Current orbital solutions for 99942 Apophis predict a close approach to the Earth in April 2029. The parameters of that approach affect the future trajectory of Apophis, potentially leading to an impact in 2036, 2056, 2068, etc. The dynamic model used for this prediction does not account for non-gravitational perturbations including solar pressure and the Yarkovsky effect. Estimates of the displacement due to these perturbations range from -1500 to 1500km by 2029, comparable to 7? uncertainty in orbital solution. Uncertainties in physical characteristics stem from a lack of direct observations and a shortage of empirical data on similar objects. These perturbations, which stem from interactions with solar radiation, are directly related to the albedo of Apophis? surface. By modifying the average albedo of Apophis by 0.5%, between 4 and 15m of displacement can be effected between 2023 and 2029, rendering this method capable of avoiding all near-nominal solution keyholes. This modification is obtained by the deposition of electrostatically charged particles. These particles are charged via tribo-electrification and cure on the surface of Apophis creating a 30 micron thick layer of material with desired properties. This study found that a change in average albedo would nominally require 160kg of polytetrafluoroethylene (PTFE) to increase by 0.5% or 290kg of PTFE to decrease by 0.5%. The Apophis Exploration and Mitigation mission concept both improves accuracy of nongravitational perturbation models and delivers the albedo modification mechanism to Apophis, launching in 2021 and modifying albedo in 2023.

The development of the Surface Albedo Treatment System (SATS) onboard a spacecraft mission to the near earth asteroid (NEA) Apophis in 2012 is an innovative concept of deflecting NEAs from possible impact with the Earth through altering the Yarkovsky effect, a non-secular force in the solar system due to uneven surface thermal emission most profoundly affecting small rotating bodies subjected to sunlight. Though this force is small, its magnitude can be dramatic if extended over a period of time and if it uses the close approach of an asteroid near Earth to magnify the perturbation. The payload dispenses colored powder called albedo changing particles (ACPs) onto the surface changing its albedo and indirectly the surface temperature which changes the Yarkovsky effect. This study gives an in-depth description of both computational and experimental parts of the design of this system with primary focus on initial ground test setup. The initial experiments proposed to design the SATS is outlined in detail and justified by the mission criterion of interest as well as modeling the actual dispersal on the surface.

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Nesta tese estudamos algumas regiões de aparente estabilidade no cinturão de asteróides e no cinturão de Kuiper, analisando a evoluçãao dinâmica dos objetos nessas regiões por intervalos de tempo muito longos, em geral, da ordem da idade do Sistema Solar. Centramos principalmente nossa atenção no estudo das populações de pequenos corpos ressonantes, analisando três exemplos diferentes: a ressonância 2/1 com Júpiter e seu entorno (falha de Hecuba), a ressonância 2/3 com Netuno (Plutinos), e a ressonância 1/1 com Júpiter (Troianos). Atacamos o problema com diferentes ferramentas numéricas e analíticas: integração numérica direta de modelos precisos, modelos estatísticos de caminhada aleatória, modelos semi-analíticos baseados no desenvolvimento assimétrico da função perturbadora, cálculo de expoentes de Lyapunov, análise de freqüências, determinação de elementos próprios e taxas de difusão, etc. Os resultados obtidos permitem elaborar conclusões sobre a possível origem e evolução dinâmica destas populações. / In this thesis, we study some regions of regular motion in the asteroid main belt and in the Kuiper belt. We analyze the dynamical evolution in these regions over time scales of the order of the age of the Solar System. We centered our study on the populations of resonant minor bodies, discussing three examples: the 2/1 mean motion resonance with Jupiter (Hecuba gap), the 2/3 resonance with Neptune (Plutinos), and the 1/1 resonance with Jupiter (Trojans). We attack the problem with several different tools, both analytic and numeric: integration of N-body models, random-walk statistical models, semi-analytical models based on the assymetric expansion of the disturbing function, calculation of the maximum Lyapunov exponent, frequancy analysis, estimates of the diffusion of proper elements, etc. The results allow to draw conclusions about the possible origin of these populations.

Nesta tese estudamos algumas regiões de aparente estabilidade no cinturão de asteróides e no cinturão de Kuiper, analisando a evoluçãao dinâmica dos objetos nessas regiões por intervalos de tempo muito longos, em geral, da ordem da idade do Sistema Solar. Centramos principalmente nossa atenção no estudo das populações de pequenos corpos ressonantes, analisando três exemplos diferentes: a ressonância 2/1 com Júpiter e seu entorno (falha de Hecuba), a ressonância 2/3 com Netuno (Plutinos), e a ressonância 1/1 com Júpiter (Troianos). Atacamos o problema com diferentes ferramentas numéricas e analíticas: integração numérica direta de modelos precisos, modelos estatísticos de caminhada aleatória, modelos semi-analíticos baseados no desenvolvimento assimétrico da função perturbadora, cálculo de expoentes de Lyapunov, análise de freqüências, determinação de elementos próprios e taxas de difusão, etc. Os resultados obtidos permitem elaborar conclusões sobre a possível origem e evolução dinâmica destas populações. / In this thesis, we study some regions of regular motion in the asteroid main belt and in the Kuiper belt. We analyze the dynamical evolution in these regions over time scales of the order of the age of the Solar System. We centered our study on the populations of resonant minor bodies, discussing three examples: the 2/1 mean motion resonance with Jupiter (Hecuba gap), the 2/3 resonance with Neptune (Plutinos), and the 1/1 resonance with Jupiter (Trojans). We attack the problem with several different tools, both analytic and numeric: integration of N-body models, random-walk statistical models, semi-analytical models based on the assymetric expansion of the disturbing function, calculation of the maximum Lyapunov exponent, frequancy analysis, estimates of the diffusion of proper elements, etc. The results allow to draw conclusions about the possible origin of these populations.