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.

Controlling the Eccentricity of Polar Lunar Orbits with Low-Thrust Propulsion

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Collision and Stable Regions around Bodies with Simple Geometric Shape

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

On the first nu(6) anti-aligned librating asteroid family of Tina

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

The role of Mab as a source for the mu ring of Uranus (Research Note)

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

The geotectonic environments of Early Precambrian granulites in Brazil

A review is presented concerning Archaean granulites occurring in some old domains of the South American Platform, which was consolidated at the end of the Brazilian Cycle (900-500 Ma). The rocks occur in different geotectonic environments and show variable ages, structures and lithological associations. The most important complexes are the Atlantic Granulite Belt in the São Francisco Craton and the Goias Granulite Belt in the Central Goias Massif, both several hundred kilometres long. The former is composed of the Caraibas Complex, the Jequié Complex, the Salvador Complex and several minor granulite occurrences along the Brazilian coast in the States of Espírito Santo and Rio de Janeiro. The latter includes the large basic-ultrabasic complexes of Barro Alto, Tocantins and Canabrava. Both belts consist of massive or foliated rocks, banded or homogeneous and varying from acidic to ultrabasic in composition. They are the result of metamorphism affecting diversified supra- and infracrustal material. The Atlantic Granulite Belt lies between greenstone/granite terrains which show ovoid and boomerang-type dome structures. The contacts between both are either tectonic or transitional. Another occurrence of Archaean granulites comprises intercalations of palaeosomes and melanosomes within migmatites and anatectic rocks. These vary in size from small lenses to irregular complexes which may attain sizes of several hundred square kilometres. Apart from migmatites, they are associated with gneisses, schists and granitoid bodies. They are located in regions which underwent remobilization of varying intensity during the Middle and Late Precambrian. The rocks show polymetamorphism, K-feldspar blastesis, tectonic overprinting and isotopic rejuvenation. These granulites are in some cases very similar to those formed during the Middle Precambrian. In some places it is therefore quite difficult to distinguish between Early and Middle Precambrian granulites - the more so, since interpretations of radiometric age values are largely controversial. At present there is no evidence of granulitic rocks related to the Late Precambrian geotectonic cycles of Brazil. © 1979.

Pulsar test of a violation of discrete symmetries in gravitation

We determine an improved limit on C and P violation to the extended gravitational potential of Leitner and Okubo using the millisecond pulsar PSR 1937+214 data. © 1989.

Quantum geometry of chiral bosons on a circle

We extend the geometric treatment done for the Majorana-Weyl fermions in two dimensions by Sanielevici and Semenoff to chiral bosons on a circle. For this case we obtain a generalized Floreanini-Jackiw Lagrangian density, and the corresponding gravitational (or Virasoro) anomalies are found as expected. © 1989 The American Physical Society.

The first case study of a thunderstorm in South Africa based on dual- Doppler radar observations

On 27 March 1991, an isolated thunderstorm passed between the two CSIR Doppler radars, spaced about 45km apart. Both radars simultaneously recorded Doppler data of the storm, and a detailed case study during an 11-min period is presented. Air motions synthesized from these data provide the first three-dimensional display of Doppler-derived wind fields within a multicell storm on the Transvaal Highveld. Regions of high divergence values (10 -2s -1) at low levels were found mostly in close proximity to reflectivity maxima (45-51 dBZ), which is consistent with findings from North America, that gravitational loading by the precipitation plays a key role in the initiation and maintenance of downdraughts. -from Authors

Collective scattering of massive stars in higher order gravity

In the weak field approximation of higher order gravity theory a gravitational potential is described by a Newtonian plus a Yukawa-like term. This new term is used to explain some aspects of galactic dynamics, without considering dark matter. Its presence modifies the scattering probability of a massive intruder star and relaxation time of the stellar system.

The magnetic field of a current carrying cosmic string

The magnetostatic field of an infinite rectilinear current placed in the stationary gravitational field of a rotating cosmic string is found. An interesting aspect of this problem is that although the metric is mathematically very simple, its physical meaning is not trivial. It depends only on topological parameters. So, the cosmic string vacuum space-time is locally equivalent to the Minkowski space-time, but not globally. The calculations are so simple that they can easily be shown in the classroom. © 1997 American Association of Physics Teachers.