objects in Low Earth Orbit (LEO) as well as in the forecast of re-entering objects. The thermosphere is characterised by its relatively low densities and high kinetic temperatures. Fluid dynamics in the low Earth orbit (LEO) altitudes is governed by the (largely unknown) laws of free molecular flow. The investigation of the dynamic consequences of thermospheric interaction is of the highest importance, and under constant efforts for development, as it improves the accuracy of orbital trajectories of space objects. Furthermore, the analysis of these dynamic effects plays a crucial role in the optimisation of spacecraft design, the mitigation of drag forces, and ultimately the improvement of total vehicle efficiency. Historically, computational fluid dynamics (CFD) simulations have been widely utilised as a major approach for the modelling of spaceship drag. Computational Fluid Dynamics (CFD), which involves the numerical solution of governing equations for fluid flow, offers a comprehensive analysis of the flow properties surrounding a spacecraft. However, this methodology frequently requires significant computational resources and time, and yet can not be employed above 100 km above sea level. Therefore, the present thesis aims to investigate alternative approaches based on Statistical Mechanics, specifically focusing on the Direct Simulation Monte Carlo (DSMC) technique, to analyse the dynamic implications of thermospheric interaction. The primary objective of this study revolves around the creation and testing of a Direct Simulation Monte Carlo (DSMC) algorithm specifically designed for the simulation of rarefied gases in 3D. The algorithm facilitates the coordination of gas particles' motion inside a grid that is built from an importable mesh. The initial code iteration is based on the assumption of a non-collisional flow. This assumption is supported by the fact that the mean free path is much larger than the size of the domain being considered. Additionally, an assessment of the effectiveness of the DSMC approach is conducted by simulating a sphere and a cylinder geometry in particular conditions. A thorough exposition and comparison of the acquired findings with some current benchmarks is performed to do so. The key performance metrics encompass the drag coefficients of a sphere, which are analysed in conjunction with atmosphere characteristics such as the energy accommodation coefficient, tangential momentum accommodation coefficient, altitude, free stream velocity, air temperature, and molecular speed ratio.

Accurate drag modelling is crucial for satellite operations and re-entries in low-Earth orbit (LEO). A proper treatment of this problem becomes increasingly important as the number of artificial satellites grows. However, atmospheric drag modelling remains as a current major challenge, mostly due to uncertainties related to the atmospheric density (ρ) and the drag coefficient (CD). The fact that the latter magnitudes cannot be disentangled from the product ρCD adds difficulty to the problem. Recent research has led to the development of new models and tools aimed to accurately determining the CD. Simultaneously, high-fidelity satellite geometry determination plus on-board measurements of their accelerations has recently pushed forward our knowledge of the physical properties of the upper thermosphere. In this thesis, we propose and test two methodologies to study satellite aerodynamics using two-line element orbital data (TLE) from real satellites and the NRLMSISE-00 atmospheric model. The KnoCD (”Known” CD) method is applied to data from 56 1U-CubeSats and two ANDE-2 spherical satellites. The CalCD (”Calculated” CD) method, is applied to 12 3U-CubeSats of the Dove constellation of Planet Labs. In the KnoCD approach, the ballistic coefficient BC was estimated by computing the average of the crosssection area of a 1U-CubeSat (or the cross-sectional area of spherical satellites). In the CalCD approach the code SPARTA and the TLEs were used to estimate BC in each period of each satellite. In both cases, the TLEs were used again to propagate the orbits using the simplified perturbation model for orbital space vectors SGP4, and then we integrated the appropriate differential equation to compute the average density between consecutive TLEs. Finally, using KnoCD the yearly average density deviation of the NRLMSISE-00 was computed. With CalCD a statistical analysis was done in order to find the energy accommodation (related to the CD) that best fitted the satellite data. The results from KnoCD show a deviation of the thermospheric density of -5.5% per decade, well in accordance with the literature. With CalCD, our preliminary results showed that not all the satellites adjust equally and filtering should be applied. We performed two simulations with different adjustments in the derived BC and showed that the energy accommodation is in the range of 0.8-0.9, well in accordance with the values found in former studies which used onboard data. Our results, therefore, confirm the potential use of small satellite data to effectively assess the thermospheric density and satellite aerodynamics. In addition, we quantify the relevance of high precision in attitude data in order to obtain reasonably accurate drag information.

The idea of Lunar-based observatories has been gaining popularity among the scientific community during the last decades. Placing a telescope on the Moon surface not only would overcome all of the current shortcomings of Earth-based observatories, such as atmospheric absorption, astronomical seeing, light pollution or Earth day-night cycle itself, but also would benefit from the exceptional observational conditions of natural satellite offers, like the lack of atmosphere, the possibility of using increased-diffractionlimited instruments or Moon¿s slow sidereal rotation. However, in order to safely operate Lunar astronomical observatories, all of the different effects the telescope would suffer due to the fact of staying at the Moons surface must be considered in advance. Some of the most significant phenomena which may cause severe impact on the observatory will be covered in this project, such as the effects of being exposed to Lunar radiation and plasma environments and hazardous space weather events. This analysis will be carried out with the aim of studying the feasibility of manufacturing, launching, transporting, building, assembling, operating and maintaining an astronomical observatory placed on the Moons surface and also defining some of the required upcoming future steps in the development of such an ambitious mission.

In astronomy and the aerospace world, determining the orientation or attitude of a system in space is of great importance, whether it's simply to determine observations or to successfully carry out space missions. One of the devices commonly used is the star tracker. These devices allow the determination of attitude based on observed stars, using a preloaded catalogue in the system that identifies which stars are captured. In this work, the catalogue preloaded in the star tracker has been specifically designed for the proposed requirements, a catalogue derived from the Hipparcos catalogue. The starting point of the design is a Lost In Space (LIS) situation, where the only reference available are the stars that this device can capture and identify correctly. Traditionally, they have been systems with limited accessibility, only for large organizations or major space projects, due to their high cost and complexity. With the rapid development and advancement of technologies in recent years, today, we can find high-performance technological elements at a reduced cost. In this case, a functional star tracker has been developed and implemented using a Raspberry Pi with the Raspberry Pi OS operating system, a camera, and an optical system. This setup allows capturing images of the celestial sphere. To capture the images, the MATLAB® package MATLAB Support Package for Raspberry Pi Hardware has been used, a package that allows direct connection between the Raspberry Pi operating system and MATLAB®, through a WiFi network or an ethernet cable. To determine the attitude, it's necessary to find the match between the stars of the preloaded catalogue and the captured stars. In this case, the three brightest stars captured after processing, correcting, and characterizing the image. To correct the light frame and eliminate random noise and outliers, the master frames of the dark, bias, and flat images have been obtained. Additionally, an average filter has been used to soften and blur the captured stars. To characterize the image, the optimal ISO value, exposure time, aperture, and focus were determined. Finally, with the corrected image, the centroid of the three brightest stars, and the match found in the catalogue, the rotation matrix was determined using the Kabsch algorithm, a matrix that has allowed determining the attitude of the star tracker. The attitude has been determined in two ways, with the quaternion and with the Euler angles, with a precision between 1 and 3 arc minutes and a 97,50% satisfactory detection rate.

Context: Understanding the origin of the oldest stars in the universe is crucial to shed light on its early chemical evolution and on the formation history of the Milky Way. The oldest stars were either the direct heirs of the Big-Bang nucleosynthesis (and thus mainly composed of H and He at their birth), or were born in clouds of primordial (zero metallicity) material polluted with the ejecta from one or a few stars. Thus their observational counterparts must be characterised by very low amounts of iron in their composition. Currently, there is a debate on whether the first stellar generations (and thus the first polluters of the interstellar medium) were composed only of massive stars, or were a combination of intermediate and massive objects. Goal: We aim to identify the nature of the progenitors of the most metal-poor stars observed ([Fe/H] ¿ ¿2 or Z ¿ 10¿4). Specifically, we intend to know whether these stars show the nucleosynthetic signatures of early supernova explosions of different types, or of a combination of the ejecta from massive and intermediate-mass stars. Methods: We compile theoretical nucleosynthetic yields existing in the literature for intermediate and massive stars. We propose a scenario in which the theoretical yields of either an intermediate mass star or a massive star, are mixed within a gas cloud of primordial matter. Our main assumption is that some of the currently observed most metal-poor stars were born in this polluted clouds and thus, their abundances should show the nucleosynthetic signatures of their parent stars. We intend to develop a code able to automatically derive abundances from theoretical nucleosynthetic yields at different degrees of dilution with primordial material, and subsequently identify statistically sound matches between the former theoretical abundances and the surface abundances of metal poor stars of [Fe/H] ¿ ¿2. Automatising this process is crucial, given the increasing number of new theoretical models and observations of very metal-poor stars presented in the recent literature. Results: The expected coincidences between the abundances of theoretical models and observations will give us information related to their progenitors¿ initial masses and metallicities. We will be able to determine, given state-of-the-art of theoretical nucleosynthetic yields, whether any of the observed stars could be the offspring of a genuine primordial (Z=0) star.

The exposure to elevated radiation levels in space poses significant risks to spacecraft, space stations or satellites. Therefore, it is crucial to assess these risks associated with prolonged radiation exposure during any space mission. This thesis primarily focuses on the radiation environment in Low Earth Orbit (LEO) and investigates the interaction between particles in this environment and various materials. By utilizing established empirical software models from SPENVIS, the thesis examines the dosage experienced as a result of radiation sources in the LEO space environment, considering factors such as orbital altitude, orbital inclination, and mission duration. The study delves into the physical processes that can lead to failures and long-term deterioration of electronic devices caused by solar radiation, high concentrations of trapped electrons and protons in the Van Allen radiation belts, as well as Galactic Cosmic Rays (GCRs). Additionally, this thesis examines the influence of these radiation sources on electronic components and systems carried on spacecraft. Moreover, the objective of this research is to provide an up-to-date overview of various methods employed to mitigate the impacts of ionizing radiation. Through the comparisons, it has been discovered that the parameters of the space radiation environment exhibit expected variations in relation to solar activity. During periods of solar maximum, the fluence of trapped electrons and solar protons tends to be higher compared to solar minimum conditions. Conversely, the fluence of trapped protons and galactic cosmic rays is greater. However, it is worth noting that during maximum solar activity, Total Ionizing Dose (TID), Total Ionizing Dose (DDD), and Single Event Effects (SEEs) all demonstrate higher values compared to minimum solar activity. For small satellites orbiting in this region, it is essential to employ shielding materials as the observed levels of TID, DDD, and SEE can potentially pose concerns for space systems engineers. However, employing aluminium shielding with a thickness of at least 1.5 mm, radiation effects can be reduced to acceptable levels, regardless of whether it is a period of maximum or minimum solar activity, even for missions lasting up to approximately five years.

Magnetic attitude control systems are suitable for very small satellites, and yet provide a simple and robust method to detumbling and attitude control. In this work we analyse the use of hard ferromagnetic materials and magnetorquers to control the attitude of a spherical femtosatellite. The model will propagate the orbit of the satellite (disregarding the effects of the atmosphere) by means of SGP4 or SGP8. Once the orbit is propagated, we will use a suitable model of the geomagnetic field (IGRF13 or WMM) to determine the magnetic field in the location of the satellite. Passive ADCS will be obtained by means of the use of hysteresis rods. In order to add some control, a set of magnetorquers will be designed.

This thesis presents a design of the system for the first stage of a mission in the NanoSat Lab, the 3Cat-8. There is an special focus on the control algorithm and the sizing of the actuators.

Over the last decade, terms such as big data and IoT have become part of our everyday vocabulary, and as time goes by, more and more systems are collecting larger amounts of data in order to provide new services or improve quality, and aerospace sector is not an exception. Space probes and rovers, which originally communicated with ground stations using S-band, have moved to higher frequencies in order to be able to transmit more information per unit of time. As the frequency of the system increases, the optical band is reached, 40 years ago, the first experiment in aerospace to demonstrate laser communication, the Airbone Flight Test System (AFTS), was conducted. Numerous efforts have been made to demonstrate that optical communications are possible. When sending an exploration mission, the scientific community maximises the performance of the instruments by taking into account multiple criteria, such as whether the particular device has been previously tested in space and the likelihood of failure. Therefore, the use of new technologies requires a process of multiple demonstration missions prior to be accepted. This thesis compiles the state of the art, i.e. the knowledge acquired over the last four decades, and covers three main points: ground infrastructures, the flight terminal and the method of communication between both systems. In the first point, the study focuses on explaining the parameters that must be taken into account when designing an international ground station network, equivalent to its counterpart in the RF band, NASA's DSN networks or ESA's ESTRACK, among others. One of the most relevant variables that determines the location of a ground stations are the atmospheric conditions. For this reason, a series of files containing information about the planet's atmosphere has been downloaded and processed from NASA's LAADS DAAC database. Secondly, the link equation of a signal emitted in optical band has been studied. Each of the terms that make up the equation are presented in detail in several sections, in particular the obscuration losses in Cassegrain type antennas, the pointing losses and those due to atmospheric absorption and turbulence. Finally, two practical studies have been carried out in which it is possible to see how the mathematics described in the previous chapters have been applied to execute missions whose purpose is to communicate in deep space. To achieve this, the JPL library and toolkit called SPICE has been used in a fictitious but realistic Mars-Earth downlink mission. Thanks to the high reliability of SPICE, all the data related to the orbital mechanics of a space mission has been obtained and compared, in order of magnitude, with a mission called Psyche and DSOC, scheduled for launch in August 2022. Apart from didactically exemplifying the terms of the link equation in a specific mission, key elements such as capacity or bit rate have also been retrieved, which allow immediate conclusions to be drawn in favour of this technology and thus contribute to its consolidation in the field of deep space communications.

The world of satellites is evolving very rapidly on the past few years, with satellites going from huge machines with complex and expensive systems, to rapidly getting smaller and smaller. Our satellite, a PocketQube, is a satellite that can fit in one's hand, being it a cube with sides of 5x5 cm. This type of cubes are the cheapest way of exploring parts of the Earth's orbit, as well as obtaining information that conventional and much bigger satellites would not even bother to get. This is the case of our satellite, which is aimed to obtain information of Earth's lower Thermosphere. As it is well known, in these upper parts of the Earth's atmosphere, the presence of air is almost non-existent and any perturbation to the satellite, or any environmental torque, can cause the satellite to spin without control and not be able to perform its tasks correctly. In the point of view of Attitude Control, this is a serious problem as many satellites require a precise pointing to its objective to perform their job well, and whereas this is almost no problem in bigger satellites as they normally carry complex systems to ensure that attitude, what happens to a satellite that weights less than 100 grams? This thesis aims to find reliable ways to ensure Attitude Control on smaller satellites, and hopefully the conclusions obtained in this thesis can help many other femto-satellites(¡100g) that might have the same problems. As stated, the aim of this project focuses on Attitude Control and Determination Systems, and all the simulations performed will be kept as simple as possible, as our objective is not to deal with complex orbital dynamics, Electro-Magnetic Compatibility (EMC) problems or other complex situations.

The lower thermosphere (between 100 and 550 km of height) is known with lesser accuracy than desired. The use of spherical satellites to determine the density could result in a substantial improvement of the present situation. The orbits of satellites at these heights are affected by drag and the inhomogeneities of the terrestrial gravitational potential (among other perturbations). This projects has as main goal to analyse how the atmospheric drag affects the orbit of a real satellite, and then, determine the thermospheric density. Hence, it will be necessary to reconstruct the orbit accounting for the perturbations in the most accurate way possible. Regarding the gravitational potential of the Earth, we have employed three approximations: spherical symmetry, a zonal model truncated at sixth order and a tesseral model truncated at tenth order. This last model has revealed as the most accurate. To achieve our goal, we have analysed the telemetry gathered by one of the satellites of the FSSCat mission. Then, we have determined its orbital elements. Afterwards, we have considered two possible methods for orbit reconstruction: Non-Linear Least Squares and Extended Kalman Filter. After this analysis, we have chosen the Non-Linear Least Squares method for the purpose of orbit reconstruction. The orbital elements determined from a physical analysis of the telemetry and the ones resulting from the non-linear least square method coincide with a remarkable accuracy.

This report presents the procedures and results obtained in the project 'Numerical Simulation of Turbulent Flows Using High Performance Computing', in which a high performance code for fluid dynamics simulation (SA3) has been extended. Firstly, sub-mesh modelling has been incorporated into the integration of the Navier-Stokes equations using a source term representative of the turbulent transport. This operator has been generalized for any field, its discretization has been implemented and it has been validated by means of the Method of Manufactured Solutions (MMS). The problem is closed by a sub-mesh viscosity calculated by Smagorinsky, WALE and Vreman models. In addition, their boundary conditions have been carefully analysed. These models have also been successfully validated using the MMS method. Finally, the effect of the sub-mesh viscosity on the Courant-FriederichLewis condition has been added for the estimation of the maximum time step, completing the extension of SA3 for the execution of Large-Eddie Simulations (LES). In the second place, the solutions obtained for the case of a Channel Flow are studied, analyzing the capacity of the code to resolve turbulent flows and boundary layers. Therefore, the statistical description of the turbulent flow and the algorithms to calculate its different parameters are presented. Next, a scalability analysis is carried out according to the density of the mesh used, and the profiles of the statistical parameters obtained without using a turbulence model are compared with the profiles obtained using the Vreman and WALE models. Based on the results obtained throughout the project, the conclusions obtained and future recommendations are finally presented

This work deals with the design of a femto-satellite for scientific studies. The goal of the femto-satellite is to model the density of the thermosphere by measuring the orbital decay caused by atmospheric drag. The proposed femto-satellite, having a mass of maximum 100 g by definition, is embedded in a PocketQube structure and equipped with solar panels in order to guarantee operability during the entire expected lifetime of approximately three years. In order to ensure a constant drag coefficient regardless of the attitude, the femto-satellite is to be covered by a spherical structure, which moreover allows for solar illumination of the solar panels.

Nowadays a large number of artificial satellites orbit the Earth, of which many of them have completed their mission or are fragments of satellites that travel without any purpose. These objects can pose a collision problem for other active missions, so these inactive satellites need to be tracked. The highest concentration of inactive satellites is found in LEO orbits, from where due to the effect of aerodynamic drag, a function of density, the satellite will end up re-entering the atmosphere. The density parameter is influenced by solar and geomagnetic activity. Currently, thermospheric density models are available to estimate density, necessary for orbital prediction. The aim of this project is to study how solar and geomagnetic activity changes density, and therefore the orbital evolution of the satellite in the thermosphere. The second objective is to determine the goodness of the NRLMSISE-00 thermospheric density model. For the first objective, the TLEs of satellites that are in periods of maximum solar activity have been analyzed. From the code made with Matlab these TLE files have been read and the epoch, the semi-major axis and the eccentricity have been extracted. The evolution of these last two parameters has been analyzed in the presence of solar activity, in the form of solar flare. For the second objective, to determine the goodness of the NRLMSISE-00 model, in the first place the density has been calculated from parameters obtained from the TLEs, at the same time, from the Matlab package NRLMSISE-00 the density that estimates the NRLMSISE-00 model for the same dates. Finally, results have been compared. However, the TLEs data are associated with a prediction error, which is unknown. Therefore, based on the DOPs (Precise Orbit Determination) of the GFZ-1 satellite, provided by the GFZ German Research Center for Geociences, it has been analyzed the error TLEs make in the prediction of the semi-major axis compared to the semi-axis obtained with greater precision from the DOPs.

The determination of a spacecraft's orientation is a major problem for every mission; payloads require specific characteristics to work and engines must aim the opposite direction to were the spacecraft is meant to move. Since the beginning of the space era, Attitude Determination has been under study and development to find the best algorithm to solve the orientation. In this work, we analyse the most promising algorithms for a CubeSat mission under development and integration at Universitat Politecnica de Catalunya (UPC) NanoSatLab. ` 3Cat-4 mission proposes a novel structure for a CubeSat that carries difficulties for Attitude Determination and Control subsystem. We study the optimisation of the most common algorithms to analyse the capability of Attitude Determination to overcome these difficulties and successfully compute the orientation of the 3Cat-4.

This project consists in the definition of the technical requirements, the design and the development of a solid rocket engine. This rocket engine must fulfil a specific mission: to propel a 0.3 kg heavy payload to a height of 100 km, while following a parabolic trajectory, in a suborbital flight. The payload could make use of the very unique conditions experienced in a suborbital flight; namely, the microgravity conditions for a certain amount of time. The rocket would take-off from a launch platform lifted up to a height of 30 km, by means of an aerostatic balloon. The engine must fulfil 3 main properties: safety, cost and robustness. It shall be safe, for anyone working on any of its associated processes: the manufacturing of its structure, the processing of the propellant, the integration of all elements, the transportation, etc. The cost of the engine shall be as low as possible, in order to pave the way for students, universities or research centres with low funds to use this launch system. Besides, the engine must be robust enough; that is, it must be able to work as expected at nominal conditions but also at slightly adverse conditions. As has already been pointed out, the project is structured in 3 phases: definition, design and development. The first phase is based on research, and it must allow detailed acknowledgement on how a solid rocket engine works, thus allowing to define the technical requirements. The design phase consists on establishing technological solutions for the requirements, while fulfilling the 3 properties of the rocket engine that have already been mentioned. Finally, the development phase is about testing some critical elements of the engine, in order to validate, or either invalidate and thus improve, the design.