Dinâmica do sistema binário Plutão-Caronte

Pós-graduação em Física - FEG

Habitabilidade em exoplanetas do tipo terrestre

A astrobiologia, ciência que estuda a origem, evolução, distribuição e futuro da vida, tem como escopo a procura por vida em outros ambientes, como por exemplo, exoplanetas, planetas estes localizados fora do sistema solar. Através de observações e modelos teóricos que estimam alguns parâmetros gerais (composição, tipos de compostos presentes) pode-se criar um ambiente possível para o exoplaneta. O ambiente em que o planeta está inserido é um fator que pode ser determinante em relação a sua habitabilidade. A Zona Habitável é um dos parâmetros passíveis de delimitar os planetas que poderiam ser habitáveis. Muitos planetas identificados até agora têm características similares à da Terra. Entretanto, a maioria dos planetas, com possibilidade de ser do tipo terrestre, identificados até hoje são considerados Super Terras Quentes (STQ), pois estão fora da zona habitável uma vez que estão muito próximos de suas estrelas (período orbital da ordem de dias ou menos). Alguns desses estariam presentes na Zona habitável de suas respectivas estrelas, como é o caso de Gl 581 g, um planeta do sistema multi-planetário da estrela Gl 581. A proximidade da estrela sugere que eles apresentam uma rotação afetada por forças de maré. Deste modo, a taxa rotacional do planeta é sincronizada, sendo que uma de suas faces não recebe a energia da estrela, tornando-se gelada e a outra face recebe constantemente a energia da estrela, tornando-se muito quente. Embora em geral descarta-se a habitabilidade em STQ, estudos de resistência de vida em ambientes extremos não são muito explorados. As características analisadas partirão da premissa que o tipo de vida procurada será semelhante ao tipo de vida que encontramos na Terra, isto é, utilizando a água como solvente e apresentando uma química baseada no elemento carbono (Kaltenegger, L. et al., 2008)... (Resumo completo, clicar acesso eletrônico abaixo)

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)

Sobre a dinâmica de rotação de um planeta através de um sistema médio

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Captura gravitacional de pequenos corpos por arrasto em um gás modelado usando equações hidrodinâmicas

In this work we have developed an apparatus in order to study the capture of asteroids by planets surrounded by a gas envelope during y-by, to do this we have brought an innovation by using a hydrodynamical gas. We began such project by studying particles trajectories with a code based on the analytical gas. After being used to this model we have started a process to elaborate a code which uses the gas in a numerical way. The hydrodynamical gas is described by equations which are not solved analytically. Therefore, it was used an algorithm able to model the gas by keeping all information of the gas in cells. Thus we have made a code to read such cell`s information and then to solve all calculations. Once this process is done, the program inform us all date about the simulated trajectories

Estudos de estabilidade no sistema Ʋ andromedae A

Pós-graduação em Física - FEG

Dinâmica secular rotacional de corpos tri-axiais: expansão de V em ressonâncias de primeira ordem

Consider a finite body of mass m (C1) with moments of inertia A, B and C. This body orbits another one of mass much larger M (C2), which at first will be taken as a point, even if it is not completely spherical. The body C1, when orbit C2, performs a translational motion near a Keplerian. It will not be a Keplerian due to external disturbances. We will use two axes systems: fixed in the center of mass of C1 and other inertial. The C1 attitude, that is, the dynamic rotation of this body is know if we know how to situate mobile system according to inertial axes system. The strong influence exerted by C2 on C1, which is a flattened body, generates torques on C1, what affects its dynamics of rotation. We will obtain the mathematical formulation of this problem assuming C1 as a planet and C2 as the sun. Also applies to case of satellite and planet. In the case of Mercury-Sun system, the disturbing potential that governs rotation dynamics, for theoretical studies, necessarily have to be developed by powers of the eccentricity. As is known, such expansions are delicate because of the convergence issue. Thus, we intend to make a development until the third order (superior orders are not always achievable because of the volume of terms generated in cases of first-order resonances). By defining a modern set of canonical variables (Andoyer), we will assemble a disturbed Hamiltonian problem. The Andoyer's Variables allow to define averages, which enable us to discard short-term effects. Our results for the resonant angle variation of Mercury are in full agreement with those obtained by D'Hoedt & Lemaître (2004) and Rambaux & Bois (2004)

Estudos de acoplamento spin-órbita em dinâmica do sistema solar

Pós-graduação em Física - FEG

Ressonâncias planetárias spin-órbita com perturbação de terceiro corpo

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamics of the 3:1 resonant planetary systems

Many of the discovered exoplanetary systems are involved inside mean-motion resonances. In this work we focus on the dynamics of the 3:1 mean-motion resonant planetary systems. Our main purpose is to understand the dynamics in the vicinity of the apsidal corotation resonance (ACR) which are stationary solutions of the resonant problem. We apply the semi-analytical method (Michtchenko et al., 2006) to construct the averaged three-body Hamiltonian of a planetary system near a 3:1 resonance. Then we obtain the families of ACR, composed of symmetric and asymmetric solutions. Using the symmetric stable solutions we observe the law of structures (Ferraz-Mello,1988), for different mass ratio of the planets. We also study the evolution of the frequencies of σ1, resonant angle, and Δω, the secular angle. The resonant domains outside the immediate vicinity of ACR are studied using dynamical maps techniques. We compared the results obtained to planetary systems near a 3:1 MMR, namely 55 Cnc b-c, HD 60532 b-c and Kepler 20 b-c.

Figures of equilibrium for tidally deformed non-homogeneous celestial bodies

Abstract (2,250 Maximum Characters): Several theories of tidal evolution, since the theory developed by Darwin in the XIX century, are based on the figure of equilibrium of the tidally deformed body. Frequently the adopted figure is a Jeans prolate spheroid. In some case, however, the rotation is important and Roche ellipsoids are used. The main limitations of these models are (a) they refer to homogeneous bodies; (b) the rotation axis is perpendicular to the plane of the orbit. This communication aims at presenting several results in which these hypotheses are not done. In what concerns the non-homogeneity, the presented results concerns initially bodies formed by N homogeneous layers and we study the non sphericity of each layer and relate them to the density distribution. The result is similar to the Clairaut figure of equilibrium, often used in planetary sciences, but taking into full account the tidal deformation. The case of the rotation axis non perpendicular to the orbital plane is much more complex and the study has been restricted for the moment to the case of homogeneous bodies.

Records of migration in the exoplanet configurations

When compared to our Solar System, many exoplanet systems exhibit quite unusual planet configurations; some of these are hot Jupiters, which orbit their central stars with periods of a few days, others are resonant systems composed of two or more planets with commensurable orbital periods. It has been suggested that these configurations can be the result of a migration processes originated by tidal interactions of the planets with disks and central stars. The process known as planet migration occurs due to dissipative forces which affect the planetary semi-major axes and cause the planets to move towards to, or away from, the central star. In this talk, we present possible signatures of planet migration in the distribution of the hot Jupiters and resonant exoplanet pairs. For this task, we develop a semi-analytical model to describe the evolution of the migrating planetary pair, based on the fundamental concepts of conservative and dissipative dynamics of the three-body problem. Our approach is based on an analysis of the energy and the orbital angular momentum exchange between the two-planet system and an external medium; thus no specific kind of dissipative forces needs to be invoked. We show that, under assumption that dissipation is weak and slow, the evolutionary routes of the migrating planets are traced by the stationary solutions of the conservative problem (Birkhoff, Dynamical systems, 1966). The ultimate convergence and the evolution of the system along one of these modes of motion are determined uniquely by the condition that the dissipation rate is sufficiently smaller than the roper frequencies of the system. We show that it is possible to reassemble the starting configurations and migration history of the systems on the basis of their final states, and consequently to constrain the parameters of the physical processes involved.

Stability and dynamics of terrestrial planets in binary star systems: application on Alpha Centauri

Binary stars are frequent in the universe, with about 50% of the known main sequence stars being located at a multiple star system (Abt, 1979). Even though, they are universally thought as second rate sites for the location of exo-planets and the habitable zone, due to the difficulties of detection and high perturbation that could prevent planet formation and long term stability. In this work we show that planets in binary star systems can have regular orbits and remain on the habitable zone. We introduce a stability criterium based on the solution of the restricted three body problem and apply it to describe the short period planar and three-dimentional stability zones of S-type orbits around each star of the Alpha Centauri system. We develop as well a semi-analytical secular model to study the long term dynamics of fictional planets in the habitable zone of those stars and we verify that planets on the habitable zone would be in regular orbits with any eccentricity and with inclination to the binary orbital plane up until 35 degrees. We show as well that the short period oscillations on the semi-major axis is 100 times greater than the Earth's, but at all the time the planet would still be found inside the Habitable zone.

Determination of dynamical and physical parameters of the system CoRoT 3

The two main tools to determine the dynamical and physical parameters of exoplanet systems are the radial velocity (RV) measurements and, when available, transit timings. The two techniques are complementary: The RV's allow us to know some of the orbital elements while the transit timings allow us to obtain the orbital inclination and planetary radius, impossible of obtain from the RV, and to resolve the indetermination in the determination of the planet mass from the RV's. The space observation of transiting planets is however not limited to transit times. They extend to long periods of time and are precise enough to provide information on variations along the orbit. Besides the effects of stellar rotation, deserve mention the Doppler shift in the radiation flux, as consequence of stellar movement around the center of mass, or Beaming Effect (BE); the Ellipsoidal Variability (EV) due to the tidal deformation of the star due to the gravitation of its close companion; and the Reflection (ER) of the stellar radiation incident on the planet and re-emitted to the observer. In the case of large hot Jupiters, these effects are enhanced by the strong gravitational interaction and the analysis of the light variation allows us independent estimates of the mass and radius of planet. The planetary system CoRoT 3 is favorable for such analysis. In this case, the secondary is a brown dwarf whose mass is of the order of 22Mj. We show results obtained from the analysis of 35 RV measurements, 236999 photometric observations and 11 additional RV observations made during a transit to determine the star rotation via the Rossiter-McLaughlin effect. The results obtained from this determination are presented in this communication. The results are compared to those resulting from other determinations.

Tidal evolution in co-orbital configurations

We study the orbital evolution of a two co-orbital planet system which undergo tidal interactions with the central star. Our main goal is to investigate the final outcome of a system originally evolving in a 1:1 resonant configuration when the tidal effect acts to change the orbital elements. Preliminary results of the numerical simulations of the exact equations of motions indicate that, at least for equal mass planets, the combined effect of resonant motion and tidal interaction leads the system to orbital instability, including collisions between the planets. We discuss the cases of two hot super-Earths and two hot-Saturn planets, comparing with the results of dynamical maps.