An increasing number of GPS applications require a high level of accuracy. To reduce the error contributed by the GPS ephemerides, an accurate modeling of the forces acting on GPS satellites is necessary. These forces can be categorized into gravitational and non-gravitational forces. The non-gravitational forces are a significant contribution to the total force on a GPS satellite but they are still not fully understood whereas the gravitational forces are well modeled. This study focuses on two non-gravitational forces: Solar Radiation Pressure (SRP) and the y-bias force. Different SRP models are available in the University of Texas Multi-Satellite Orbit Determination Program (MSODP). The recently developed University College London model was implemented for the purpose of this study. Several techniques to compute parameters associated with SRP models and the y-bias force during an orbit prediction were examined. Using the International GNSS Service (IGS) precise ephemerides as a reference, five different models were compared in the study. Satellite Laser Ranging (SLR) residuals were also studied to validate the approach. Results showed that the analytical UCL model performed as well as a purely empirical model such as the Extended CODE model. This is important since analytical models attempt to represent the physical phenomena and thus might be better suited to separate SRP from other forces. The y-bias force was then shown to have a once per revolution effect. The time evolution of the y-bias was found to be dependent on the SRP model used, the satellite Block type, the orbital plane, and the attitude of the satellite which suggests that estimates of y-bias contain errors from other sources, particularly the SRP models. The dependency of the y-bias evolution on the orbital plane suggests that the orientation of the plane towards the Sun is important. / text

Dark matter is now accepted as an integral part of our universe, and galaxy dynamics have long provided the most convincing observational evidence for dark matter. Spiral galaxies have traditionally been used for these studies because of their more simple kinematics, however elliptical galaxies need to be understood as well. In this dissertation I present deep long-slit spectroscopy from the University of Texas’ Hobby-Eberly Telescope for a sample of elliptical galaxies. For a subsample of galaxies I fit axisymmetric orbit-superposition models with a range of dark halo density profiles. I find that all three galaxies modeled require a significant dark halo to explain their motions. However, the shape of the dark halo is not the expected NFW profile, but rather a profile with a flat central slope. I also discuss the galaxy masses, anisotropies, and stellar mass-to-light ratios. / text

This concept of calculating, optimizing, and utilizing a trajectory known as a ``Free Return Trajectory" to facilitate spacecraft rendezvous with Near-Earth Asteroids is presented in this dissertation. A Free Return Trajectory may be defined as a trajectory that begins and ends near the same point, relative to some central body, without performing any deterministic velocity maneuvers (i.e., no maneuvers are planned in a theoretical sense for the nominal mission to proceed). Free Return Trajectories have been utilized previously for other purposes in astrodynamics, but they have not been previously applied to the problem of Near-Earth Asteroid rendezvous. Presented here is a series of descriptions, algorithms, and results related to trajectory initial guess calculation and optimal trajectory convergence. First, Earth-centered Free Return Trajectories are described in a general manner, and these trajectories are classified into several families based on common characteristics. Next, these trajectories are used to automatically generate initial conditions in the three-body problem for the purpose of Near-Earth Asteroid rendezvous. For several bodies of interest, example initial conditions are automatically generated, and are subsequently converged, resulting in feasible, locally-optimal, round-trip trajectories to Near-Earth Asteroids utilizing Free Return Trajectories. Subsequently, a study is performed on using an unpowered flyby of the Moon to lower the overall DV cost for a nominal round-trip voyage to a Near-Earth Asteroid. Using the Moon is shown to appreciably decrease the overall mission cost. In creating the formulation and algorithms for the Lunar flyby problem, an initial guess routine for generic planetary and lunar flyby tours was developed. This continuation algorithm is presented next, and details a novel process by which ballistic trajectories in a simplistic two-body force model may be iteratively converged in progressively more realistic dynamical models until a final converged ballistic trajectory is found in a full-ephemeris, full-dynamics model. This procedure is useful for constructing interplanetary transfers and moon tours in a realistic dynamical framework; an interplanetary and an inter-moon example are both shown. To summarize, the material in this dissertation consists of: novel algorithms to compute Free Return Trajectories, and application of the concept to Near-Earth Asteroid rendezvous; demonstration of cost-savings by using a Lunar flyby; and a novel routine to transfer trajectories from a simplistic model to a more realistic dynamical representation. / text

Ce travail est une contribution ab initio à la caractérisation d'halogénures diatomiques de métaux de transition. Nous avons choisi de caractériser la structure électronique des chlorures de métaux de transition du groupe Vb (NbCl et TaCl) et du fluorure de nickel car une série de spectres les concernant ont été enregistrés mais aucune donnée théorique fiable n'était disponible dans la littérature. Pour étudier ces molécules, nous avons appliqué une procédure de calcul à deux étapes qui permet de tenir compte des effets de corrélation électronique et des effets relativistes. Dans la première étape, nous avons réalisé des calculs CASSCF/ICMRCI+Q de grande taille qui tiennent compte de l'énergie de corrélation et introduisent des effets relativistes scalaires. Dans la deuxième étape, le couplage spin-orbite est traité par la "state interacting method" implémentée dans le logiciel MOLPRO. Nous avons développé des stratégies de calcul basées sur ces méthodes de calcul et adaptées aux différentes molécules ciblées. Ainsi, pour les molécules NbCl et TaCl, nous avons utilisé des pseudopotentiels relativistes scalaires et spin-orbite, tandis que pour la molécule NiF, nous avons réalisé des calculs tous électrons. Nous avons d'abord testé la stratégie de calcul sur les cations Nb+ et Ta+. Ensuite, nous avons calculé pour la première fois les structures électroniques relativiste scalaire et spin-orbite des molécules NbCl (de 0 à 17000 cm-1) et TaCl (de 0 à 23000 cm-1). A l'aide de ces données théoriques, nous avons interprété les spectres expérimentaux en collaboration avec Bernath et al. Nous avons proposé plusieurs attributions de transitions électroniques en accord avec l'expérience mais nos résultats théoriques ne nous ont pas permis de les attribuer toutes. Néanmoins, nous avons mis en évidence une série d'autres transitions électroniques probables qui pourraient, à l'avenir, servir à l'interprétation de nouveaux spectres mieux résolus. Outre son intérêt expérimental, cette étude a permis de comparer les structures électroniques des molécules isovalencielles VCl, NbCl et TaCl, mettant en évidence des différences importantes. L'élaboration d'une nouvelle stratégie de calcul pour décrire les systèmes contenant l'atome de nickel représentait un véritable défi en raison de la complexité des effets de corrélation électronique. Notre stratégie de calcul a consisté à introduire ces effets en veillant à réduire au maximum la taille des calculs qui devenait considérable. Nous l'avons testée sur l'atome Ni et appliquée ensuite au calcul des structures électroniques relativiste scalaire et spin-orbite de la molécule NiF entre 0 à 2500 cm-1. Nous avons obtenus des résultats qui corroborent l'expérience.

<p>NR 20140805</p>

The ultimate goal in the rapidly burgeoning field of spintronics is to realize semiconductor-based devices that utilize the spin degree of freedom of a single charge carrier (electron or hole) or an ensemble of such carriers to achieve novel and/or enhanced device functionalities such as spin based light emitting devices, spin transistors and femto-Tesla magnetic field sensors. These devices share a common feature: they all rely on controlled transport of spins in semiconductors. A prototypical spintronic device has a transistor-like configuration in which a semiconducting channel is sandwiched between two contacts (source and drain) with a gate electrode sitting on top of the channel. Unlike conventional charge-based transistors, the source electrode of a spin transistor is a ferromagnetic (or half-metallic) material which injects spin polarized electrons in the channel. During transit, the spin polarizations of the electrons are controllably rotated by a gate electric field mediated spin-orbit coupling effect. The drain contact is ferromagnetic (or half-metallic) as well and the transmission probability of an electron through this drain electrode depends on the relative orientation of electron spin polarization and the (fixed) magnetization of the drain. When the spins of the electrons are parallel to the drain magnetization, they are transmitted by the drain resulting in a large device current (ON state of spin FET). However, these electrons will be completely blocked if their spins are antiparallel to the drain magnetization, and ideally, in this situation device current will be zero (OFF state of spinFET). Thus, if we vary the gate voltage, we can modulate the channel current by controlling the spin orientations of the electrons with respect to the drain magnetization. This is how transistor action is realized (Datta-Das model). However, during transport, electrons' velocities change randomly with time due to scattering and hence different electrons experience different spin-orbit magnetic fields. As a result, even though all electrons start their journey with identical spin orientations, soon after injection spins of different electrons point along different directions in space. This randomization of initial spin polarization is referred to as spin relaxation and this is detrimental to the spintronic devices. In particular, for Datta-Das transistor, this will lead to inefficient gate control and large leakage current in the OFF state of the spinFET. The aim of this work is to understand various spin relaxation processes that are operative in semiconductor nanostructures and to indicate possible ways of minimizing them. The theoretical aspect of this work (Chapters 2-5) focuses on the D'yakonov-Perel' process of spin relaxation in a semiconductor quantum wire. This process of spin relaxation occurs because during transport electron spin precesses like a spinning top about the spin-orbit magnetic field. We show that the conventional drift-diffusion model of spin transport, which has been used extensively in literature, completely breaks down in case of a quantum confined system (e.g. a quantum wire). Our approach employs a semi-classical model which couples the spin density matrix evolution with the Boltzmann transport equation. Using this model we have thoroughly studied spin relaxation in a semiconductor quantum wire and identified several inconsistencies of the drift-diffusion formalism.The experimental side of this work (Chapters 6-8) deals with two different issues: (a) performing spin transport experiments in order to extract spin relaxation length and time in various materials (e.g. Cu, Alq3) under one-dimensional confinement, and (b) measurement of the ensemble spin dephasing time in self-assembled cadmium sulfide quantum dots using electron spin resonance technique. The spin transport experiment, as described in Chapter 7 of this dissertation, shows that the spin relaxation time in organic semiconductor (Alq3) is extremely long, approaching a few seconds at low temperatures. Alq3 is the chemical formula of tris- 8 hydroxy-quinoline aluminum, which is a small molecular weight organic semiconductor. This material is extensively used in organic display industry as the electron transport and emission layer in green organic light emitting diodes. The long spin relaxation time in Alq3 makes it an ideal platform for spintronics. This also indicates that it may be possible to realize spin based organic light emitting diodes which will have much higher internal quantum efficiency than their conventional non-spin counterparts. From spin transport experiments mentioned above we have also identified Elliott-Yafet mode as the dominant spin relaxation mechanism operative in organic semiconductors. Electron spin resonance experiment performed on self-assembled quantum dots (Chapter 8) allows us to determine the ensemble spin dephasing time (or transverse spin relaxation time) of electrons confined in these systems. In quantum dots electrons are strongly localized in space. Surprisingly, the ensemble spin dephasing time shows an increasing trend as we increase temperature. The most likely explanation for this phenomenon is that spin dephasing in quantum dots (unlike quantum wells and wires) is dominated by nuclear hyperfine interaction, which weakens progressively with temperature. We hope that our work, which elaborates on all of the above mentioned topics in great detail, will be a significant contribution towards the current state of knowledge of subtle spin-based issues operative in nanoscale device structures, and will ultimately lead to realization of novel nano-spintronic devices.

L'état supraconducteur étant un condensat de paires de Cooper constitué d'électrons de moments et de spins opposés, il peut être fortement influencé par des effets de spin. Au cours de cette thèse, nous étudions l'effet d'un fort champ d'échange et d'un effet spin-orbite de type Rashba sur les propriétés supraconductrices. Dans une première partie, on étudie les effets associés à l'interaction entre supraconductivité et fort champ d'échange, se caractérisant par une transition de phase vers un état supraconducteur inhomogène découvert par Fulde, Ferrell, Larkin et Ovchinnikov (FFLO). On étudie tout particulièrement les fluctuations supraconductrices à l'approche de la transition de phase. On montre que ces fluctuations peuvent servir de révélateur à cette phase. Notamment, la capacité calorifique et la paraconductivité divergent de façon caractéristique à la transition vers un état modulé. On décrit également comment les effets paramagnétiques modifient les fluctuations de l'aimantation, annulant la réponse diamagnétique ou produisant des oscillations entre réponse para- et dia-magnétique. La seconde partie est dévolue aux jonctions supraconducteur-ferromagnétique (S/F). Dans les jonctions Josephson S/F/S, le champ d'échange donne lieu à des oscillations du courant critique en fonction de la longueur de la jonction, charactérisées par une alternance des états 0 et . On prédit une transition entre les états 0 et induite par la température, même dans la limite ballistique. Dans cette limite ballistique, on montre également que le courant de Josephson s'atténu sous la forme de lois de puissance en fonction de la longueur de la jonction, alors que le cas diffusif présente une atténuation exponentielle. On étudie ensuite la seconde harmonique de la relation courant-phase en présence d'une faible quantité d'impuretés. La dernière partie traite des effets de proximité lorsque les deux effets paramagnétique et spin-orbite sont présents dans une jonction Josephson. On montre que l'association d'une interaction Rashba et d'un champ d'échange induit un couplage direct entre les ordres magnétique et supraconducteur. En particulier, ce couplage permet de générer toute la dynamique magnétique par l'application d'une simple tension électrique. / The superconducting state being a Cooper pair condensate built on opposite spin and momentum electrons, it can be strongly influenced by any spin effect. In this thesis, we investigate the roles of strong paramagnetic and spin-orbit effects on superconducting properties. In a first part, the interplay between paramagnetic effect and bulk superconductivity is studied, leading to the modulated Fulde, Ferrell, Larkin and Ovchinnikov phase (FFLO phase). We focus on superconducting fluctuations near to the FFLO state. We show that these fluctuations can serve as a smoking gun for this phase. Noticeably, the fluctuation heat capacity and paraconductivity diverge in a characteristic way when approaching the phase transition towards a modulated state. Moreover, the fluctuation induced magnetization is predicted to be drastically quenched or to oscillate between dia- and para-magnetic responses. The second part is devoted to superconductor-ferromagnetic (S/F) junctions. In S/F/S Josephson junctions, the exchange field is responsible for the critical current oscillation, characterized by alternative 0- and -states, with respect to the junction length. We predict a temperature induced (0-) state transition, even in the ballistic case. Moreover, the ballistic case exhibits some power law decays of the Josephson current, in contrast to the exponentially decaying current in dirty limit. The moderately dirty limit is then investigated, and the second harmonic of the current-phase relation is established. The last part deals with proximity effects when both paramagnetic and spin-orbit interactions are present in a Josephson junction. We show that the association of both Rashba interaction and exchange field induces a direct coupling between magnetic and superconducting orders. Particularly, this coupling generates the complete magnetization dynamics by applying an appropriate d.c. voltage.

Nous étudions les triangulations dans des espaces de courbure négative constante, en théorie et en pratique. Ce travail est motivé par des applications dans des domaines variés. Nous considérons les complexes de Delaunay et les diagrammes de Voronoï dans la boule de Poincaré, modèle conforme de l'espace hyperbolique, en dimension quelconque. Nous utilisons l'espace des sphères pour la description des algorithmes. Nous étudions aussi les questions algébriques et arithmétiques et observons que les calculs effectués sont rationnels. Les démonstrations sont basées sur des raisonnements géométriques et n'utilisent aucune formulation analytique de la distance hyperbolique. Nous présentons une implantation complète, exacte et efficace en dimension deux. Le code est développé en vue d'une intégration dans la bibliothèque CGAL, qui permettra une diffusion à un large public. Nous étudions ensuite les triangulations de Delaunay des surfaces hyperboliques fermées. Nous définissons une triangulation comme un complexe simplicial afin de permettre l'adaptation de l'algorithme incrémentiel connu pour le cas euclidien. Le cœur de l'approche consiste à montrer l'existence d'un revêtement fini dans lequel les fibres définissent toujours une triangulation de Delaunay. Nous montrons une condition suffisante sur la longueur des boucles non contractiles du revêtement. Dans le cas particulier de la surface de Bolza, nous proposons une méthode pour construire un tel revêtement, en étudiant les sous groupes distingués du groupe fuchsien définissant la surface. Nous considérons des aspects liés à l'implantation. / We study triangulations of spaces of constant negative curvature -1 from both theoretical and practical points of view. This is originally motivated by applications in various fields such as geometry processing and neuro mathematics. We first consider Delaunay complexes and Voronoi diagrams in the Poincaré ball, a conformal model of the hyperbolic space, in any dimension. We use the framework of the space of spheres to give a detailed description of algorithms. We also study algebraic and arithmetic issues, observing that only rational computations are needed. All proofs are based on geometric reasoning, they do not resort to any use of the analytic formula of the hyperbolic distance. We present a complete, exact, and efficient implementation of the Delaunay complex and Voronoi diagram in the 2D hyperbolic space. The implementation is developed for future integration into the CGAL library to make it available to a broad public. Then we study the problem of computing Delaunay triangulations of closed hyperbolic surfaces. We define a triangulation as a simplicial complex, so that the general incremental algorithm for Euclidean Delaunay triangulations can be adapted. The key idea of the approach is to show the existence of a finite-sheeted covering space for which the fibers always define a Delaunay triangulation. We prove a sufficient condition on the length of the shortest non-contractible loops of the covering space. For the specific case of the Bolza surface, we propose a method to actually construct such a covering space, by studying normal subgroups of the Fuchsian group defining the surface. Implementation aspects are considered.

Au cours de cette thèse, on étudie les systèmes différents : graphène (une monocouche de carbone), graphène fonctionnalisé et les nanofils de Bismuth en induisant la supraconductivité par l’effet proximité. On montre que l’effet proximité fonctionne comme un probe sensible pour les effets des interactions, de couplage spin-orbite, etc.La structure de band de graphène a une relation dispersion linéaire au niveau de Fermi, et le band de conductance et le band de valence est lié aux six points dans l’espace réciproque, appelé le point Dirac. Autour du point Dirac, graphène occupe d’une densité d’état faible (par rapport aux métaux). Alors le niveau de Fermi dans graphene est modulable. On fabrique les jonctions S/Graphene/S avec les contacts de matériaux différents (Al, ReW, Nb). En comparant avec la théorie, on a complété le diagramme du produit R_N I_c (R_N la résistance d’état normal, I_c le courant critique dans une jonction) vs l’énergie Thouless E_Th (une énergie caractéristique intervient dans la jonction SNS longue et dépend la partie normale). Une réduction de R_N I_c globale de la jonction courte à la jonction longue, surtout dans la limite de la jonction longue, la réduction est 10 fois plus grande que celle de la jonction courte. On l’explique par une réduction d’une énergie Thouless effective à cause l’interface S/G imparfaite. Une suppression du supercourant près du point Dirac dans les jonctions longues est considérée comme une signature de la réflexion Andreev spéculaire sur les « puddles » dans le graphène. Aussi, l’injection des paires de Cooper dans les états de bord de l’effet Hall quantique du graphène est étudiée dans cette thèse.L’interaction du couplage spin-orbite et l’effet proximité peut produire les physiques très intéressantes comme le supra de triplet, jonction π, et récemment la formation des Fermions majoranas. Motivé par ces possibilités d’explorer les nouvelles physiques, on a essayé d’induire le couplage spin-orbite dans graphène dans lequel ce couplage est initialement très faible. En greffant les molécules de Pt-porphyrines, qui tiennent un atome de Pt au milieu, on espère que le couplage spin-orbite fort dans l’atome de Pt peut « diffuser » dans le graphène. Au lieu d’avoir vu le couplage spin-orbite, on a plutôt découvert un magnétisme qui dépend la grille dans le graphène induit par les molécules. Plusieurs échantillons avec les contacts normaux ou supraconducteurs sont mesurés avant et après mettant les molécules. Un transfert de charge dans deux sens (électron ou trou) est observé à la température ambiante. Il est lié à l’alignement des niveaux de Fermi des molécules et le graphène. A basse température (~70mK), les hystérésis dans la magnétorésistance (MR) et une asymétrie en B_(//) et B_⊥ impliquent un magnétisme dans graphène. Plus spectaculaire, une asymétrie en la dépendance de la grille du supercurrent est détectée. Bismuth est un élément très lourd et un matériau avec le couplage Rashba spin-orbite fort. On a connecté les nanofils de Bismuth avec tungstène (H_c∼12T) électrodes par FIB (Focused Ions Beam) et induit l’effet proximité dans les fils. Les résultats les plus étonnants sont : (1) le supercourant se tient au champ magnétique jusqu’à 11 Tesla. (2) Il y a des oscillations dans le courant critique en fonction du champ avec une période de centaine gauss qui ressemble à celui d’une structure de SQUID (composé des deux jonctions Josephson en parallèles. (3) Sur ces oscillations, nous trouvons aussi une modulation quasi-périodique lente de quelque milles gauss. Pour expliquer tous ces phénomènes, nous proposons qu’il y a quelques canaux étroites balistiques 1D se forment aux bords des certaines surfaces qui se tiennent au champ jusqu’à 11T et se construisent une interférence entre eux. L’effet Zeeman cause une modulation de phase entre les quasi-particules dans une paire d’Andreev qui module donc le supercourant en échelle de quelques milles gauss. / In this thesis we investigated graphene and Bi nanowire systems by inducing superconducting proximity effect in them. Typically the samples are realized in the form of S/N/S junction. The special properties of these systems are revealed by observing some unusual proximity effect in them. The interplay of the superconducting proximity effect and other effects (spin-orbit coupling, Zeeman effect, quantum Hall effect, impurities, etc...) at the mesoscopic scale gives rise to new physics. Some of our main results are listed below.GrapheneWe succeeded to induce superconducting proximity effect in the very long junction limit, thus completing the diagram of the superconducting proximity effect in graphene. Since by changing the gate voltage, one changes the carrier density in graphene and eventually the transport characteristic quantities (l_e, E_Th etc...). We could scan a whole range of Thouless energy. We present a diagram of eR_N I_c vs Thouless energy compared to theoretical prediction. The Thouless energy dependence of the eR_N I_c products varies from the long junction limit to the short junction limit. The discrepancy (mainly due to the imperfect S/G interface) between theory and experiment is also limit dependent: in the short junction limit, the eR_N I_c products are smaller than the theoretical prediction (with a perfect interface) by a factor of about 3-4; in the long junction limit, however, the disagreement is increased to about 100. We show that the factor deduced from the junctions in different limits is length dependent. This can be explained by the effect of finite transmission at the S/G interface in both the critical current I_c and the induced mini-gap in the graphene. In another hand, a suppression of supercurrent near the Dirac point is observed in long junctions which is attributed to the indication of the specular Andreev reflection upon the puddles in graphene. Also the injection of the Cooper pairs into the QHE edge states is investigated in this thesis.Graphene grafted with Pt-porphyrinsBy grafting the Pt-porphyrins onto graphene, we observed a charge transfer between molecules and the graphene both for electrons and holes. One of the important consequences of the charge transfer is that when the molecules are ionized, a collective magnetic order can be formed by the long range RKKY interaction: the magnetic moments interact via the carrier in graphene. This effect is detected by a hysteretic magnetoresistance of the graphene in a perpendicular field and the asymmetric magnetoresistance in parallel field. Even more striking, the observation of a unipolar supercurrent in S/G/S junction implies that this magnetism induced by porphyrins is gate dependent. The theoretical calculations by Uchoa et al. using the Anderson model indeed find that the gate voltage should tune the impurities in graphene between non-magnetic state and magnetic state.Bi nanowireThe observation of a SQUID-like oscillations persisting up to 10 T and thousands Gauss range modulation in I_c hints to a complex physic in the W-Bi nanowire-W junctions. The results are consistent with a SQUID structure consisting of 2 edges channels which could have an I_c oscillation with period defined by the area between the two edges, typically the size of the nanowire. The origin of the edge states formation is attributed to the strong spin-orbit coupling in Bi that leads to the quantum spin Hall (QSH) state. The thousands Gauss range modulation is the consequence of the interplay between the Zeeman effect and the proximity effect. The phase accumulation in an Andreev quasiparticle pair is Δϕ=g_eff⋅μ_B⋅B_(//) (ℏv_F/L) which is of the order of few thousands Gauss. In one particular sample, a full modulation of the critical current with about 1 T range is observed. This is similar to the proximity effect in S/F/S junctions which suggests a 0-π junction transition.

[pt] Este trabalho está relacionado ao problema do uso eficiente da órbita de satélite geoestacionário. A utilização eficiente da órbita é obtida através de um algoritmo de otimização que permite escolher as posições orbitais para os diversos sistemas de modo a reduzir ao máximo o percentual do arco orbital utilizado. Sendo assim, desenvolvido um modelo matemático que considerou além de aspectos de interferência, detalhes da geometria envolvida no problema (posições orbitais dos satélites, posições das estações terrenas, apontamento de antenas, etc.). Este modelo foi utilizado na definição de um problema de otimização com restrição cuja função objetivo se baseia na parcela do arco orbital utilizado. Neste problema de otimização com restrição foram consideradas restrições de níveis máximos de interferência (de entrada única e agregada) além de restrições de arcos orbitais, impostas por aspecto de propagação. O algoritmo de otimização utilizado requer o cálculo do Vetor Gradiente e da Matriz Hessiana. Para evitar erros de origem numéricos essas quantidades foram calculadas utilizando expressões analíticas desenvolvidas neste trabalho. O método matemático foi aplicado a situações específicas conduzindo a resultados que mostraram um uso eficiente da órbita de satélites geoestacionários através de soluções onde a parcela utilizada do arco é minimizada. / [en] This work is related to the efficient use of the geostationary satellite orbit. It presents and describes an optimization model which chooses the best orbital position for each satellite so that the length used orbital arc is minimized. A mathematical model considering aspects such as interference, geometry details (orbital position of the systems, earth station position, boresight of the antenna, etc) is proposed. This model was used in the definition of a constrained optimization problem in which the cost function is the length of the used orbital arc. Constrained imposed by propagation aspects (minimum elevation angle) and by the maximum allowable interference levels (aggregate and single-entry) are considered. The optimization algorithm requires the evaluation of the Gradient vector and the Hessian matrix. To avoid numeric problems, analytic expressions of these quantities were derived. Results of the application of this model to specific situations involving real data were also described and conducted to solutions where the length of the orbit used was minimized