Much effort in recent times has been devoted to the study of low energy transport in multibody gravitational systems. Despite continuing advancements in computational abilities, such studies can often be demanding or time consuming in the three-body and four-body settings. In this work, the Hamiltonian describing the planar circular restricted three-body problem is rewritten for systems having small mass parameters, resulting in a 2D symplectic twist map describing the evolution of a particle's Keplerian motion following successive close approaches with the secondary. This map, like the true dynamics, admits resonances and other invariant structures in its phase space to be analyzed. Particularly, the map contains rotational invariant circles reminiscent of McGehee's invariant tori blocking transport in the true phase space, adding a new quantitative description to existing chaotic zone estimates about the secondary. Used in a patched three-body setting, the map also serves as a tool for investigating transfer trajectories connecting loose captures about one secondary to the other without any propulsion systems. Any identified initial conditions resulting in such a transfer could then serve as initial guesses to be iterated upon in the continuous system. In this work, the projection of the McGehee torus within the interior realm is identified and quantified, and a transfer from Earth to Venus is exemplified. / Master of Science / The transport of a particle between celestial bodies, such as planets and moons, is an important phenomenon in astrodynamics. There are multiple ways to mediate this objective; commonly, the motion can be influenced directly via propulsion systems or, more exotically, by utilizing the passive dynamics admitted by the system (such as gravitational assists). Gravitational assists are traditionally modelled using two-body dynamics. That is, a space- craft or particle performs a flyby within that body's sphere of influence where momentum is exchanged in the process. Doing so provides accurate and reliable results, but the design space effecting the desired outcome is limited when considering the space of all possibilities. Utilizing three-body dynamics, however, provides a significant improvement in the fidelity and variety of trajectories over the two-body approach, and thus a broader space through which to search. Through a series of approximations from the three-body problem, a discrete map describing the evolution of nearly Keplerian orbits through successive close encounters with the body is formed. These encounters occur outside of the body's sphere of influence and are thus uniquely formed from three-body dynamics. The map enables computation of a trajectory's fate (in terms of transit) over numerical integration and also provides a boundary for which transit is no longer possible. Both of these features are explored to develop an algorithm able to rapidly supply guesses of initial conditions for a transfer in higher fidelity models and further develop the existing literature on the chaotic zone surrounding the body.

Orientadores: Alberto Vazquez Saa, Marcus Aloizio Martinez de Aguiar / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-27T13:28:54Z (GMT). No. of bitstreams: 1 Vieira_RonaldoSavioliSume_D.pdf: 9121576 bytes, checksum: eab8bcedfd86d048afd51f4b65fe9501 (MD5) Previous issue date: 2015 / Resumo: Neste trabalho analisamos aspectos dinâmicos de sistemas astrofísicos que possuem uma componente discoidal proeminente. Estudamos o movimento de partículas de teste (estrelas) que cruzam discos galácticos bidimensionais e axialmente simétricos, obtendo uma fórmula para o envelope das órbitas que depende somente da densidade superficial $\Sigma$ do disco. Essa fórmula nos dá uma terceira integral de movimento aproximada para o sistema. Também analisamos a estabilidade das órbitas circulares equatoriais nesses discos, chegando à condição de estabilidade vertical $\Sigma>0$. Esse formalismo é estendido para discos tridimensionais, assim como para a relatividade geral (em que obtivemos que a \textit{condição de energia forte} é suficiente para a estabilidade vertical das órbitas circulares em discos infinitesimais, no caso estático e axialmente simétrico). Trabalhamos também com a aproximação pós-newtoniana (1PN), obtendo o formalismo hamiltoniano para uma distribuição arbitrária de matéria, assim como as correções 1PN nas frequências epicíclicas radial e vertical para configurações estacionárias e axialmente simétricas e a terceira integral de movimento aproximada para discos infinitesimais (estacionários). Outro resultado obtido foi a dependência das frequências epicíclicas com a curvatura riemanniana do espaço-tempo para distribuições suaves de matéria-energia, no caso estático e axialmente simétrico em relatividade geral. A segunda parte desta tese corresponde aos resultados para discos de acreção. Analisamos o movimento de partículas de teste na métrica de Kehagias & Sfetsos (solução esfericamente simétrica da gravitação de Horava no caso em que o espaço-tempo é assintoticamente plano), na região de parâmetros em que a singularidade central é nua. Por fim, estudamos a espessura dos discos de acreção super-Eddington obtida por simulações globais recentes de radiation magnetohydrodynamics em relatividade geral. O resultado foi comparado com modelos de discos slim para taxas de acreção similares, levando à conclusão de que o estado final (estacionário) dos fluxos de acreção gerados por essas simulações é um disco slim, e não um disco espesso, como seria esperado pelas características das configurações iniciais do tipo Polish Doughnuts usualmente adotadas / Abstract: In this work, we analyze dynamical aspects of astrophysical systems containing a prominent discoidal component. We study the motion of test particles (stars) which cross bidimensional, axially symmetric galactic disks, obtaining a formula for the orbits' envelope which depends solely on the disk's surface density. This formula gives us an approximate third integral of motion for the system. We also analyze the stability of equatorial circular orbits in these disks, arriving at the vertical stability condition $\Sigma>0$. This formalism is extended to three-dimensional disks, as well as to general relativity (in which we obtained that the \textit{strong energy condition} is sufficient for vertical stability of circular orbits in infinitesimal disks, in the static and axially symmetric case). We also worked with the post-Newtonian approximation (1PN), obtaining the Hamiltonian formalism for an arbitrary matter distribution, as well as the 1PN corrections to the radial and vertical epicyclic frequencies for stationary and axially symmetric configurations, and the approximated third integral of motion for (stationary) infinitesimal disks. Another result obtained was the dependence of the epicyclic frequencies on the Riemannian spacetime curvature for smooth matter-energy distributions, in the static and axially symmetric case. The second part of this thesis corresponds to the results concerning accretion disks. We analyzed the motion of test particles in the Kehagias & Sfetsos metric (spherically symmetric solution to Horava's gravity in the case in which the spacetime is asymptotically flat), in the parameter region in which the singularity is naked. Finally, we studied the thickness of super-Eddington accretion disks, obtained via recent global radiation magnetohydrodynamics simulations in general relativity. The result was compared with slim-disk models for similar accretion rates, leading to the conclusion that the final (stationary) state of accretion flows generated by these simulations is a slim disk, and not a thick disk, as it would be expected by the characteristics of the usually adopted Polish Doughnuts initial configurations / Doutorado / Física / Doutor em Ciências

Estudo das ressonâncias de três corpos na zona habitável (ZH), da estrela GJ 581 (Gliese 581), envolvendo dois planetas conhecidos e um terceiro planeta dentro da ZH. Séries de Lie são usadas para obter o Hamiltoniano médio (de segunda ordem nas massas) e teoria de Chirikov é usada para gerar um novo sistema de varáveis canônicas em que os momentos se orientam ao longo e através da ressonância. Um mapa de Hadjidemetriou é construido e permite o cálculo rápido da difusão das órbitas em uma extensa grade de condições iniciais. / Study of three-body resonances in the habitable zone (ZH), the star GJ 581 (Gliese 581), involving two known planets, and a third planet in the ZH. Lie series are used to obtain the average Hamiltonian (the second-order mass) and Chirikov theory is used to generate a new canonical variables system in which the moments are oriented along and across the resonance. A map of Hadjidemetriou is constructed and allows rapid calculation of the diffusion of orbits in an extensive grid of initial conditions.

Estudo das ressonâncias de três corpos na zona habitável (ZH), da estrela GJ 581 (Gliese 581), envolvendo dois planetas conhecidos e um terceiro planeta dentro da ZH. Séries de Lie são usadas para obter o Hamiltoniano médio (de segunda ordem nas massas) e teoria de Chirikov é usada para gerar um novo sistema de varáveis canônicas em que os momentos se orientam ao longo e através da ressonância. Um mapa de Hadjidemetriou é construido e permite o cálculo rápido da difusão das órbitas em uma extensa grade de condições iniciais. / Study of three-body resonances in the habitable zone (ZH), the star GJ 581 (Gliese 581), involving two known planets, and a third planet in the ZH. Lie series are used to obtain the average Hamiltonian (the second-order mass) and Chirikov theory is used to generate a new canonical variables system in which the moments are oriented along and across the resonance. A map of Hadjidemetriou is constructed and allows rapid calculation of the diffusion of orbits in an extensive grid of initial conditions.