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.

Inner satellites of Neptune: I the disturbing function

In this work, we focus our attention to the expansion of the disturbing function (R) which governs the dynamics of a satellite (natural or artificial) in the Neptune-Triton system. What makes this problem quite unusual, is the fact that a small inner satellite can be strongly disturbed by Triton which is moving in a highly inclined and retrograde orbit. These features are unique in our solar system. Although a lot of retrograde satellites are currently known, all of them have negligible mass and the), do not offer almost any perturbation on the others satellites. However, in the case of the inner satellites of Neptune, Triton is an interesting exception. In a highly inclined orbit, the perturbation it exerts on the neighbouring satellites of Neptune cannot be ignored even for the present scenario. However, in the future, this perturbation will be much more important because due to the tides, the orbit of Triton is contracting, whereas the semi major axes of the remaining inner satellites of Neptune will remain almost unaffected by the tides. In this work we first obtain the disturbing function in the retrograde case. After that, we generalize R for arbitrary inclination. Several numerical tests are presented and a possible future case of resonant configuration is briefly discussed as well. (c) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

Numerical exploration of resonant dynamics in the system of Saturnian major satellites

We numerically investigate the long-term dynamics of the Saturnian system by analyzing the Fourier spectra of ensembles of orbits taken around the current orbits of Mimas, Enceladus, Tethys, Rhea and Hyperion. We construct dynamical maps around the current position of these satellites in their respective phase spaces. The maps are the result of a great deal of numerical simulations where we adopt dense sets of initial conditions and different satellite configurations. Several structures associated to the current two-body mean-motion resonances, unstable regions associated to close approaches between the satellites, and three-body mean-motion resonances in the system, are identified in the map. (C) 2010 Elsevier Ltd. All rights reserved.

Instability zones for satellites of asteroids: The example of the (87) Sylvia system

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

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

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

1968-2008: O Veja Way of Life

O artigo aborda, segundo a nossa hipótese, o Jornalismo espetacular, marcado pelo entretenimento, utilizado pela revista Veja para noticiar os episódios do movimento estudantil - principal movimento engajado na luta da ditadura - já em 1968. Foram feitos pesquisa bibliográfica e estudo comparativo da abordagem de edições de 1998 e de 2008. Durante as comemorações deste ano ímpar, a nossa conclusão é a de que Veja agrega, cada vez mais, elementos sensacionalistas com o intuito de denegrir a imagem do movimento estudantil, corroborando, assim, com a indústria cultural e a sociedade do espetáculo que visam a produzir uma juventude democrática, ou seja, que almeja o sucesso econômico por meio do direito de consumir e da manutenção do sistema político vigente.

Sample size for single, double and thee-way hybrid corn ear traits

O uso dos tamanhos de amostras adequados nas unidades experimentais melhora a eficiência da pesquisa. Foi conduzido um experimento no ano agrícola 2004/2005 em Santa Maria, Rio Grande do Sul, com o objetivo de estimar o tamanho de amostra para o comprimento de espiga, o diâmetro de espiga e de sabugo, o peso da espiga, dos grãos por espiga, do sabugo e de 100 grãos, o número de fileiras de grãos por espiga, o número de grãos por espiga e o comprimento dos grãos de dois híbridos simples (P30F33 e P Flex), dois híbridos triplos (AG8021 e DG501) e dois híbridos duplos (AG2060 e DKB701) de milho. Para uma precisão de 5% (D5), características de peso (peso de espiga despalhada, de grãos, de sabugo e de 100 grãos) podem ser amostradas com 21 espigas, características de tamanho (comprimento de espiga e de grão, diâmetro de espiga e de sabugo) com oito espigas, e dados de contagem (número de grãos e de fileiras) com 13 espigas. O tamanho de amostra é variável em função da característica da espiga e do tipo de híbrido: simples, triplo ou duplo. A variabilidade genética existente entre os híbridos de milho, na forma crescente: simples, triplo e duplo, não reflete na mesma ordem no tamanho de amostra de caracteres da espiga.

Orbital propagation for Brazilian satellites using NORAD models

The performance of the NORAD models for near Earth satellites (SGP, SGP4, SGP8) using two Brazilian flying satellites, SCD-1 and SCD-2, and the Chinese-Brazilian satellite CBERS-1 is compared. The achievable accuracy of such models is compared against the predicted 2-lines elements set for the satellites. Every week an updated fresh set of 2-lines elements for these satellites is made available through the Internet. About ten years of observations of the SCD-1 satellite are available and therefore solar activity influences on the orbit can be analyzed. Data are selected considering also orbital (for CBERS-1) and attitude (for SCD-2) maneuvers - (C) 2002 COSPAR. Published by Elsevier B.V. Ltd. All rights reserved.

The use of nonparametric contrasts in one-way layouts and random block designs

Nonparametric simple-contrast estimates for one-way layouts based on Hodges-Lehmann estimators for two samples and confidence intervals for all contrasts involving only two treatments are found in the literature.Tests for such contrasts are performed from the distribution of the maximum of the rank sum between two treatments. For random block designs, simple contrast estimates based on Hodges-Lehmann estimators for one sample are presented. However, discussions concerning the significance levels of more complex contrast tests in nonparametric statistics are not well outlined.This work aims at presenting a methodology to obtain p-values for any contrast types based on the construction of the permutations required by each design model using a C-language program for each design type. For small samples, all possible treatment configurations are performed in order to obtain the desired p-value. For large samples, a fixed number of random configurations are used. The program prompts the input of contrast coefficients, but does not assume the existence or orthogonality among them.In orthogonal contrasts, the decomposition of the value of the suitable statistic for each case is performed and it is observed that the same procedure used in the parametric analysis of variance can be applied in the nonparametric case, that is, each of the orthogonal contrasts has a chi(2) distribution with one degree of freedom. Also, the similarities between the p-values obtained for nonparametric contrasts and those obtained through approximations suggested in the literature are discussed.

Two-way regionalized classification of multivariate datasets and its application to the assessment of hydrodynamic dispersion

Zones of mixing between shallow groundwaters of different composition were unravelled by two-way regionalized classification, a technique based on correspondence analysis (CA), cluster analysis (ClA) and discriminant analysis (DA), aided by gridding, map-overlay and contouring tools. The shallow groundwaters are from a granitoid plutonite in the Funda o region (central Portugal). Correspondence analysis detected three natural clusters in the working dataset: 1, weathering; 2, domestic effluents; 3, fertilizers. Cluster analysis set an alternative distribution of the samples by the three clusters. Group memberships obtained by correspondence analysis and by cluster analysis were optimized by discriminant analysis, gridded memberships as follows: codes 1, 2 or 3 were used when classification by correspondence analysis and cluster analysis produced the same results; code 0 when the grid node was first assigned to cluster 1 and then to cluster 2 or vice versa (mixing between weathering and effluents); code 4 in the other cases (mixing between agriculture and the other influences). Code-3 areas were systematically surrounded by code-4 areas, an observation attributed to hydrodynamic dispersion. Accordingly, the extent of code-4 areas in two orthogonal directions was assumed proportional to the longitudinal and transverse dispersivities of local soils. The results (0.7-16.8 and 0.4-4.3 m, respectively) are acceptable at the macroscopic scale. The ratios between longitudinal and transverse dispersivities (1.2-11.1) are also in agreement with results obtained by other studies.

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.

Irregular Satellites of Jupiter: a study of the capture direction

The irregular satellites of Jupiter are believed to be captured asteroids or planetesimals. In the present work is studied the direction of capture of these objects as a function of their orbital inclination. We performed numerical simulations of the restricted three-body problem, Sun-Jupiter-particle, taking into account the growth of Jupiter. The integration was made backward in time. Initially, the particles have orbits as satellites of Jupiter, which has its present mass. Then, the system evolved with Jupiter losing mass and the satellites escaping from the planet. The reverse of the escape direction corresponds to the capture direction. The results show that the Lagrangian points L1 and L2 mainly guide the direction of capture. Prograde satellites are captured through these two gates with very narrow amplitude angles. In the case of retrograde satellites, these two gates are wider. The capture region increases as the orbital inclination increases. In the case of planar retrograde satellites the directions of capture cover the whole 360 degrees around Jupiter. We also verified that prograde satellites are captured earlier in actual time than retrograde ones.

Stability analysis of the attitude of artificial satellites subject to gravity gradient torque

Using a canonical formulation, the stability of the rotational motion of artificial satellites is analyzed considering perturbations due to the gravity gradient torque. Here Andoyer's variables are used to describe the rotational motion. One of the approaches that allow the analysis of the stability of Hamiltonian systems needs the reduction of the Hamiltonian to a normal form. Firstly equilibrium points are found. Using generalized coordinates, the Hamiltonian is expanded in the neighborhood of the linearly stable equilibrium points. In a next step a canonical linear transformation is used to diagonalize the matrix associated to the linear part of the system. The quadratic part of the Hamiltonian is normalized. Based in a Lie-Hori algorithm a semi-analytic process for normalization is applied and the Hamiltonian is normalized up to the fourth order. Once the Hamiltonian is normalized up to order four, the analysis of stability of the equilibrium point is performed using the theorem of Kovalev and Savichenko. This semi-analytical approach was applied considering some data sets of hypothetical satellites. For the considered satellites it was observed few cases of stable motion. This work contributes for space missions where the maintenance of spacecraft attitude stability is required.