Thesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics and Statistics.

Pines’ and Gottlieb’s Formulations for the gravitational potential provides expressions for the gravitational potential, U, and its derivatives in a co-ordinate system that produces non-singular values. This report summarizes the origin of the singularities due to the spherical co-ordinate system and a discussion of the methods by which the singularity produced by the conventional representation of the gravitational potential is removed by the implementations described in this report. / text

Orientador: Othon Cabo Winter / Banca: Rafael Sfair de Oliveira / Banca: Roberto Vieira Martins / Resumo: Tendo em vista que asteroides são objetos remanescentes dos primórdios do Sistema Solar, estamos interessados na composição deles. Existem missões que estão sendo analisadas com a finalidade de enviar sondas em direção a asteroides do grupo Near Earth Asteroids (NEAs), que representa uma das mais peculiares classes de objetos no Sistema Solar visto que suas órbitas podem se aproximar ou até mesmo cruzar a terrestre. Esse grupo é considerado representativo da população de asteroides, uma vez que podem fornecer informações sobre a mistura química a partir da qual os planetas teriam se formado a bilhões de anos atrás, possibilitando a compreensão da origem e evolução do Sistema Solar e quem sabe até a origem da vida na Terra. Dessa forma, um estudo detalhado a fim de compreender a superfície, a composição e a estrutura interna de um NEA será um grande passo para a Ciência. Nessa pesquisa, inicialmente reproduzimos os dados do potencial gravitacional pelo método dos poliedros para o asteroide 2063 Bacchus, um NEA, a fim de validar os resultados encontrados em Moura (2014). O método dos poliedros fornece uma precisão muito boa da forma irregular do corpo. Por meio de estudo dos modelos de potenciais gravitacionais para corpos não esféricos e implementação de rotinas computacionais foi realizada uma breve análise em relação ao formato do asteroide 2063 Bacchus, bem como das suas superfícies equipotenciais e curvas de velocidade zero. Os objetivos dessa dissertação são realizar um estudo detalhado a respeito dos pontos de equilíbrio no campo gravitacional de 2063 Bacchus, bem como da estabilidade desses pontos levando em consideração os autovalores da equação característica. Além disso, alteramos os valores do período de rotação e da densidade desse objeto a fim de verificar ... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Given that asteroids are remnant objects of the Solar system beginnings, we are interested in their composition. There are missions that are being analyzed with the purpose of sending probes toward asteroids from the group Near Earth Asteroids (NEAs), which is one of the most peculiar classes of objects in the solar system because their orbits can approach or even cross the Earth's orbit. This group is considered representative of the population of asteroids, since they can provide information about the chemical mixture from which the planets would have been formed billions of years ago, enabling the understanding of the origin and evolution of the Solar System and maybe even on the origin of life on Earth. Thus a detailed study in order to understand the surface, the composition and internal structure of a NEA will be a big step for Science. In this research, initially we reproduce the data of the gravitational potential by the method of polyhedra for asteroid 2063 Bacchus, a NEA, in order to validate the results found Moura (2014). The method of polyhedra provides a very good accuracy of the irregular shape of the body. Through study of gravitational potential designs for non-spherical bodies and computational routines implementing a brief analysis was performed with respect to the asteroid shape of 2063 Bacchus, as well as its equipotential surfaces and zero-velocity curves. The objectives of this work are to conduct a detailed study on the equilibrium points in the gravitational field of 2063 Bacchus, and the stability of these points taking into account the eigenvalues of the characteristic equation. In addition, we varied the values of the rotation period and density of the object in order to see how the location and stability of equilibrium points changed when a parameter is altered. The main motivation is to achieve a more realistic study and thus, also ... (Complet abstract click electronic access below) / Mestre

Mars has an intriguing topographic and crustal dichotomy that divides the planet into a Northern Hemisphere and a Southern Hemisphere. The biggest question is to understand how this dichotomy was formed and what are the implications to the interior evolution of the planet. This study uses topography and gravity data obtained from the Mars Global Surveyor satellite observations in a crustal thickness program written by Mark Wieczorek. This program uses an algorithm that incorporates spherical harmonic coefficients of topography and gravity and calculates the Moho topography given a set of user-input parameters; it also generates crustal thickness maps. I modified the code to produce gravity misfit maps for interpretation of crustal and mantle structures. Experiments were performed to test various parameters in the program and observe their effects on the resulting crustal thickness. The algorithm assumes a uniform density for the crust and mantle. A crustal density of 2900 kg/m3 and a mantle density of 3500 kg/m3 were used to represent a basaltic crust and an olivine mantle, derived from petrologic studies of meteorites assumed to have originated from Mars. As the crustal density is held constant while varying the mantle density (and vice versa), it is the total density contrast that changes the crustal thickness; the larger the density contrast, the smaller the crustal thickness. Higher-order terms in the algorithm equation were also tested. Results show that the higher-order terms do not affect the overall crustal thickness by much thus are negligible. In modeling the crustal thickness, a minimum crustal thickness of 5 km was used to anchor the topography so that the resulting crust do not have negative or zero thickness. By using this minimum thickness, there is about 40 km thickness difference between the Northern Lowlands and the Southern Highlands. Crustal thickness and gravity misfit maps show a plume-like track from the South Pole to the Tharsis Rise region, consistent with the theory proposed by Zhong (2010) on a mantle plume track. A ring-like feature in the misfit maps resembles a regional-scale impact crater that may have created the Borealis Basin in the Northern Lowlands, also consistent with current hypotheses about the formation of the Northern Lowlands. A result of Airy isostacy (with only the linear terms in topography) is that the Moho topography will be related to the surface topography with a scale factor depending on the crust-mantle density contrast. Isostatic studies here reveal that Mars may be more or less isostatic at spherical harmonic degree-1 wavelength scale where as at spherical harmonic degree-2, an impact-like structure is revealed just east of the Tharsis Rise region, suggesting a possible impact. Due to the non-uniqueness of gravity, these models have a limited constraint on the crustal thickness and further studies involving a seismometer are needed to get a more precise look into Mars' interior. / Master of Science

Submitted by Tamires dos Santos de Moura null (tamiresmoura@hotmail.com) on 2016-08-26T16:55:16Z No. of bitstreams: 1 dissertacao.pdf: 3467990 bytes, checksum: 5dda701bb1d00619df06b7d38eef0bc1 (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-08-29T20:39:29Z (GMT) No. of bitstreams: 1 moura_ts_me_guara.pdf: 3467990 bytes, checksum: 5dda701bb1d00619df06b7d38eef0bc1 (MD5) / Made available in DSpace on 2016-08-29T20:39:29Z (GMT). No. of bitstreams: 1 moura_ts_me_guara.pdf: 3467990 bytes, checksum: 5dda701bb1d00619df06b7d38eef0bc1 (MD5) Previous issue date: 2016-07-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Tendo em vista que asteroides são objetos remanescentes dos primórdios do Sistema Solar, estamos interessados na composição deles. Existem missões que estão sendo analisadas com a finalidade de enviar sondas em direção a asteroides do grupo Near Earth Asteroids (NEAs), que representa uma das mais peculiares classes de objetos no Sistema Solar visto que suas órbitas podem se aproximar ou até mesmo cruzar a terrestre. Esse grupo é considerado representativo da população de asteroides, uma vez que podem fornecer informações sobre a mistura química a partir da qual os planetas teriam se formado a bilhões de anos atrás, possibilitando a compreensão da origem e evolução do Sistema Solar e quem sabe até a origem da vida na Terra. Dessa forma, um estudo detalhado a fim de compreender a superfície, a composição e a estrutura interna de um NEA será um grande passo para a Ciência. Nessa pesquisa, inicialmente reproduzimos os dados do potencial gravitacional pelo método dos poliedros para o asteroide 2063 Bacchus, um NEA, a fim de validar os resultados encontrados em Moura (2014). O método dos poliedros fornece uma precisão muito boa da forma irregular do corpo. Por meio de estudo dos modelos de potenciais gravitacionais para corpos não esféricos e implementação de rotinas computacionais foi realizada uma breve análise em relação ao formato do asteroide 2063 Bacchus, bem como das suas superfícies equipotenciais e curvas de velocidade zero. Os objetivos dessa dissertação são realizar um estudo detalhado a respeito dos pontos de equilíbrio no campo gravitacional de 2063 Bacchus, bem como da estabilidade desses pontos levando em consideração os autovalores da equação característica. Além disso, alteramos os valores do período de rotação e da densidade desse objeto a fim de verificar como a localização e a estabilidade dos pontos de equilíbrio alteram quando um parâmetro é mudado. A motivação principal é realizar um estudo o mais realista possível e, dessa forma, observar também como os pontos de equilíbrio se comportam quando introduzimos o efeito da força de pressão de radiação solar que, nesse caso, passam a ser chamados de pontos equivalentes. O trabalho possibilita ampliação do conhecimento não somente para o caso de asteroides, mas também para outros corpos não esféricos como cometas, contribuindo para o desenvolvimento de estudos direcionados a origem e evolução do Sistema Solar. / Given that asteroids are remnant objects of the Solar system beginnings, we are interested in their composition. There are missions that are being analyzed with the purpose of sending probes toward asteroids from the group Near Earth Asteroids (NEAs), which is one of the most peculiar classes of objects in the solar system because their orbits can approach or even cross the Earth’s orbit. This group is considered representative of the population of asteroids, since they can provide information about the chemical mixture from which the planets would have been formed billions of years ago, enabling the understanding of the origin and evolution of the Solar System and maybe even on the origin of life on Earth. Thus a detailed study in order to understand the surface, the composition and internal structure of a NEA will be a big step for Science. In this research, initially we reproduce the data of the gravitational potential by the method of polyhedra for asteroid 2063 Bacchus, a NEA, in order to validate the results found Moura (2014). The method of polyhedra provides a very good accuracy of the irregular shape of the body. Through study of gravitational potential designs for non-spherical bodies and computational routines implementing a brief analysis was performed with respect to the asteroid shape of 2063 Bacchus, as well as its equipotential surfaces and zero-velocity curves. The objectives of this work are to conduct a detailed study on the equilibrium points in the gravitational field of 2063 Bacchus, and the stability of these points taking into account the eigenvalues of the characteristic equation. In addition, we varied the values of the rotation period and density of the object in order to see how the location and stability of equilibrium points changed when a parameter is altered. The main motivation is to achieve a more realistic study and thus, also observe how the equilibrium points behave when we introduce the effect of solar radiation pressure force. The new points are called equivalent points. The work enables expansion of the knowledge, not only in the case of asteroids, but also to other non-spherical bodies like comets, contributing to the development of studies addressing the origin and evolution of the solar system.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Neste trabalho vamos investigar quais as modificaÃÃes que o potencial gravitacional com termo de Chern-Simons sofre com a adiÃÃo da teoria nÃo-comutativa no espaÃo-tempo. Faremos isto em dois casos: o primeiro utilizando somente a teoria de Einstein-Hilbert e no segundo caso acrescentando o termo de gravidade topolÃgica tipo Chern-Simons. As modificaÃÃes que estamos investigando ocorrem em um espalhamento de dois bÃsons vetoriais trocando um grÃviton. Atà podermos chegar a uma conclusÃo de como a nÃo comutatividade altera o potencial gravitacional, iremos iniciar nosso estudo com um modelo de gravidade em baixas dimensÃes. ApÃs apreender como calcular o propagador do grÃviton para teoria quadrÃticas da gravidade, expandimos os conceitos para uma gravidade topologicamente massiva. Revisaremos tÃpicos importantes da teoria nÃo-comutativa no espaÃo-tempo. Por fim analisando a interaÃÃo com campo do grÃviton com matÃria escreveremos o vÃrtice da teoria e encontraremos as modificaÃÃes oriundas da nÃo comutatividade dos dois casos citados acima. Verificamos que a nÃo-comutatividade altera a forma do potencial gravitacional tanto na origem, deixando-o bem comportado, quanto no infinito. / In this paper we investigate what changes the gravitational potential with Chern-Simons term suffers from the addition of the noncommutative theory in space-time. We do this in two cases: the first using only the theory of Einstein-Hilbert and in the second case, adding the term topological Chern-Simons gravity type. The changes that occur are investigating on a scattering of two vector bosons exchanging a graviton. Until we reach a conclusion as the noncommutativity changes the gravitational potential, we will begin our study with a gravity model in low dimensions. After learning how to calculate the graviton propagator for quadratic theory of gravity, we expanded the concepts for a topologically massive gravity. We will review important topics of noncommutative theory in space-time. Finally analyzing the interaction with the graviton field with matter, write the vertex of the theory and find the changes arising from the noncommutativity of the two cases cited above. We found that the noncommutativity alters the shape of the gravitational potential both in origin, leaving him well behaved, as at infinity.

<p>Globular clusters have linear sizes (tidal radii) which are theoretically de- termined by their mass and by the gravitational potential of their host galaxy. However observationally, cluster sizes are simply a determination of where the cluster’s surface brightness profile becomes zero. This distance is also known as the limiting radius. While it is commonly assumed that the tidal radius and the limiting radius of a globular cluster are the same thing, it has yet to be validated. The purpose of this thesis is to explore the assumption that cluster tidal radii and limiting radii are equal by comparing the tidal radii of an observed and simulated globular cluster population.</p> <p>An established link between cluster tidal radii and limiting radii will yield new methods of utilizing globular clusters as tools for studying galaxies. If cluster sizes are truly imposed by the tidal field of the host galaxy, then tidal radii measurements can be used to trace the mass distribution within a galaxy, including the dark matter halo. Additionally, as we will demonstrate in this thesis, cluster sizes can also be used a tracer for the orbital anisotropy profile of a galaxy.</p> <p>To explore the assumption that tidal radii and limiting radii are equal, we utilize the globular cluster population of the Virgo giant M87. Unusually deep, high signal-to-noise images of M87 are used to determine the radius for approximately 2000 globular clusters. To compare with these observations, we simulate a globular cluster population that has the same characteristics to the observed M87 cluster population. These characteristics include cluster radial distribution, mass distribution, central concentration distribution and line of sight velocity dispersion. Placing these simulated clusters in the well-studied tidal field of M87, the orbit of each cluster is solved and the theoretical tidal radius of each cluster is determined. We compare the predicted relationship between cluster size and projected galactocentric distance found in our sim- ulation to observations in order to test whether a cluster’s tidal radius and limiting radius are equal. We find that for an isotropic distribution of cluster velocities, theoretical tidal radii are approximately equal to observed limiting radii. The simulation predicts the observed increase in cluster size with galac- tocentric distance, which is expected if tidal radii are dependent on the tidal field. Additionally, simulated cluster sizes are of the same order of magnitude as observed cluster sizes. However the simulation does underestimate cluster sizes in the inner regions of M87. To minimize the discrepancy between theory and observations, we further explore the effects of orbital anisotropy on cluster sizes, and suggest a possible orbital anisotropy profile for M87 which yields the best fit between theory and observations. Finally, we suggest multiple future studies which will aid in our understanding of tidal theory and in establishing a stronger link between tidal radii and limiting radii.</p> / Master of Science (MSc)

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-07T19:46:54Z No. of bitstreams: 1 sebastiaomaurofilho.pdf: 422464 bytes, checksum: 2d72827356c924e509ef415cf17ff6bc (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-06-26T17:47:29Z (GMT) No. of bitstreams: 1 sebastiaomaurofilho.pdf: 422464 bytes, checksum: 2d72827356c924e509ef415cf17ff6bc (MD5) / Made available in DSpace on 2017-06-26T17:47:29Z (GMT). No. of bitstreams: 1 sebastiaomaurofilho.pdf: 422464 bytes, checksum: 2d72827356c924e509ef415cf17ff6bc (MD5) Previous issue date: 2012-02-29 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Recentemente foi demonstrado [17] que correções quânticas para o potencial gravitacional de Newton explica as curvas de rotação em galáxias espirais sem introduzir o halo de matéria escura. O único parâmetro fenomenológico aѵ da teoria cresce com a massa da galáxia. A fim de melhor investigar a dependência de aѵ com a massa é preciso verificar o limite superior para aѵ em uma escala menor. Aqui nós realizamos o cálculo correspondente por meio da análise da dinâmica do vetor de Laplace-Runge-Lenz e da condição de equilíbrio de anãs-brancas. A limitação resultante sobre correções quânticas sugerem uma dependência de aѵ com a massa. / Recently it was shown that quantum corrections to the Newton potential can explain the rotation curves in spiral galaxies without introducing the Dark Matter halo. The unique phenomenological parameter aѵ of the theory grows with the mass of the galaxy. In order to better investigate the mass-dependence of aѵ one needs to check the upper bound for aѵ at a smaller scale. Here we perform the corresponding calculation by analyzing the dynamics of the Laplace-Runge-Lenz vector and the equilibrium condition of white-dwarf. The resulting limitation on quantum corrections is suggesting a mass-dependence of aѵ.

Cette thèse traite de la compensation magnétique de pesanteur. Tout d’abord, des expériences de lévitation magnétique de fluides sont interprétées à l’aide d’un potentiel magnéto-gravitationnel SL. Puis, l’utilisation d’une méthode générale d’analyse de la force magnétique grâce aux harmoniques du champ magnétique est développée. Elle souligne l’importance et le rôle de chacun des trois premiers harmoniques du champ magnétique sur les configurations de forces résultantes inhérentes à la compensation magnétique de pesanteur. En géométrie cylindrique (invariante par translation) diverses combinaisons de forces d’origines magnétique, gravitationnelle et centrifuge offrent des perspectives nouvelles pour la lévitation magnétique. Une combinaison judicieuse des forces magnétiques et centrifuges permet de compenser exactement la pesanteur sur des matériaux diamagnétiques. En géométrie axisymétrique (invariante par rotation), le dimensionnement de stations de lévitation d’oxygène, techniquement réalisables (NbTi@4,2K), est présenté. Ces stations permettent de léviter des volumes d’oxygène supérieurs à 1 litre avec des inhomogénéités inférieures à 1%. La constitution de ces stations rend possible les variations spatiales et temporelles des configurations d’accélérations résultantes. Enfin, la compensation magnétique dynamique de gravité, à l’aide d’une station de lévitation réelle, est étudiée afin de simuler des phases d’accélération ou de décélération d’engins spatiaux / The thesis deals with magnetic gravity compensation. First of all magnetic levitation experiments are explained with the help of a magneto-gravitational potential SL. Next, a general analysis method of the magnetic force is developed which employs magnetic field harmonics. The method underlines both the significance and role of the first three magnetic field harmonics on the resulting forces inherent in magnetic gravity compensation. In cylindrical geometry – with translational invariance – various combination of magnetic, gravitational and centrifugal forces open new possibilities for the magnetic levitation. A suitable combination of both magnetic and centrifugal forces allows exactly compensating gravity on diamagnetic materials. In axisymmetric geometry – with rotational invariance – designs of feasible oxygen magnetic levitation stations are introduced (NbTi@4,2K). Levitation of oxygen volumes more than one litre with inhomogeneities less than 1% can be accomplished within these magnetic levitation facilities. The constitution of the stations makes possible both spatial and temporal variations of the resulting acceleration configurations. At last the dynamic magnetic compensation of gravity with a real coil system is studied so as to simulate both acceleration and deceleration of spaceships

The Vlasov-Poisson system is most commonly used to model the movement of charged particles in a plasma or of stars in a galaxy. It consists of a kinetic equation known as the Vlasov equation coupled with a force determined by the Poisson equation. The system in Euclidean space is well-known and has been extensively studied under various assumptions. In this paper, we derive the Vlasov-Poisson equations assuming the particles exist only on the 2-sphere, then take an in-depth look at particles which initially lie along a great circle of the sphere. We show that any great circle is an invariant set of the equations of motion and prove that the total energy, number of particles, and entropy of the system are conserved for circular initial distributions. / Graduate