Estudo da dinâmica do sistema Prometeu - Pandora - anel F de saturno

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Reanálise das defasagens de Prometeu e Pandora

In the present work it is proposed to do a revision on some studies on the dynamics of the Prometheus-Pandora system. In special, those studies that deal with anomalous behaviours observed on its components, identi ed as angular lags in these satellite`s orbits. Initially, it is presented a general description, contextualising the main characteristics of this system. The main publications related to this subject are analised and commented, in chronological order, showing the advances made in the knowledge of such dynamics. An analysis of the initial conditions, used by Goldreich e Rappaport (2003a ,b) e Cruz (2004), obtained through observations made by the Voyager 1 and 2 spacecrafts and by the Hubble space telescope, it is made in order to try to reproduce their results. However, no clear conclusion of the values used were found. The tests addopted in the analysis are from Cruz (2004), which reproduced the results and o ered a new explanation on the origin of the observed angular lags. The addopetd methodology involves the numerical integration of the equations of motion of the system, including the zonal harmonics J2, J4 and J6 of Saturn's gravitational potential. A fundamental consideration in this study is the use of geometric elements instead of osculating elements. It was found the set of initial data that best reproduces the results from Goldreich e Rappaport (2003a, b) and Cruz (2004)

A study of the errors of the averaged models in the restricted three-body problem in a short time scale

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Investigation on the Navigation Anomaly of Pioneer 10 and 11 probes

The present work consists of the investigation of the navigation of Pioneer 10 and 11 probes becoming known as the “Pioneer Anomaly”: the trajectories followed by the spacecrafts did not match the ones retrieved with standard navigation software. Mismatching appeared as a linear drift in the Doppler data received by the spacecrafts, which has been ascribed to a constant sunward acceleration of about 8.5×10-10 m/s2. The study presented hereafter tries to find a convincing explanation to this discrepancy. The research is based on the analysis of Doppler tracking data through the ODP (Orbit Determination Program), developed by NASA/JPL. The method can be summarized as: seek for any kind of physics affecting the dynamics of the spacecraft or the propagation of radiometric data, which may have not been properly taken into account previously, and check whether or not these might rule out the anomaly. A major effort has been put to build a thermal model of the spacecrafts for predicting the force due to anisotropic thermal radiation, since this is a model not natively included in the ODP. Tracking data encompassing more than twenty years of Pioneer 10 interplanetary cruise, plus twelve years of Pioneer 11 have been analyzed in light of the results of the thermal model. Different strategies of orbit determination have been implemented, including single arc, multi arc and stochastic filters, and their performance compared. Orbital solutions have been obtained without the needing of any acceleration other than the thermal recoil one indicating it as the responsible for the observed linear drift in the Doppler residuals. As a further support to this we checked that inclusion of additional constant acceleration as does not improve the quality of orbital solutions. All the tests performed lead to the conclusion that no anomalous acceleration is acting on Pioneers spacecrafts.

Orbits design for Leo space based solar power satellite system

Space Based Solar Power satellites use solar arrays to generate clean, green, and renewable electricity in space and transmit it to earth via microwave, radiowave or laser beams to corresponding receivers (ground stations). These traditionally are large structures orbiting around earth at the geo-synchronous altitude. This thesis introduces a new architecture for a Space Based Solar Power satellite constellation. The proposed concept reduces the high cost involved in the construction of the space satellite and in the multiple launches to the geo-synchronous altitude. The proposed concept is a constellation of Low Earth Orbit satellites that are smaller in size than the conventional system. For this application a Repeated Sun-Synchronous Track Circular Orbit is considered (RSSTO). In these orbits, the spacecraft re-visits the same locations on earth periodically every given desired number of days with the line of nodes of the spacecraft’s orbit fixed relative to the Sun. A wide range of solutions are studied, and, in this thesis, a two-orbit constellation design is chosen and simulated. The number of satellites is chosen based on the electric power demands in a given set of global cities. The orbits of the satellites are designed such that their ground tracks visit a maximum number of ground stations during the revisit period. In the simulation, the locations of the ground stations are chosen close to big cities, in USA and worldwide, so that the space power constellation beams down power directly to locations of high electric power demands. The j2 perturbations are included in the mathematical model used in orbit design. The Coverage time of each spacecraft over a ground site and the gap time between two consecutive spacecrafts visiting a ground site are simulated in order to evaluate the coverage continuity of the proposed solar power constellation. It has been observed from simulations that there always periods in which s spacecraft does not communicate with any ground station. For this reason, it is suggested that each satellite in the constellation be equipped with power storage components so that it can store power for later transmission. This thesis presents a method for designing the solar power constellation orbits such that the number of ground stations visited during the given revisit period is maximized. This leads to maximizing the power transmission to ground stations.

Algorithms for spacecraft formation flying navigation based on wireless positioning system measurements

Spacecraft formation flying navigation continues to receive a great deal of interest. The research presented in this dissertation focuses on developing methods for estimating spacecraft absolute and relative positions, assuming measurements of only relative positions using wireless sensors. The implementation of the extended Kalman filter to the spacecraft formation navigation problem results in high estimation errors and instabilities in state estimation at times. This is due tp the high nonlinearities in the system dynamic model. Several approaches are attempted in this dissertation aiming at increasing the estimation stability and improving the estimation accuracy. A differential geometric filter is implemented for spacecraft positions estimation. The differential geometric filter avoids the linearization step (which is always carried out in the extended Kalman filter) through a mathematical transformation that converts the nonlinear system into a linear system. A linear estimator is designed in the linear domain, and then transformed back to the physical domain. This approach demonstrated better estimation stability for spacecraft formation positions estimation, as detailed in this dissertation. The constrained Kalman filter is also implemented for spacecraft formation flying absolute positions estimation. The orbital motion of a spacecraft is characterized by two range extrema (perigee and apogee). At the extremum, the rate of change of a spacecraft’s range vanishes. This motion constraint can be used to improve the position estimation accuracy. The application of the constrained Kalman filter at only two points in the orbit causes filter instability. Two variables are introduced into the constrained Kalman filter to maintain the stability and improve the estimation accuracy. An extended Kalman filter is implemented as a benchmark for comparison with the constrained Kalman filter. Simulation results show that the constrained Kalman filter provides better estimation accuracy as compared with the extended Kalman filter. A Weighted Measurement Fusion Kalman Filter (WMFKF) is proposed in this dissertation. In wireless localizing sensors, a measurement error is proportional to the distance of the signal travels and sensor noise. In this proposed Weighted Measurement Fusion Kalman Filter, the signal traveling time delay is not modeled; however, each measurement is weighted based on the measured signal travel distance. The obtained estimation performance is compared to the standard Kalman filter in two scenarios. The first scenario assumes using a wireless local positioning system in a GPS denied environment. The second scenario assumes the availability of both the wireless local positioning system and GPS measurements. The simulation results show that the WMFKF has similar accuracy performance as the standard Kalman Filter (KF) in the GPS denied environment. However, the WMFKF maintains the position estimation error within its expected error boundary when the WLPS detection range limit is above 30km. In addition, the WMFKF has a better accuracy and stability performance when GPS is available. Also, the computational cost analysis shows that the WMFKF has less computational cost than the standard KF, and the WMFKF has higher ellipsoid error probable percentage than the standard Measurement Fusion method. A method to determine the relative attitudes between three spacecraft is developed. The method requires four direction measurements between the three spacecraft. The simulation results and covariance analysis show that the method’s error falls within a three sigma boundary without exhibiting any singularity issues. A study of the accuracy of the proposed method with respect to the shape of the spacecraft formation is also presented.

CODE’s new solar radiation pressure model for GNSS orbit determination

The Empirical CODE Orbit Model (ECOM) of the Center for Orbit Determination in Europe (CODE), which was developed in the early 1990s, is widely used in the International GNSS Service (IGS) community. For a rather long time, spurious spectral lines are known to exist in geophysical parameters, in particular in the Earth Rotation Parameters (ERPs) and in the estimated geocenter coordinates, which could recently be attributed to the ECOM. These effects grew creepingly with the increasing influence of the GLONASS system in recent years in the CODE analysis, which is based on a rigorous combination of GPS and GLONASS since May 2003. In a first step we show that the problems associated with the ECOM are to the largest extent caused by the GLONASS, which was reaching full deployment by the end of 2011. GPS-only, GLONASS-only, and combined GPS/GLONASS solutions using the observations in the years 2009–2011 of a global network of 92 combined GPS/GLONASS receivers were analyzed for this purpose. In a second step we review direct solar radiation pressure (SRP) models for GNSS satellites. We demonstrate that only even-order short-period harmonic perturbations acting along the direction Sun-satellite occur for GPS and GLONASS satellites, and only odd-order perturbations acting along the direction perpendicular to both, the vector Sun-satellite and the spacecraft’s solar panel axis. Based on this insight we assess in the third step the performance of four candidate orbit models for the future ECOM. The geocenter coordinates, the ERP differences w. r. t. the IERS 08 C04 series of ERPs, the misclosures for the midnight epochs of the daily orbital arcs, and scale parameters of Helmert transformations for station coordinates serve as quality criteria. The old and updated ECOM are validated in addition with satellite laser ranging (SLR) observations and by comparing the orbits to those of the IGS and other analysis centers. Based on all tests, we present a new extended ECOM which substantially reduces the spurious signals in the geocenter coordinate z (by about a factor of 2–6), reduces the orbit misclosures at the day boundaries by about 10 %, slightly improves the consistency of the estimated ERPs with those of the IERS 08 C04 Earth rotation series, and substantially reduces the systematics in the SLR validation of the GNSS orbits.

CHEOPS Performance for Exomoons: The Detectability of Exomoons by Using Optimal Decision Algorithm

Many attempts have already been made to detect exomoons around transiting exoplanets, but the first confirmed discovery is still pending. The experiences that have been gathered so far allow us to better optimize future space telescopes for this challenge already during the development phase. In this paper we focus on the forthcoming CHaraterising ExOPlanet Satellite (CHEOPS), describing an optimized decision algorithm with step-by-step evaluation, and calculating the number of required transits for an exomoon detection for various planet moon configurations that can be observable by CHEOPS. We explore the most efficient way for such an observation to minimize the cost in observing time. Our study is based on PTV observations (photocentric transit timing variation) in simulated CHEOPS data, but the recipe does not depend on the actual detection method, and it can be substituted with, e.g., the photodynamical method for later applications. Using the current state-of-the-art level simulation of CHEOPS data we analyzed transit observation sets for different star planet moon configurations and performed a bootstrap analysis to determine their detection statistics. We have found that the detection limit is around an Earth-sized moon. In the case of favorable spatial configurations, systems with at least a large moon and a Neptune-sized planet, an 80% detection chance requires at least 5-6 transit observations on average. There is also a nonzero chance in the case of smaller moons, but the detection statistics deteriorate rapidly, while the necessary transit measurements increase quickly. After the CoRoT and Kepler spacecrafts, CHEOPS will be the next dedicated space telescope that will observe exoplanetary transits and characterize systems with known Doppler-planets. Although it has a smaller aperture than Kepler (the ratio of the mirror diameters is about 1/3) and is mounted with a CCD that is similar to Kepler's, it will observe brighter stars and operate with larger sampling rate; therefore, the detection limit for an exomoon can be the same as or better, which will make CHEOPS a competitive instruments in the quest for exomoons.

Use of a modified delphi process for establishing occupational exposure limits in support of health surveillance for space travelers

On-orbit exposures can come from numerous factors related to the space environment as evidenced by almost 50 years of environmental samples collected for water analysis, air analysis, radiation analysis, and physiologic parameters. For astronauts and spaceflight participants the occupational exposures can be very different from those experienced by workers performing similar tasks in workplaces on Earth, because the duration of the exposure could be continuous for very long orbital, and eventually interplanetary, missions. The establishment of long-term exposure standards is vital to controlling the quality of the spacecraft environment over long periods. NASA often needs to update and revise its prior exposure standards (Spacecrafts Maximum Allowable Concentrations (SMACs)). Traditional standards-setting processes are often lengthy, so a more rapid method to review and establish standards would be a substantial advancement in this area. This project investigates use of the Delphi method for this purpose. ^ In order to achieve the objectives of this study a modified Delphi methodology was tested in three trials executed by doctoral students and a panel of experts in disciplines related to occupational safety and health. During each test/trial modifications were made to the methodology. Prior to submission of the Delphi Questionnaire to the panel of experts a pilot study/trial was conducted using five doctoral students with the goals of testing and adjusting the Delphi questionnaire to improve comprehension, work out any procedural issues and evaluate the effectiveness of the questionnaire in drawing the desired responses. The remainder of the study consisted of two trials of the Modified Delphi process using 6 chemicals that currently have the potential of causing occupational exposures to NASA astronauts or spaceflight participants. To assist in setting Occupational Exposure Limits (OEL), the expert panel was established consisting of experts from academia, government and industry. Evidence was collected and used to create close-ended questionnaires which were submitted to the Delphi panel of experts for the establishment of OEL values for three chemicals from the list of six originally selected (trial 1). Once the first Delphi trial was completed, adjustments were made to the Delphi questionnaires and the process above was repeated with the remaining 3 chemicals (trial 2). ^ Results indicate that experience in occupational safety and health and with OEL methodologies can have a positive effect in minimizing the time experts take in completing this process. Based on the results of the questionnaires and comparison of the results with the SMAC already established by NASA, we conclude that use of the Delphi methodology is appropriate for use in the decision-making process for the selection of OELs.^

Zero-G Gauging systems. CONTRACT No 17/8/4

Various systems for measuring propellant content in spacecrafts under weightlessness conditions are reviewed. The cavity resonator method is found to be the most suitable measurement; technique. This method is analyzed in detail. A determination of errors intrinsec to the method is carried out.

PIC computation of electron current collection to a moving bare tether in the mesothermal condition

In tethered satellite technology, it is important to estimate how many electrons a spacecraft can collect from its ambient plasma by a bare electrodynamic tether. The analysis is however very difficult because of the small but significant Geo-magnetic field and the spacecraft’s relative motion to both ions and electrons. The object of our work is the development of a numerical method, for this purpose. Particle-In-Cell (PIC) method, for the calculation of electron current to a positive bare tether moving at orbital velocity in the ionosphere, i.e. in a flowing magnetized plasma under Maxwellian collisionless conditions. In a PIC code, a number of particles are distributed in phase space and the computational domain has a grid on which Poisson equation is solved for field quantities. The code uses the quasi-neutrality condition to solve for the local potential at points in the plasma which coincide with the computational outside boundary. The quasi-neutrality condition imposes ne - ni on the boundary. The Poisson equation is solved in such a way that the presheath region can be captured in the computation. Results show that the collected current is higher than the Orbital Motion Limit (OML) theory. The OML current is the upper limit of current collection under steady collisionless unmagnetized conditions. In this work, we focus on the flowing effects of plasma as a possible cause of the current enhancement. A deficit electron density due to the flowing effects has been worked and removed by introducing adiabatic electron trapping into our model.

Methodologies for Collision Risk Computation = Metodologías para Cálculo de Riesgo de Colisión

Esta tesis aborda metodologías para el cálculo de riesgo de colisión de satélites. La minimización del riesgo de colisión se debe abordar desde dos puntos de vista distintos. Desde el punto de vista operacional, es necesario filtrar los objetos que pueden presentar un encuentro entre todos los objetos que comparten el espacio con un satélite operacional. Puesto que las órbitas, del objeto operacional y del objeto envuelto en la colisión, no se conocen perfectamente, la geometría del encuentro y el riesgo de colisión deben ser evaluados. De acuerdo con dicha geometría o riesgo, una maniobra evasiva puede ser necesaria para evitar la colisión. Dichas maniobras implican un consumo de combustible que impacta en la capacidad de mantenimiento orbital y por tanto de la visa útil del satélite. Por tanto, el combustible necesario a lo largo de la vida útil de un satélite debe ser estimado en fase de diseño de la misión para una correcta definición de su vida útil, especialmente para satélites orbitando en regímenes orbitales muy poblados. Los dos aspectos, diseño de misión y aspectos operacionales en relación con el riesgo de colisión están abordados en esta tesis y se resumen en la Figura 3. En relación con los aspectos relacionados con el diseño de misión (parte inferior de la figura), es necesario evaluar estadísticamente las características de de la población espacial y las teorías que permiten calcular el número medio de eventos encontrados por una misión y su capacidad de reducir riesgo de colisión. Estos dos aspectos definen los procedimientos más apropiados para reducir el riesgo de colisión en fase operacional. Este aspecto es abordado, comenzando por la teoría descrita en [Sánchez-Ortiz, 2006]T.14 e implementada por el autor de esta tesis en la herramienta ARES [Sánchez-Ortiz, 2004b]T.15 proporcionada por ESA para la evaluación de estrategias de evitación de colisión. Esta teoría es extendida en esta tesis para considerar las características de los datos orbitales disponibles en las fases operacionales de un satélite (sección 4.3.3). Además, esta teoría se ha extendido para considerar riesgo máximo de colisión cuando la incertidumbre de las órbitas de objetos catalogados no es conocida (como se da el caso para los TLE), y en el caso de querer sólo considerar riesgo de colisión catastrófico (sección 4.3.2.3). Dichas mejoras se han incluido en la nueva versión de ARES [Domínguez-González and Sánchez-Ortiz, 2012b]T.12 puesta a disposición a través de [SDUP,2014]R.60. En fase operacional, los catálogos que proporcionan datos orbitales de los objetos espaciales, son procesados rutinariamente, para identificar posibles encuentros que se analizan en base a algoritmos de cálculo de riesgo de colisión para proponer maniobras de evasión. Actualmente existe una única fuente de datos públicos, el catálogo TLE (de sus siglas en inglés, Two Line Elements). Además, el Joint Space Operation Center (JSpOC) Americano proporciona mensajes con alertas de colisión (CSM) cuando el sistema de vigilancia americano identifica un posible encuentro. En función de los datos usados en fase operacional (TLE o CSM), la estrategia de evitación puede ser diferente debido a las características de dicha información. Es preciso conocer las principales características de los datos disponibles (respecto a la precisión de los datos orbitales) para estimar los posibles eventos de colisión encontrados por un satélite a lo largo de su vida útil. En caso de los TLE, cuya precisión orbital no es proporcionada, la información de precisión orbital derivada de un análisis estadístico se puede usar también en el proceso operacional así como en el diseño de la misión. En caso de utilizar CSM como base de las operaciones de evitación de colisiones, se conoce la precisión orbital de los dos objetos involucrados. Estas características se han analizado en detalle, evaluando estadísticamente las características de ambos tipos de datos. Una vez concluido dicho análisis, se ha analizado el impacto de utilizar TLE o CSM en las operaciones del satélite (sección 5.1). Este análisis se ha publicado en una revista especializada [Sánchez-Ortiz, 2015b]T.3. En dicho análisis, se proporcionan recomendaciones para distintas misiones (tamaño del satélite y régimen orbital) en relación con las estrategias de evitación de colisión para reducir el riesgo de colisión de manera significativa. Por ejemplo, en el caso de un satélite en órbita heliosíncrona en régimen orbital LEO, el valor típico del ACPL que se usa de manera extendida es 10-4. Este valor no es adecuado cuando los esquemas de evitación de colisión se realizan sobre datos TLE. En este caso, la capacidad de reducción de riesgo es prácticamente nula (debido a las grandes incertidumbres de los datos TLE) incluso para tiempos cortos de predicción. Para conseguir una reducción significativa del riesgo, sería necesario usar un ACPL en torno a 10-6 o inferior, produciendo unas 10 alarmas al año por satélite (considerando predicciones a un día) o 100 alarmas al año (con predicciones a tres días). Por tanto, la principal conclusión es la falta de idoneidad de los datos TLE para el cálculo de eventos de colisión. Al contrario, usando los datos CSM, debido a su mejor precisión orbital, se puede obtener una reducción significativa del riesgo con ACPL en torno a 10-4 (considerando 3 días de predicción). Incluso 5 días de predicción pueden ser considerados con ACPL en torno a 10-5. Incluso tiempos de predicción más largos se pueden usar (7 días) con reducción del 90% del riesgo y unas 5 alarmas al año (en caso de predicciones de 5 días, el número de maniobras se mantiene en unas 2 al año). La dinámica en GEO es diferente al caso LEO y hace que el crecimiento de las incertidumbres orbitales con el tiempo de propagación sea menor. Por el contrario, las incertidumbres derivadas de la determinación orbital son peores que en LEO por las diferencias en las capacidades de observación de uno y otro régimen orbital. Además, se debe considerar que los tiempos de predicción considerados para LEO pueden no ser apropiados para el caso de un satélite GEO (puesto que tiene un periodo orbital mayor). En este caso usando datos TLE, una reducción significativa del riesgo sólo se consigue con valores pequeños de ACPL, produciendo una alarma por año cuando los eventos de colisión se predicen a un día vista (tiempo muy corto para implementar maniobras de evitación de colisión).Valores más adecuados de ACPL se encuentran entre 5•10-8 y 10-7, muy por debajo de los valores usados en las operaciones actuales de la mayoría de las misiones GEO (de nuevo, no se recomienda en este régimen orbital basar las estrategias de evitación de colisión en TLE). Los datos CSM permiten una reducción de riesgo apropiada con ACPL entre 10-5 y 10-4 con tiempos de predicción cortos y medios (10-5 se recomienda para predicciones a 5 o 7 días). El número de maniobras realizadas sería una en 10 años de misión. Se debe notar que estos cálculos están realizados para un satélite de unos 2 metros de radio. En el futuro, otros sistemas de vigilancia espacial (como el programa SSA de la ESA), proporcionarán catálogos adicionales de objetos espaciales con el objetivo de reducir el riesgo de colisión de los satélites. Para definir dichos sistemas de vigilancia, es necesario identificar las prestaciones del catalogo en función de la reducción de riesgo que se pretende conseguir. Las características del catálogo que afectan principalmente a dicha capacidad son la cobertura (número de objetos incluidos en el catalogo, limitado principalmente por el tamaño mínimo de los objetos en función de las limitaciones de los sensores utilizados) y la precisión de los datos orbitales (derivada de las prestaciones de los sensores en relación con la precisión de las medidas y la capacidad de re-observación de los objetos). El resultado de dicho análisis (sección 5.2) se ha publicado en una revista especializada [Sánchez-Ortiz, 2015a]T.2. Este análisis no estaba inicialmente previsto durante la tesis, y permite mostrar como la teoría descrita en esta tesis, inicialmente definida para facilitar el diseño de misiones (parte superior de la figura 1) se ha extendido y se puede aplicar para otros propósitos como el dimensionado de un sistema de vigilancia espacial (parte inferior de la figura 1). La principal diferencia de los dos análisis se basa en considerar las capacidades de catalogación (precisión y tamaño de objetos observados) como una variable a modificar en el caso de un diseño de un sistema de vigilancia), siendo fijas en el caso de un diseño de misión. En el caso de las salidas generadas en el análisis, todos los aspectos calculados en un análisis estadístico de riesgo de colisión son importantes para diseño de misión (con el objetivo de calcular la estrategia de evitación y la cantidad de combustible a utilizar), mientras que en el caso de un diseño de un sistema de vigilancia, los aspectos más importantes son el número de maniobras y falsas alarmas (fiabilidad del sistema) y la capacidad de reducción de riesgo (efectividad del sistema). Adicionalmente, un sistema de vigilancia espacial debe ser caracterizado por su capacidad de evitar colisiones catastróficas (evitando así in incremento dramático de la población de basura espacial), mientras que el diseño de una misión debe considerar todo tipo de encuentros, puesto que un operador está interesado en evitar tanto las colisiones catastróficas como las letales. Del análisis de las prestaciones (tamaño de objetos a catalogar y precisión orbital) requeridas a un sistema de vigilancia espacial se concluye que ambos aspectos han de ser fijados de manera diferente para los distintos regímenes orbitales. En el caso de LEO se hace necesario observar objetos de hasta 5cm de radio, mientras que en GEO se rebaja este requisito hasta los 100 cm para cubrir las colisiones catastróficas. La razón principal para esta diferencia viene de las diferentes velocidades relativas entre los objetos en ambos regímenes orbitales. En relación con la precisión orbital, ésta ha de ser muy buena en LEO para poder reducir el número de falsas alarmas, mientras que en regímenes orbitales más altos se pueden considerar precisiones medias. En relación con los aspectos operaciones de la determinación de riesgo de colisión, existen varios algoritmos de cálculo de riesgo entre dos objetos espaciales. La Figura 2 proporciona un resumen de los casos en cuanto a algoritmos de cálculo de riesgo de colisión y como se abordan en esta tesis. Normalmente se consideran objetos esféricos para simplificar el cálculo de riesgo (caso A). Este caso está ampliamente abordado en la literatura y no se analiza en detalle en esta tesis. Un caso de ejemplo se proporciona en la sección 4.2. Considerar la forma real de los objetos (caso B) permite calcular el riesgo de una manera más precisa. Un nuevo algoritmo es definido en esta tesis para calcular el riesgo de colisión cuando al menos uno de los objetos se considera complejo (sección 4.4.2). Dicho algoritmo permite calcular el riesgo de colisión para objetos formados por un conjunto de cajas, y se ha presentado en varias conferencias internacionales. Para evaluar las prestaciones de dicho algoritmo, sus resultados se han comparado con un análisis de Monte Carlo que se ha definido para considerar colisiones entre cajas de manera adecuada (sección 4.1.2.3), pues la búsqueda de colisiones simples aplicables para objetos esféricos no es aplicable a este caso. Este análisis de Monte Carlo se considera la verdad a la hora de calcular los resultados del algoritmos, dicha comparativa se presenta en la sección 4.4.4. En el caso de satélites que no se pueden considerar esféricos, el uso de un modelo de la geometría del satélite permite descartar eventos que no son colisiones reales o estimar con mayor precisión el riesgo asociado a un evento. El uso de estos algoritmos con geometrías complejas es más relevante para objetos de dimensiones grandes debido a las prestaciones de precisión orbital actuales. En el futuro, si los sistemas de vigilancia mejoran y las órbitas son conocidas con mayor precisión, la importancia de considerar la geometría real de los satélites será cada vez más relevante. La sección 5.4 presenta un ejemplo para un sistema de grandes dimensiones (satélite con un tether). Adicionalmente, si los dos objetos involucrados en la colisión tienen velocidad relativa baja (y geometría simple, Caso C en la Figura 2), la mayor parte de los algoritmos no son aplicables requiriendo implementaciones dedicadas para este caso particular. En esta tesis, uno de estos algoritmos presentado en la literatura [Patera, 2001]R.26 se ha analizado para determinar su idoneidad en distintos tipos de eventos (sección 4.5). La evaluación frete a un análisis de Monte Carlo se proporciona en la sección 4.5.2. Tras este análisis, se ha considerado adecuado para abordar las colisiones de baja velocidad. En particular, se ha concluido que el uso de algoritmos dedicados para baja velocidad son necesarios en función del tamaño del volumen de colisión proyectado en el plano de encuentro (B-plane) y del tamaño de la incertidumbre asociada al vector posición entre los dos objetos. Para incertidumbres grandes, estos algoritmos se hacen más necesarios pues la duración del intervalo en que los elipsoides de error de los dos objetos pueden intersecar es mayor. Dicho algoritmo se ha probado integrando el algoritmo de colisión para objetos con geometrías complejas. El resultado de dicho análisis muestra que este algoritmo puede ser extendido fácilmente para considerar diferentes tipos de algoritmos de cálculo de riesgo de colisión (sección 4.5.3). Ambos algoritmos, junto con el método Monte Carlo para geometrías complejas, se han implementado en la herramienta operacional de la ESA CORAM, que es utilizada para evaluar el riesgo de colisión en las actividades rutinarias de los satélites operados por ESA [Sánchez-Ortiz, 2013a]T.11. Este hecho muestra el interés y relevancia de los algoritmos desarrollados para la mejora de las operaciones de los satélites. Dichos algoritmos han sido presentados en varias conferencias internacionales [Sánchez-Ortiz, 2013b]T.9, [Pulido, 2014]T.7,[Grande-Olalla, 2013]T.10, [Pulido, 2014]T.5, [Sánchez-Ortiz, 2015c]T.1. ABSTRACT This document addresses methodologies for computation of the collision risk of a satellite. Two different approaches need to be considered for collision risk minimisation. On an operational basis, it is needed to perform a sieve of possible objects approaching the satellite, among all objects sharing the space with an operational satellite. As the orbits of both, satellite and the eventual collider, are not perfectly known but only estimated, the miss-encounter geometry and the actual risk of collision shall be evaluated. In the basis of the encounter geometry or the risk, an eventual manoeuvre may be required to avoid the conjunction. Those manoeuvres will be associated to a reduction in the fuel for the mission orbit maintenance, and thus, may reduce the satellite operational lifetime. Thus, avoidance manoeuvre fuel budget shall be estimated, at mission design phase, for a better estimation of mission lifetime, especially for those satellites orbiting in very populated orbital regimes. These two aspects, mission design and operational collision risk aspects, are summarised in Figure 3, and covered along this thesis. Bottom part of the figure identifies the aspects to be consider for the mission design phase (statistical characterisation of the space object population data and theory computing the mean number of events and risk reduction capability) which will define the most appropriate collision avoidance approach at mission operational phase. This part is covered in this work by starting from the theory described in [Sánchez-Ortiz, 2006]T.14 and implemented by this author in ARES tool [Sánchez-Ortiz, 2004b]T.15 provided by ESA for evaluation of collision avoidance approaches. This methodology has been now extended to account for the particular features of the available data sets in operational environment (section 4.3.3). Additionally, the formulation has been extended to allow evaluating risk computation approached when orbital uncertainty is not available (like the TLE case) and when only catastrophic collisions are subject to study (section 4.3.2.3). These improvements to the theory have been included in the new version of ESA ARES tool [Domínguez-González and Sánchez-Ortiz, 2012b]T.12 and available through [SDUP,2014]R.60. At the operation phase, the real catalogue data will be processed on a routine basis, with adequate collision risk computation algorithms to propose conjunction avoidance manoeuvre optimised for every event. The optimisation of manoeuvres in an operational basis is not approached along this document. Currently, American Two Line Element (TLE) catalogue is the only public source of data providing orbits of objects in space to identify eventual conjunction events. Additionally, Conjunction Summary Message (CSM) is provided by Joint Space Operation Center (JSpOC) when the American system identifies a possible collision among satellites and debris. Depending on the data used for collision avoidance evaluation, the conjunction avoidance approach may be different. The main features of currently available data need to be analysed (in regards to accuracy) in order to perform estimation of eventual encounters to be found along the mission lifetime. In the case of TLE, as these data is not provided with accuracy information, operational collision avoidance may be also based on statistical accuracy information as the one used in the mission design approach. This is not the case for CSM data, which includes the state vector and orbital accuracy of the two involved objects. This aspect has been analysed in detail and is depicted in the document, evaluating in statistical way the characteristics of both data sets in regards to the main aspects related to collision avoidance. Once the analysis of data set was completed, investigations on the impact of those features in the most convenient avoidance approaches have been addressed (section 5.1). This analysis is published in a peer-reviewed journal [Sánchez-Ortiz, 2015b]T.3. The analysis provides recommendations for different mission types (satellite size and orbital regime) in regards to the most appropriate collision avoidance approach for relevant risk reduction. The risk reduction capability is very much dependent on the accuracy of the catalogue utilized to identify eventual collisions. Approaches based on CSM data are recommended against the TLE based approach. Some approaches based on the maximum risk associated to envisaged encounters are demonstrated to report a very large number of events, which makes the approach not suitable for operational activities. Accepted Collision Probability Levels are recommended for the definition of the avoidance strategies for different mission types. For example for the case of a LEO satellite in the Sun-synchronous regime, the typically used ACPL value of 10-4 is not a suitable value for collision avoidance schemes based on TLE data. In this case the risk reduction capacity is almost null (due to the large uncertainties associated to TLE data sets, even for short time-to-event values). For significant reduction of risk when using TLE data, ACPL on the order of 10-6 (or lower) seems to be required, producing about 10 warnings per year and mission (if one-day ahead events are considered) or 100 warnings per year (for three-days ahead estimations). Thus, the main conclusion from these results is the lack of feasibility of TLE for a proper collision avoidance approach. On the contrary, for CSM data, and due to the better accuracy of the orbital information when compared with TLE, ACPL on the order of 10-4 allows to significantly reduce the risk. This is true for events estimated up to 3 days ahead. Even 5 days ahead events can be considered, but ACPL values down to 10-5 should be considered in such case. Even larger prediction times can be considered (7 days) for risk reduction about 90%, at the cost of larger number of warnings up to 5 events per year, when 5 days prediction allows to keep the manoeuvre rate in 2 manoeuvres per year. Dynamics of the GEO orbits is different to that in LEO, impacting on a lower increase of orbits uncertainty along time. On the contrary, uncertainties at short prediction times at this orbital regime are larger than those at LEO due to the differences in observation capabilities. Additionally, it has to be accounted that short prediction times feasible at LEO may not be appropriate for a GEO mission due to the orbital period being much larger at this regime. In the case of TLE data sets, significant reduction of risk is only achieved for small ACPL values, producing about a warning event per year if warnings are raised one day in advance to the event (too short for any reaction to be considered). Suitable ACPL values would lay in between 5•10-8 and 10-7, well below the normal values used in current operations for most of the GEO missions (TLE-based strategies for collision avoidance at this regime are not recommended). On the contrary, CSM data allows a good reduction of risk with ACPL in between 10-5 and 10-4 for short and medium prediction times. 10-5 is recommended for prediction times of five or seven days. The number of events raised for a suitable warning time of seven days would be about one in a 10-year mission. It must be noted, that these results are associated to a 2 m radius spacecraft, impact of the satellite size are also analysed within the thesis. In the future, other Space Situational Awareness Systems (SSA, ESA program) may provide additional catalogues of objects in space with the aim of reducing the risk. It is needed to investigate which are the required performances of those catalogues for allowing such risk reduction. The main performance aspects are coverage (objects included in the catalogue, mainly limited by a minimum object size derived from sensor performances) and the accuracy of the orbital data to accurately evaluate the conjunctions (derived from sensor performance in regards to object observation frequency and accuracy). The results of these investigations (section 5.2) are published in a peer-reviewed journal [Sánchez-Ortiz, 2015a]T.2. This aspect was not initially foreseen as objective of the thesis, but it shows how the theory described in the thesis, initially defined for mission design in regards to avoidance manoeuvre fuel allocation (upper part of figure 1), is extended and serves for additional purposes as dimensioning a Space Surveillance and Tracking (SST) system (bottom part of figure below). The main difference between the two approaches is the consideration of the catalogue features as part of the theory which are not modified (for the satellite mission design case) instead of being an input for the analysis (in the case of the SST design). In regards to the outputs, all the features computed by the statistical conjunction analysis are of importance for mission design (with the objective of proper global avoidance strategy definition and fuel allocation), whereas for the case of SST design, the most relevant aspects are the manoeuvre and false alarm rates (defining a reliable system) and the Risk Reduction capability (driving the effectiveness of the system). In regards to the methodology for computing the risk, the SST system shall be driven by the capacity of providing the means to avoid catastrophic conjunction events (avoiding the dramatic increase of the population), whereas the satellite mission design should consider all type of encounters, as the operator is interested on avoiding both lethal and catastrophic collisions. From the analysis of the SST features (object coverage and orbital uncertainty) for a reliable system, it is concluded that those two characteristics are to be imposed differently for the different orbital regimes, as the population level is different depending on the orbit type. Coverage values range from 5 cm for very populated LEO regime up to 100 cm in the case of GEO region. The difference on this requirement derives mainly from the relative velocity of the encounters at those regimes. Regarding the orbital knowledge of the catalogues, very accurate information is required for objects in the LEO region in order to limit the number of false alarms, whereas intermediate orbital accuracy can be considered for higher orbital regimes. In regards to the operational collision avoidance approaches, several collision risk algorithms are used for evaluation of collision risk of two pair of objects. Figure 2 provides a summary of the different collision risk algorithm cases and indicates how they are covered along this document. The typical case with high relative velocity is well covered in literature for the case of spherical objects (case A), with a large number of available algorithms, that are not analysed in detailed in this work. Only a sample case is provided in section 4.2. If complex geometries are considered (Case B), a more realistic risk evaluation can be computed. New approach for the evaluation of risk in the case of complex geometries is presented in this thesis (section 4.4.2), and it has been presented in several international conferences. The developed algorithm allows evaluating the risk for complex objects formed by a set of boxes. A dedicated Monte Carlo method has also been described (section 4.1.2.3) and implemented to allow the evaluation of the actual collisions among a large number of simulation shots. This Monte Carlo runs are considered the truth for comparison of the algorithm results (section 4.4.4). For spacecrafts that cannot be considered as spheres, the consideration of the real geometry of the objects may allow to discard events which are not real conjunctions, or estimate with larger reliability the risk associated to the event. This is of particular importance for the case of large spacecrafts as the uncertainty in positions of actual catalogues does not reach small values to make a difference for the case of objects below meter size. As the tracking systems improve and the orbits of catalogued objects are known more precisely, the importance of considering actual shapes of the objects will become more relevant. The particular case of a very large system (as a tethered satellite) is analysed in section 5.4. Additionally, if the two colliding objects have low relative velocity (and simple geometries, case C in figure above), the most common collision risk algorithms fail and adequate theories need to be applied. In this document, a low relative velocity algorithm presented in the literature [Patera, 2001]R.26 is described and evaluated (section 4.5). Evaluation through comparison with Monte Carlo approach is provided in section 4.5.2. The main conclusion of this analysis is the suitability of this algorithm for the most common encounter characteristics, and thus it is selected as adequate for collision risk estimation. Its performances are evaluated in order to characterise when it can be safely used for a large variety of encounter characteristics. In particular, it is found that the need of using dedicated algorithms depend on both the size of collision volume in the B-plane and the miss-distance uncertainty. For large uncertainties, the need of such algorithms is more relevant since for small uncertainties the encounter duration where the covariance ellipsoids intersect is smaller. Additionally, its application for the case of complex satellite geometries is assessed (case D in figure above) by integrating the developed algorithm in this thesis with Patera’s formulation for low relative velocity encounters. The results of this analysis show that the algorithm can be easily extended for collision risk estimation process suitable for complex geometry objects (section 4.5.3). The two algorithms, together with the Monte Carlo method, have been implemented in the operational tool CORAM for ESA which is used for the evaluation of collision risk of ESA operated missions, [Sánchez-Ortiz, 2013a]T.11. This fact shows the interest and relevance of the developed algorithms for improvement of satellite operations. The algorithms have been presented in several international conferences, [Sánchez-Ortiz, 2013b]T.9, [Pulido, 2014]T.7,[Grande-Olalla, 2013]T.10, [Pulido, 2014]T.5, [Sánchez-Ortiz, 2015c]T.1.

Spacecraft launch depressurization loads

The pressure variation inside the launch vehicle fairing during climb through the atmosphere induces structural loads on the walls of closed-type spacecrafts or equipment boxes. If the evacuation of the air is not fast enough, excessive pressure loading can result in damage of elements exposed to the rising pressure jump, which depends mainly on the geometry of venting holes, the effective volume of air to be evacuated, and the characteristic time of pressure variation under the fairing. A theoretical study of the reservoir discharge forced by the fairing time-dependent pressure variation is presented. The basic mathematical model developed can yield both a numerical solution for the pressure jump and an asymptotic solution for the most relevant case, the small-prcssurc-jump limit, showing the dependence on a single nondimensional parameter: the ratio of the reservoir discharge to the fairing pressure profile characteristic times. The asymptotic solution validity range upper limit, obtained by comparison with the numerical solution, is determined by the starting of choked operation. Very high sensitivity of the maximum pressure jump to the ratio of characteristic times has been observed. Another relevant finding is that the pressure profiles for different launchers can be considered similar when rewritten in appropriate form and only their characteristic times are required for the analysis. The simple expressions of the asymptotic solution are a useful tool for preliminarily sizing the reservoir discharge geometry and estimating depressurization loads

Análisis teórico del contacto plasma-superficie y sus aplicaciones industriales

Actualmente, la física de plasmas constituye una parte importante de la investigación en física que está siendo desarrollada. Su campo de aplicación varía desde el estudio de plasmas interestelares y cósmicos, como las estrellas, las nebulosas, el medio intergaláctico, etc.; hasta aplicaciones más terrenales como la producción de microchips o los dispositivos de iluminación. Resulta particularmente interesante el estudio del contacto de una superficie metálica con un plasma. Siendo la razón que, la dinámica de la interfase formada entre un plasma imperturbado y una superficie metálica, resulta de gran importancia cuando se trata de estudiar problemas como: la implantación iónica en una oblea de silicio, el grabado por medio de plasmas, la carga de una aeronave cuando atraviesa la ionosfera y la diagnosis de plasmas mediante sondas de Langmuir. El uso de las sondas de Langmuir está extendido a través de multitud de aplicaciones tecnológicas e industriales como método de diagnosis de plasmas. Algunas de estas aplicaciones han sido mencionadas justo en el párrafo anterior. Es más, su uso también es muy popular en la investigación en física de plasmas, por ser una de las pocas técnicas de diagnosis que proporciona información local sobre el plasma. El equipamiento donde es habitualmente implementado varía desde plasmas de laboratorio de baja temperatura hasta plasmas de fusión en dispositivos como tokamaks o stellerators. La geometría más popular de este tipo de sondas es cilíndrica, y la principal magnitud que se usa para diagnosticar el plasma es la corriente recogida por la sonda cuando se encuentra polarizada a un cierto potencial. Existe un interes especial en diagnosticar por medio de la medida de la corriente iónica recogida por la sonda, puesto que produce una perturbación muy pequeña del plasma en comparación con el uso de la corriente electrónica. Dada esta popularidad, no es de extrañar que grandes esfuerzos se hayan realizado en la consecución de un modelo teórico que explique el comportamiento de una sonda de Langmuir inmersa en un plasma. Hay que remontarse a la primera mitad del siglo XX para encontrar las primeras teorías que permiten diagnosticar parámetros del plasma mediante la medida de la corriente iónica recogida por la sonda de Langmuir. Desde entonces, las mejoras en estos modelos y el desarrollo de otros nuevos ha sido una constante en la investigación en física de plasmas. No obstante, todavía no está claro como los iones se aproximan a la superficie de la sonda. Las dos principales, a la par que opuestas, aproximaciones al problema que están ampliamente aceptadas son: la radial y la orbital; siendo el problema que ambas predicen diferentes valores para la corriente iónica. Los experimentos han arrojado resultados de acuerdo con ambas teorías, la radial y la orbital; y lo que es más importante, una transición entre ambos ha sido recientemente observada. La mayoría de los logros conseguidos a la hora de comprender como los iones caen desde el plasma hacia la superficie de la sonda, han sido llevados a cabo en el campo de la dinámica de fluidos o la teoría cinética. Por otra parte, este problema puede ser abordado mediante el uso de simulaciones de partículas. La principal ventaja de las simulaciones de partículas sobre los modelos de fluidos o cinéticos es que proporcionan mucha más información sobre los detalles microscópicos del movimiento de las partículas, además es relativamente fácil introducir interacciones complejas entre las partículas. No obstante, estas ventajas no se obtienen gratuitamente, ya que las simulaciones de partículas requieren grandísimos recursos. Por esta razón, es prácticamente obligatorio el uso de técnicas de procesamiento paralelo en este tipo de simulaciones. El vacío en el conocimiento de las sondas de Langmuir, es el que motiva nuestro trabajo. Nuestra aproximación, y el principal objetivo de este trabajo, ha sido desarrollar una simulación de partículas que nos permita estudiar el problema de una sonda de Langmuir inmersa en un plasma y que está negativamente polarizada con respecto a éste. Dicha simulación nos permitiría estudiar el comportamiento de los iones en los alrededores de una sonda cilíndrica de Langmuir, así como arrojar luz sobre la transición entre las teorías radiales y orbitales que ha sido observada experimentalmente. Justo después de esta sección introductoria, el resto de la tesis está dividido en tres partes tal y como sigue: La primera parte está dedicada a establecer los fundamentos teóricos de las sondas de Langmuir. En primer lugar, se realiza una introducción general al problema y al uso de sondas de Langmuir como método de diagnosis de plasmas. A continuación, se incluye una extensiva revisión bibliográfica sobre las diferentes teorías que proporcionan la corriente iónica recogida por una sonda. La segunda parte está dedicada a explicar los detalles de las simulaciones de partículas que han sido desarrolladas a lo largo de nuestra investigación, así como los resultados obtenidos con las mismas. Esta parte incluye una introducción sobre la teoría que subyace el tipo de simulaciones de partículas y las técnicas de paralelización que han sido usadas en nuestros códigos. El resto de esta parte está dividido en dos capítulos, cada uno de los cuales se ocupa de una de las geometrías consideradas en nuestras simulaciones (plana y cilíndrica). En esta parte discutimos también los descubrimientos realizados relativos a la transición entre el comportamiento radial y orbital de los iones en los alrededores de una sonda cilíndrica de Langmuir. Finalmente, en la tercera parte de la tesis se presenta un resumen del trabajo realizado. En este resumen, se enumeran brevemente los resultados de nuestra investigación y se han incluido algunas conclusiones. Después de esto, se enumeran una serie de perspectivas futuras y extensiones para los códigos desarrollados.

Machine Learning Unsupervised Methods in the Design of an On-board Health Monitoring System for Satellite Applications

The dissertation starts by providing a description of the phenomena related to the increasing importance recently acquired by satellite applications. The spread of such technology comes with implications, such as an increase in maintenance cost, from which derives the interest in developing advanced techniques that favor an augmented autonomy of spacecrafts in health monitoring. Machine learning techniques are widely employed to lay a foundation for effective systems specialized in fault detection by examining telemetry data. Telemetry consists of a considerable amount of information; therefore, the adopted algorithms must be able to handle multivariate data while facing the limitations imposed by on-board hardware features. In the framework of outlier detection, the dissertation addresses the topic of unsupervised machine learning methods. In the unsupervised scenario, lack of prior knowledge of the data behavior is assumed. In the specific, two models are brought to attention, namely Local Outlier Factor and One-Class Support Vector Machines. Their performances are compared in terms of both the achieved prediction accuracy and the equivalent computational cost. Both models are trained and tested upon the same sets of time series data in a variety of settings, finalized at gaining insights on the effect of the increase in dimensionality. The obtained results allow to claim that both models, combined with a proper tuning of their characteristic parameters, successfully comply with the role of outlier detectors in multivariate time series data. Nevertheless, under this specific context, Local Outlier Factor results to be outperforming One-Class SVM, in that it proves to be more stable over a wider range of input parameter values. This property is especially valuable in unsupervised learning since it suggests that the model is keen to adapting to unforeseen patterns.