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.

Can Drag Force Suppress Fermi Acceleration in a Bouncer Model?

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

High-pressure granulites from Carire, Borborema Province, NE Brazil: Tectonic setting, metamorphic conditions and U-Pb, Lu-Hf and Sm-Nd geochronology

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A história da ciência na formação do professor de física: subsídios para um curso sobre o tema atração gravitacional visando às mudanças de postura na ação docente

O objetivo desta pesquisa foi estudar como a evolução histórica dos modelos de atração entre corpos, tendo como pano de fundo a evolução dos modelos de mundo, pode auxiliar na formação inicial do docente de Física. Para tanto, sugerimos um planejamento de curso sobre o tema atração gravitacional, destinado principalmente a docentes de Física que atuam no ensino médio. O planejamento do curso foi baseado: em dados sobre a evolução dos modelos de mundo, buscando evidenciar como o conceito de atração gravitacional desenvolveu-se historicamente; nas concepções alternativas mais comuns encontradas na literatura, incluindo um breve esboço de noções diagnosticadas em uma amostra de docentes de Física de ensino médio; e em sugestões de leituras de resultados de pesquisas recentes sobre os processos de ensino e aprendizagem de ciências. Pretende-se fornecer aos docentes elementos de reflexão que lhes proporcionem mudanças de postura, através do questionamento da visão de ciência enquanto processo de construção e sobre sua própria prática de ensino. Partindo de resultados recentes da pesquisa em Ensino de Ciências, a metodologia sugerida privilegia o trabalho coletivo, com a realização de debates e sínteses. As atividades mencionadas são acompanhadas de justificativas sobre a escolha do tema e objetivos.

Perfil dos alunos usuários de lentes de contato do curso de Medicina da Universidade Estadual Paulista - UNESP - Botucatu

OBJETIVO: Analisar o perfil dos usuários de lentes de contato entre os estudantes de medicina da Faculdade de Medicina de Botucatu da Universidade Estadual Paulista - UNESP - Botucatu (SP), quanto à ametropia, à aquisição, aos cuidados e às complicações. MÉTODOS: Foi aplicado um questionário aos alunos do 1º ao 6º ano de Medicina da Faculdade de Medicina de Botucatu da Universidade Estadual Paulista - UNESP - Botucatu (SP), perfazendo um estudo analítico transversal. RESULTADOS: Foram 566 entrevistados. Destes, 155 (27,4%) usavam lente de contato. Das lentes de contato usadas, 94,8% eram gelatinosas, e em 98,7% o grau era negativo. O descarte dessas lentes era mensal em 46,9% dos entrevistados e 63,9% a utilizavam, em média, 14 horas/dia. Faziam aquisição da lente de contato em óptica ou farmácia 14,1% dos estudantes. Faziam a higiene ao colocá-las e ao retirá-las dos olhos, 46,5%. As complicações referentes aos olhos vermelhos eram 51,0%; 44,5%, embaçamento; e 42,6%, sensação de corpo estranho, além de 4 estudantes relatarem ceratite. CONCLUSÕES: A maioria dos alunos utilizava lentes hidrofílicas, descarte mensal e grau negativo. A adaptação inadequada, aquisição de lentes de contato em ópticas ou farmácias e complicações graves ocorreram, mesmo nos usuários socioculturalmente considerados diferenciados. em vista disso, demanda a extrema necessidade de maior atenção na abordagem do tema em questão, a fim de prevenir o comprometimento visual permanente.

Relatos de jovens deficientes mentais sobre a sexualidade através de diferentes estratégias

O objetivo deste trabalho consistiu em utilizar estratégias para obter e analisar relatos sobre sexualidade de cinco jovens, ambos os sexos, com deficiência mental, por diferentes procedimentos metodológicos: 1) Desenho da Figura Humana; 2) Apresentação de bonecos da família sexuada; 3) Apresentação das pranchas dos temas: namoro, casamento, masturbação, jogos sexuais, menstruação, relação sexual, gravidez, parto, amamentação e abuso sexual. Observou-se que os jovens: a) têm noção de identidade e papéis sexuais; b) diferenciam e nomeiam órgãos sexuais humanos, especialmente o órgão sexual masculino adulto; c) apesar de saberem nomeá-los, nem todos sabem sua função; d) com frases curtas e objetivas os jovens mostraram os conceitos sobre os diferentes temas apresentados. As estratégias utilizadas foram eficientes para incentivar o relato de jovens com limitação intelectual em temas complexos como a sexualidade.

Attitude stabilization of a rigid spacecraft in the geomagnetic field

An analytical method is proposed to study the attitude stability of a triaxial spacecraft moving in a circular Keplerian orbit in the geomagnetic field. The method is developed based on the electrodynamics effect of the influence of the Lorentz force acting on the charged spacecraft's surface. We assume that the rigid spacecraft is equipped with an electrostatic charged protective shield, having an intrinsic magnetic moment. The main elements of this shield are an electrostatic charged cylindrical screen surrounding the protected volume of the spacecraft. The rotational motion of the spacecraft about its centre of mass due to torques from gravitational force, as well Lorentz and magnetic forces is investigated. The equilibrium positions of the spacecraft in the orbital coordinate system are obtained. The necessary and sufficient conditions for the stability of the spacecraft's equilibrium positions are constructed using Lyapunov's direct method. The numerical results have shown that the Lorentz force has a significant influence on the stability of the equilibrium positions, which can affect the attitude stabilization of the spacecraft. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

The Ni-Cu-PGE sulfide ores of the komatiite-hosted Fortaleza de Minas deposit, Brazil: Evidence of hydrothermal remobilization

The Fortaleza de Minas Ni-Cu-PGE sulfide deposit is hosted by Archean komatiitic rocks of the Morro do Ferro greenstone belt, near the southwestern margin of the Sa (aFrancisco) over tildeo Francisco craton, Minas Gerais state, Brazil. The deposit contains 6 million tonnes of ore with an average grade of 2.2 wt% Ni, 0.4% Cu, 0.05% Co and 1.2 ppm PGE+Au, and comprises (i) a main orebody, which is metamorphosed, deformed and transposed along a regional shear zone, consisting mainly of disseminated, brecciated and stringer sulfide ores that are interpreted to be of early magmatic origin, and (ii) PGE-rich discordant veins that are hosted in N-S- and NE-SW-trending late faults that cross-cut the main orebody. The discordant PGE-rich ore (up to 4 ppm total PGE) is characterized by thin, discontinuous and irregular veins and lenses of massive sulfides hosted by serpentinite and talc schist, and is relatively undeformed if compared with the early types of ore. It is composed mainly of pyrrhotite, pentlandite, chalcopyrite, magnetite, carbonates, and amphiboles, with minor cobaltite-gersdorffite, sphalerite, ilmenite, and quartz, and rarely maucherite (Ni11Asg), tellurides and platinum-group minerals (PGM). Omeeite, irarsite, sperrylite, and Ni-bearing merenskyite are the main PGM, followed by minor amounts of testibiopalladite and an unknown phase containing Ru, Te, and As. The PGM occur either included in, or at the margins of, sulfides, sulfarsenides, silicates and oxides, or filling fractures in pyrrhotite, pentlandite, and chalcopyrite, suggesting that they started to precipitate with these minerals and continued to precipitate after the sulfides were formed. The mantle-normalized metal distribution of the two samples of discordant veins shows distinct patterns: one richer in Ni-Pd-Ir-Rh-Ru-Os and another with higher amounts of Cu-Pt-Bi. Both are strongly depleted in Cr if compared with the metamorphosed magmatic ore of this deposit, which follows the general Kambalda-type magmatic trend. on the basis of structural, mineralogical and geochemical evidence, we propose that the PGE-rich discordant ore may have formed by remobilization of metals from the deformed, metamorphosed magmatic orebody (which shows a depleted pattern in these elements) by reduced (pyrrhotite - pentlandite - pyrite are stable), neutral to alkaline and carbonic fluids (carbonate-stable). The PGE may have been transported as bisulfide complexes, and precipitated as tellurides (mainly Pd) and arsenides (Pt, Rh, Ru, Os, Ir) in the late N-S and NE-SW-trending faults owing to a decrease in the activity of S caused by the precipitation of sulfides in the veins.

The Liapunov exponent as a tool for exploring phase space

We have used the Liapunov exponent to explore the phase space of a dynamical system. Considering the planar, circular restricted three-body problem for a mass ratio mu = 10(-3) (close to the Jupiter/Sun case), we have integrated similar to 16,000 starting conditions for orbits started interior to that of the perturber and we have estimated the maximum Liapunov characteristic exponent for each starting condition. Despite the fact that the integrations, in general, are for only a few thousand orbital periods of the secondary, a comparative analysis of the Liapunov exponents for various values of the 'cut-off' gives a good overview of the structure of the phase space. It provides information about the diffusion rates of the various chaotic regions, the location of the regular regions associated with primary resonances and even details such as the location of secondary resonances that produce chaotic regions inside the regular regions of primary resonances.

Testing the principle of equivalence by supernova neutrinos

We study the possible impact of the neutrino oscillation which could be induced by a tiny violation of equivalence principle (VEP) on the observation of neutrinos emitted from supernova driven by gravitational collapse. We show that using supernova neutrinos, one can probe very small values of VEP parameters, delta(tau) less than or similar to O(10(-31)) for massless or degenerated neutrinos and delta(tau) less than or similar to O(10(-16)) x (Deltam(2)/10(-5) eV(2)) for massive neutrinos. (C) 2002 Elsevier B.V. B.V. All rights reserved.

THE PARAMETERS OF THE LEWIS METRIC FOR THE WEYL CLASS

We provide physical interpretation for the four parameters of the stationary Lewis metric restricted to the Weyl class. Matching this spacetime to a completely anisotropic, rigidly rotating, fluid cylinder, we obtain from the junction conditions that one of these parameters is proportional to the vorticity of the source. From the Newtonian approximation a second parameter is found to be proportional to the energy per unit of length. The remaining two parameters may be associated to a gravitational analog of the Aharanov-Bohm effect. We prove, using the Cartan scalars, that the Weyl class metric and static Levi-Civita metric are locally equivalent, i.e., indistinguishable in terms of its curvature.

Collisions with the Earth: the Moon's contribution

In the present work is analyzed the contribution of the Moon on the collisional process of the Earth with asteroids (NEOs). The dynamical system adopted is the restricted four-body problem Sun-Earth-Moon-particle. Using a simple analytical approach one can verify that, the orbit of an object can be significantly affected by the Moon's gravitational field when their relative velocity is smaller than 5 km/s. Therefore, the present work is based on hypothetical asteroids whose velocities relative to Moon are of the order of 1 km/s. In fact, there are several real objects (NEOs) with such velocities at the point they cross the Earth's orbit. The net results obtained indicate that the Moon helps to avoid collisions (2.6%) more than it contributes to extra collisions (0.6%). (C) 2003 COSPAR. Published by Elsevier Ltd. All rights reserved.

Peculiar trajectories around the Lagrangian equilateral points

In the present work we analyse the behaviour of a particle under the gravitational influence of two massive bodies and a particular dissipative force. The circular restricted three body problem, which describes the motion of this particle, has five equilibrium points in the frame which rotates with the same angular velocity as the massive bodies: two equilateral stable points (L-4, L-5) and three colinear unstable points (L-1, L-2, L-3). A particular solution for this problem is a stable orbital libration, called a tadpole orbit, around the equilateral points. The inclusion of a particular dissipative force can alter this configuration. We investigated the orbital behaviour of a particle initially located near L4 or L5 under the perturbation of a satellite and the Poynting-Robertson drag. This is an example of breakdown of quasi-periodic motion about an elliptic point of an area-preserving map under the action of dissipation. Our results show that the effect of this dissipative force is more pronounced when the mass of the satellite and/or the size of the particle decrease, leading to chaotic, although confined, orbits. From the maximum Lyapunov Characteristic Exponent a final value of gamma was computed after a time span of 10(6) orbital periods of the satellite. This result enables us to obtain a critical value of log y beyond which the orbit of the particle will be unstable, leaving the tadpole behaviour. For particles initially located near L4, the critical value of log gamma is -4.07 and for those particles located near L-5 the critical value of log gamma is -3.96. (c) 2006 Elsevier B.V. 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.

Refractive and geometric lens characterization through multi-wavelength digital speckle pattern interferometry

Physical parameters of different types of lenses were measured through digital speckle pattern interferometry (DSPI) using a multimode diode laser as light source. When such lasers emit two or more longitudinal modes simultaneously the speckle image of an object appears covered of contour fringes. By performing the quantitative fringe evaluation the radii of curvature as well as the refractive indexes of the lenses were determined. The fringe quantitative evaluation was carried out through the four- and the eight-stepping techniques and the branch-cut method was employed for phase unwrapping. With all these parameters the focal length was calculated. This whole-field multi-wavelength method does enable the characterization of spherical and aspherical lenses and of positive and negative ones as well. (C) 2007 Elsevier B.V. All rights reserved.