Co-orbital satellites of Saturn: congenital formation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Friction factors, convective heat transfer coefficients and the Colburn analogy for industrial sugarcane juices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effect of Jupiter's mass growth on satellite capture

We study the effects of Jupiter mass growth in order to permanently capture prograde satellites. Adopting the restricted three-body problem, Sun-Jupiter-Particle, we performed numerical simulations backward in time while considering the decrease in Jupiter's mass. We considered the particle's initial conditions to be prograde, at pericenter, in the region 100R(4) <= a <= 400R(4) and 0 <= e <= 0.5. The results give Jupiter's mass at the moment when the particle escapes from the planet. Such values give an indication of the conditions that are necessary for capture. An analysis of these results shows that prograde satellite capture is more complex than a retrograde one. It occurs in a two-step process. First, when the particles get inside about 0.85R(Hill) (Hills' radius), they become weakly bound to Jupiter. Then, they keep migrating toward the planet with a strong decrease in eccentricity, while the planet is growing. The radial oscillation of the particles reduces significantly when they reach a radial distance that is less than about 0.45R(Hill) from the planet. Three-dimensional simulations for the known prograde satellites of Jupiter were performed. The results indicate that Leda, Himalia, Lysithea, and Elara could have been permanently captured when Jupiter had between 50% and 60% of its present mass.

Possible effects of secular resonances in Phobos and Triton

Due to the tides, the orbits of Phobos and Triton are contracting. While their semi major axes are decreasing, several possibilities of secular resonances involving node, argument of the pericenter and mean motion of the Sun will take place. In the case of Mars, if the obliquity (epsilon), during the passage through some resonances, is not so small, very significant variations of the inclination will appear. In one case, capture is almost certain provided that epsilon greater than or equal to 20degrees. For Triton there are also similar situations, but capture seems to be not possible, mainly because in S-1 state, Triton's orbit is sufficiently inclined (far) with respect to the Neptune's equator. Following Chyba et al. (Astron. Astrophys. 219 (1989) 123), a simplified equation that gives the evolution of the inclination versus the semi major axis, is derived. The time needed for Triton crash onto Neptune is longer than that one obtained by these authors, but the main difference is due to the new data used here. In general, even in the case of non-capture passages, some significant jumps in inclination and in eccentricities are possible. (C) 2002 Elsevier B.V. Ltd. All rights reserved.

The effect of Jupiter's mass growth on satellite capture - Retrograde case

Gravitational capture can be used to explain the existence of the irregular satellites of giants planets. However, it is only the first step since the gravitational capture is temporary. Therefore, some kind of non-conservative effect is necessary to to turn the temporary capture into a permanent one. In the present work we study the effects of Jupiter mass growth for the permanent capture of retrograde satellites. An analysis of the zero velocity curves at the Lagrangian point L-1 indicates that mass accretion provides an increase of the confinement region ( delimited by the zero velocity curve, where particles cannot escape from the planet) favoring permanent captures. Adopting the restricted three-body problem, Sun-Jupiter-Particle, we performed numerical simulations backward in time considering the decrease of M-4. We considered initial conditions of the particles to be retrograde, at pericenter, in the region 100 R-4 less than or equal to a less than or equal to 400 R-4 and 0 less than or equal to e < 0.5. The results give Jupiter's mass at the moment when the particle escapes from the planet. Such values are an indication of the necessary conditions that could provide capture. An analysis of these results shows that retrograde satellites would be captured as soon as they get inside the Hills' radius and after that they keep migrating toward the planet while it is growing. For the region where the orbits of the four old retrograde satellites of Jupiter ( Ananke, Carme, Pasiphae and Sinope) are located we found that such satellites could have been permanently captured when Jupiter had between 62% and 93% of its present mass.

Some aspects of the dynamics of fictitious Earth's satellites

In this work we study the dynamics of fictitious satellites of the Earth. In the first part we do not consider the effect of the Moon and study the dynamics in the restrict three-body model, i.e., a massless satellite under the effect of the gravitational force of an oblate Earth and that of the Sun. We show that a satellite starting with an almost circular orbit suffers very large variations of eccentricity, depending on the initial inclination of the orbit with respect to the reference plane. As the eccentricity may be driven to very large values (approximate to0.9) mutual collisions between satellites or collisions with the planet may occur. In the second part, we include the gravitational effect of the Moon. In this case, we find two regions with large variations of eccentricity due to the presence of the Moon. Consequently, in both scenarios, we find some large regions of the phase space where the long-term stability of some fictitious Earth's satellites is not possible. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Stable satellites around extrasolar giant planets

In this work, we study the stability of hypothetical satellites of extrasolar planets. Through numerical simulations of the restricted elliptic three-body problem we found the borders of the stable regions around the secondary body. From the empirical results, we derived analytical expressions of the critical semimajor axis beyond which the satellites would not remain stable. The expressions are given as a function of the eccentricities of the planet, e(P), and of the satellite, e(sat). In the case of prograde, satellites, the critical semimajor axis, in the units of Hill's radius, is given by a(E) approximate to 0.4895 (1.0000 - 1.0305e(P) - 0.2738e(sat)). In the case of retrograde satellites, it is given by a(E) approximate to 0.9309 (1.0000 - 1.0764e(P) - 0.9812e(sat)). We also computed the satellite stability region (a(E)) for a set of extrasolar planets. The results indicate that extrasolar planets in the habitable zone could harbour the Earth-like satellites.

Variation of the Equator due to a Highly Inclined and Eccentric Disturber

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

Efeitos de doses de fósforo em mamoneira (Ricinus communis L.) cultivar 'Guarani'

O presente trabalho teve como objetivo estudar os efeitos de doses crescentes de fósforo na produção, no teor de óleo das sementes e nas concentrações de macronutrientes, exceto o S, das sementes e da casca da mamona, em cultivar 'Guarani'. As doses utilizadas foram 0-40-80-120-160-200 kg/ha de P2O5, num Latossolo Vermelho Escuro - fase arenosa de baixa fertilidade, no Município de São Manuel, Estado de São Paulo. Os resultados mostraram que o fósforo aumentou o número de frutos por cacho, diminuiu a porcentagem de casca no fruto e aumentou o peso de sementes por cacho. Disto resultou um aumento médio na produção de 100,21%, em relação à produção do tratamento sem fósforo. No que tange aos teores dos elementos nos frutos, observou-se um aumento de P e uma tendência de diminuir o N, nas sementes colhidas dos tratamentos adubados com fósforo. Os efeitos do fósforo no teor de óleo das sementes não ficou bem caracterizado, devendo o problema merecer maiores estudos.

Efeitos de doses não equidistantes de N, P, K nas concentrações destes macronutrientes na folha e na produção do milho (Zea mays L.)

Os experimentos foram conduzidos, em um podzólico de Lins e Marília - variação Lins, de textora barrento-arenosa, localizado no Município de Monte Azul Paulista, SP. O híbrido de milho duplo H-6999B foi utilizado. Cada experimento constou de 5 tratamentos e de 4 repetições. Os níveis de nitrogênio foram: 0, 50, 100, 200 e 400 kg/ha, sendo aplicados também90 kg/ha de P²O5 e 50 kg/ha de K2O. Os níveis de fósforo foram: 0,40, 80, I60 e 320 kg/ha de P²O5, sendo aplicados também 100 kg/ha de N e 50 kg/ha de K2O. Os níveis de potássio foram: 0, 25, 50, 100 e 200 kg/ha de K2O, sendo aplicados também 100 kg/ha de N e 90 kg/ha de P²O5. A aplicação tanto das doses de fósforo comodas de nitrogênio fez aumentar a produção de milho, a qual foi da ordem de 3 a 7 vezes superior à média de produção do Estado de São Paulo. A dose econômica e a sua consequente produção, determinadas pelas equações de Mitscherlichr-Pimentel Gomes foram: para o fósforo, de 253 kg/ha de P²O5 correspondente a urna produção de o.877 kg/ha de milho em grão; para o nitrogênio, foi de 228 kg/ha de N correspondente a uma produção de 11.100 kg/ha de milho e para o potássio, foi de 62 kg/ha de K2O correspondente a urna produção de 9-252 kg/ha de milho. Os níveis críticos econômicos, nas folhas, determinados pelas equações de MALAVOLTA & PIMENTEL GOMES (1961) e correspondentes às doses econômicas, foram de: 0,293% de P, de 3,27% de N e de 2,07% de K. A folha escolhida, ou seja, aquela oposta à espiga mais alta, reflete bem o estado nutricional da planta e consequentemente o nível de fertilidade do solo.

Influence of liming on residual soil respiration and chemical properties in a tropical no-tillage system

Devido às mudanças climáticas do planeta, principalmente ao aquecimento global, as formas de utilização dos solos na agricultura têm atraído grande atenção de pesquisadores. Mudanças de manejo podem influenciar a respiração do solo e, por conseguinte, alterar drasticamente o sequestro de C. Os objetivos deste trabalho foram avaliar, em semeadura direta, a influência da calagem nas emissões de CO2 do solo e correlacioná-las aos atributos químicos deste após dois anos da calagem. Utilizou-se o delineamento em blocos casualizados, com seis repetições. Os tratamentos constituíram de quatro doses de calcário e uma testemunha. Decorridos dois anos da calagem, avaliou-se a emissão residual de CO2 do solo, coletaram-se amostras nas camadas de 0-5, 5-10, 10-20 e 20-30 cm de profundidade e determinaram-se os teores de P, Ca2+ e Mg2+ e valores de pH e de saturação por bases. A emissão residual de CO2 do solo, quando a dose recomendada foi aplicada, foi 24,1 % superior, quando comparada à do solo sem aplicação de calcário, e 47,4 % maior, quando se aplicou o dobro da dose recomendada. A calagem melhorou as condições químicas do solo, e a emissão de CO2 aumentou linearmente com o aumento das doses. A emissão de CO2 do solo apresentou correlações positivas com os teores de P, Ca2+ e Mg2+ e com os valores de pH e de saturação por bases e negativas com os teores de H + Al e Al3+. Maiores coeficientes de correlação entre as taxas de emissão de CO2 do solo e os atributos químicos deste ocorreram na camada de 10-20 cm.

Time analysis for temporary gravitational capture - Stable orbits

In a previous work, Vieira Neto & Winter (2001) numerically explored the capture times of particles as temporary satellites of Uranus. The study was made in the framework of the spatial, circular, restricted three-body problem. Regions of the initial condition space whose trajectories are apparently stable were determined. The criterion adopted was that the trajectories do not escape from the planet during an integration of 10(5) years. These regions occur for a wide range of orbital initial inclinations (i). In the present work it is studied the reason for the existence of such stable regions. The stability of the planar retrograde trajectories is due to a family of simple periodic orbits and the associated quasi-periodic orbits that oscillate around them. These planar stable orbits had already been studied (Henon 1970; Huang & Innanen 1983). Their results are reviewed using Poincare surface of sections. The stable non-planar retrograde trajectories, 110 degrees less than or equal to i < 180, are found to be tridimensional quasi-periodic orbits around the same family of periodic orbits found for the planar case (i = 180 degrees). It was not found any periodic orbit out of the plane associated to such quasi-periodic orbits. The largest region of stable prograde trajectories occurs at i = 60 degrees. Trajectories in such region are found to behave as quasi-periodic orbits evolving similarly to the stable retrograde trajectories that occurs at i = 120 degrees.

A possible stellar metallic enhancement in post-T Tauri stars by a planetesimal bombardment

The photospheres of stars hosting planets have larger metallicity than stars lacking planets. This could be the result of a metallic star contamination produced by the bombarding of hydrogen-deficient solid bodies. In the present work we study the possibility of an earlier metal enrichment of the photospheres by means of impacting planetesimals during the first 20-30 Myr. Here we explore this contamination process by simulating the interactions of an inward migrating planet with a disc of planetesimal interior to its orbit. The results show the percentage of planetesimals that fall on the star. We identified the dependence of the planet's eccentricity (e(p)) and time-scale of migration (tau) on the rate of infalling planetesimals. For very fast migrations (tau= 10(2) and 10(3) yr) there is no capture in mean motion resonances, independently of the value of e(p). Then, due to the planet's migration the planetesimals suffer close approaches with the planet and more than 80 per cent of them are ejected from the system. For slow migrations (tau= 10(5)and 10(6) yr) the percentage of collisions with the planet decreases with the increase of the planet's eccentricity. For e(p) = 0 and 0.1 most of the planetesimals were captured in the 2:1 resonance and more than 65 per cent of them collided with the star. Whereas migration of a Jupiter mass planet to very short pericentric distances requires unrealistic high disc masses, these requirements are much smaller for smaller migrating planets. Our simulations for a slowly migrating 0.1 M-Jupiter planet, even demanding a possible primitive disc three times more massive than a primitive solar nebula, produces maximum [Fe/H] enrichments of the order of 0.18 dex. These calculations open possibilities to explain hot Jupiter exoplanet metallicities.

Some comments on the F ring-Prometheus-Pandora environment

The system formed by the F ring and two close satellites, Prometheus and Pandora, has been analysed since the time that Voyager visited the planet Saturn. During the ring plane crossing in 1995 the satellites were found in different positions as predicted by the Voyager data. Besides the mutual effects of Prometheus and Pandora, they are also disturbed by a massive F ring. Showalter et al. [Icarus 100 (1992) 394] proposed that, the core of the ring has a mass which corresponds to a moonlet varying in size from 15 to 70 kin in radius which can prevent the ring from spreading due to dissipative forces, such as Poynting-Robertson drag and collisions. We have divided this work into two parts. Firstly we analysed the secular interactions between Prometheus-Pandora and a massive F ring using the secular theory. Our results show the variation in eccentricity and inclination of the satellites and the F ring taking into account a massive ring corresponding to a moonlet of different sizes. There is also a population of dust particles in the ring in the company of moonlets at different sizes [Icarus 109 (1997) 304]. We also analysed the behaviour of these particles under the effects of the Poynting-Robertson drag and radiation pressure. Our results show that the time scale proposed for a dust particle to leave the ring is much shorter than predicted before even in the presence of a coorbital moonlet. This result does not agree with the confinement model proposed by Dermott et al. [Nature 284 (1980) 309]. In 2004, Cassini mission will perform repeated observations of the whole system, including observations of the satellites and the F ring environment. These data will help us to better understand this system. (C) 2003 COSPAR. Published by Elsevier Ltd. All rights reserved.

The strands of the F ring disturbed by its closest satellites

Some Voyager images showed that the F ring of Saturn is composed of at least four separate, non-intersecting, strands covering about 45 degrees in longitude. According to Murray et al. [Murray, C.D., Gordon, M., Giuliatti Winter, S.M. Unraveling the strands of Saturn's F ring. Icarus 129, 304, 1997.] this structure may be caused by undetected satellites embedded in the gaps.Due to precession, the satellites Prometheus and Pandora and the ring particles can experience periodic close encounters. Giuliatti Winter et al. [Giuliatti Winter, S.M, Murray, C.D., Gordon, M. Perturbations to Saturn's F-ring strands at their closest approach to Prometheus. Plan. Space Sciences, 48, 817, 2000.] analysed the behaviour of these four strands at closest approach with the satellite Prometheus. Their work suggests that Prometheus can induce the ring particles to scatter in the direction of the planet, thus increasing the population of small bodies in this region.In this work we analysed the effects of Prometheus on the radial structure of Saturn's F ring during the Voyager and early Cassini epochs. Our results show that at Voyager epoch Prometheus, and also Pandora, had a negligible influence in the strands. However, during the Cassini encounter Prometheus could affect the strands significantly, scattering particles of the inner strand in the direction of the planet. This process can contribute to the replenishment of material in the region between the F ring and the A ring, where two rings have recently been discovered [Porco, C. et al. Cassini imaging science. Initial results on Saturn's rings and small Satellites. Science, 307, 1226, 2005].We also analyse the behaviour of undetected satellites under the effects of these two satellites by computing the Lyapunov Characteristic Exponent. Our results show that these satellites have a chaotic behaviour which leads to a much more complex scenario. The new satellite S/2004 S6 also presents a chaotic behaviour with can alter the dynamic of the system, since this satellite crosses the orbit of the strands. (C) 2006 COSPAR. Published by Elsevier Ltd. All rights reserved.