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.

Thermal decomposition of crystalline Ni-II-Cr-III layered double hydroxide: A structural study of the segregation process

A structural study of the thermal evolution of Ni0.69Cr0.31(OH)(2)(CO3)(0.155)(.)nH(2)O into NiO and tetragonal NiCr2O4 is reported. The characteristic structural parameters of the two coexisting crystalline phases, as well as their relative abundance, were determined by Rietveld refinement of powder x-ray diffraction (PXRD) patterns. The results of the simulations allowed us to elucidate the mechanism of the demixing process of the oxides. It is demonstrated that nucleation of a metastable nickel chromite within the common oxygen framework of the parent Cr-III-doped bunsenite is the initial step of the cationic redistribution. The role that trivalent cations play in the segregation of crystalline spinels is also discussed.

GRAVITATIONAL LASER BACKSCATTERING

A possible way of producing gravitons in the laboratory is investigated. We evaluate the cross section for electron + photon --> electron + graviton in the framework of linearized gravitation, and analyze this reaction considering the photon coming either from a laser beam or from a Compton backscattering process.

Orbital maneuvers using gravitational capture times

Artificial satellites around the Earth can be temporarily captured by the Moon via gravitational mechanisms., How long the capture remains depends on the phase space region where the trajectory is located. This interval of time (capture time) ranges from less than one day (a single passage), up to 500 days, or even more. Orbits of longer times might be very useful for certain types of missions. The advantage of the ballistic capture is to save fuel consumption in an orbit transference from around the Earth to around the Moon. Some of the impulse needed in the transference is saved by the use of the gravitational forces involved. However, the time needed for the transference is elongated from days to months. In the present work we have mapped a significant part of the phase space of the Earth-Moon system, determining the length of the capture times and the origin of the trajectory, if it comes from the Earth direction, or from the opposite direction. Using such map we present a set of missions considering the utilization of the long capture times. (C) 2003 COSPAR. Published by Elsevier B.V. Ltd. All rights reserved.

FERMION HELICITY FLIP IN WEAK GRAVITATIONAL-FIELDS

The helicity flip of a spin-1/2 Dirac particle interacting gravitationally with a scalar field is analyzed in the context of linearized quantum gravity. It is shown that massive fermions may have their helicity flipped by gravity, in opposition to massless fermions which preserve their helicity.

Gravitational interactions of integrable models

We couple non-linear sigma-models to Liouville gravity, showing that integrability properties of symmetric space models still hold for the matter sector. Using similar arguments for the fermionic counterpart, namely Gross-Neveu-type models, we verify that such conclusions must also hold for them, as recently suggested.

Effects of the eccentricity on the primaries in the gravitational capture phenomenon

Gravitational capture is a characteristic of some dynamical systems in celestial mechanics, as in the elliptic restricted three-body problem that is considered in this paper. The basic idea is that a spacecraft (or any particle with negligible mass) can change a hyperbolic orbit with a small positive energy around a celestial body into an elliptic orbit with a small negative energy without the use of any propulsive system. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third body involved in the dynamics. In this way, this force is used as a zero cost control, equivalent to a continuous thrust applied in the spacecraft. One of the most important applications of this property is the construction of trajectories to the Moon. The objective of the present paper is to study in some detail the effects of the eccentricity of the primaries in this maneuver.

The influence of cation segregation on the methanol decomposition on nanostructured SnO2

Here we describe a new route to synthesize ultrafine rare earth doped and undoped tin oxide particles for catalytic applications. The catalytic behavior observed in SnO2 samples suggests the control of the catalytic activity and the selectivity of the products by the segregation of a layer of a rare earth compound with the increase of the heat-treatment temperature. The ultrafine particles were characterized by means of BET, XPS, TEM, XRD and Rietveld refinement. It was demonstrated that the effects of the dopant on the methanol decomposition reaction and on the H-2 selectivity were correlated with the segregation of a rare earth layer on the tin oxide samples. (C) 2002 Published by Elsevier B.V. B.V.

Sphere of influence and gravitational capture radius: a dynamical approach

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Exact solutions related to nonminimal gravitational coupling

We obtain exact analytic solutions for a typical autonomous dynamical system, related to the problem of a vector field nonminimally coupled to gravity. © 1995.

Gravitational Lorentz force and the description of the gravitational interaction

In the context of a gauge theory for the translation group, we have obtained, for a spinless particle, a gravitational analogue of the Lorentz force. Then, we have shown that this force equation can be rewritten in terms of magnitudes related to either the teleparallel or the Riemannian structures induced in spacetime by the presence of the gravitational field. In the first case, it gives a force equation, with torsion playing the role of force. In the second, it gives the usual geodesic equation of general relativity. The main conclusion is that scalar matter is able to feel any one of the above spacetime geometries, the teleparallel and the metric ones. Furthermore, both descriptions are found to be completely equivalent in the sense that they give the same physical trajectory for a spinless particle in a gravitational field.

Riemannian and teleparallel descriptions of the scalar field gravitational interaction

A comparative study between the metric and the teleparallel descriptions of gravitation is made for the case of a scalar field. In contrast to the current belief that only spin matter could detect the teleparallel geometry, scalar matter being able to feel the metric geometry only, we show that a scalar field is able not only to feel anyone of these geometries, but also to produce torsion. Furthermore, both descriptions are found to be completely equivalent, which means that in fact, besides coupling to curvature, a scalar field couples also to torsion.