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 note on the horseshoe confinement model: the Poynting-Robertson effect

In the present work we numerically simulated the motion of particles coorbital to a small satellite under the Poynting-Robertson light drag effect in order to verify the symmetry suggested by Dermott et al. (1979, 1980) on their ring confinement model. The results reveal a more complex scenario, especially for very small particles (micrometer sizes), which present chaotic motion. Despite the complexity of the trajectories the particles remain confined inside the coorbital region. However, the dissipative force caused by the solar radiation also includes the radiation pressure component which can change this configuration. Our results show that the inclusion of the radiation pressure, which is not present in the original confinement model, can destroy the configuration in a time much shorter than the survival time predicted for a dust particle in a horseshoe orbit with a satellite.

On the scattering of comets by a planet

In this paper, numerical simulations are made, using the three-dimensional restricted three-body problem as the mathematical model, to calculate the effects of a swing-by with the planet Saturn in the orbit of a comet. To show the results, the orbit of the comet is classified in four groups: elliptic direct, elliptic retrograde, hyperbolic direct and hyperbolic retrograde. Then, the modification in the orbit of the comet due to the close approach is shown in plots that specify from which group the comet's orbit is coming and to which group it is going. Several families of orbits are found and shown in detail. An analysis about the trends as parameters (position and velocity at the periapse) vary is performed and the influence of each of them is shown and explained. The result is a collection of maps that describe the evolution of the trajectory of the comet due to the close approach. Those maps can be used to estimate the probability of some events, like the capture or escape of a comet. An example of this technique is shown in the paper. (C) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

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.

UNITARY POLE APPROXIMATION FOR THE COULOMB-PLUS-YAMAGUCHI POTENTIAL AND APPLICATION TO A 3-BODY BOUND-STATE CALCULATION

The unitary pole approximation is used to construct a separable representation for a potential U which consists of a Coulomb repulsion plus an attractive potential of the Yamaguchi type. The exact bound-state wave function is employed. U is chosen as the potential which binds the proton in the 1d5/2 single-particle orbit in F-17. Using the separable representation derived for U, and assuming a separable Yamaguchi potential to describe the 1d5/2 neutron in O-17, the energies and wave functions of the ground state (1+) and the lowest 0+ state of F-18 are calculated in the Gore-plus-two-nucleons model solving the Faddeev equations.

ANATOMICAL STUDY OF THE OPOSSUM (DIDELPHIS-ALBIVENTRIS) EXTRAOCULAR-MUSCLES

The anatomy of the extraocular muscles was studied in 10 adult opossums (Didelphis albiventris) of both sexes. Eight extraocular muscles were identified: 4 rectus muscles, 2 oblique muscles, the levator palpebrae superioris and the retractor ocular bulbi. The rectus muscles originate very close one to another between the orbital surfaces of the presphenoid and palatine bones. These muscles diverge on the way to their insertion which occurs at about 2 mm from the limbus. The levator palpebrae superioris originates with the dorsal rectus and is positioned dorsally in relation to it. The retractor ocular bulbi forms a cone which embraces the optic nerve and is located internally in relation to the rectus muscles. The dorsal oblique originates on the presphenoid bone and after a tendinous trajectory through a trochlea on the medial wall of the orbit, inserts into the ocular bulb. The only muscle arising from the anterior orbital floor is the ventral oblique. The main nerve supply for these muscles is the oculomotor, except for the dorsal oblique which is innervated by the trochlear nerve, and the lateral rectus which is innervated by the abducens nerve. The retractor ocular bulbi receives branches from the inferior division of the oculomotor nerve and some branches from the abducens nerve.

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.

Q-ANALOG REALIZATION OF NUCLEON PAIRING

A q-deformed analogue of zero-coupled nucleon pair states is constructed and the possibility of accounting for pairing correlations examined. For the single orbit case, the deformed pairs are found to be more strongly bound than the pairs with zero deformation, when a real-valued q parameter is used. It is found that an appropriately scaled deformation parameter reproduces the empirical few nucleon binding energies for nucleons in the 1f7/2 orbit and 1g9/2 orbit. The deformed pair Hamiltonian apparently accounts for many-body correlations, the strength of higher-order force terms being determined by the deformation parameter q. An extension to the multishell case, with deformed zero-coupled pairs distributed over several single particle orbits, has been realized. An analysis of calculated and experimental ground state energies and the energy spectra of three lowermost 0+ states, for even-A Ca isotopes, reveals that the deformation simulates the effective residual interaction to a large extent.

Interspecies variation in orbital bone structure of psittaciform birds (with emphasis on Psittacidae)

Objectives: This text presents an anatomical study of the normal bony orbital structure of a sample of different bird species belonging to the order Psittaciformes.Procedures: the bony anatomy of Psittaciformes' skulls was examined and described using cadavers of birds that were presented already dead to the Federal University of Parana, Brazil or had been euthanized for humane reasons. Dissections of the orbital cavity were performed under 2-4 x magnification, and descriptions of the orbital bones were made from observations of macerated skulls that had been boiled and cleaned. The present paper discusses the main features of the bony orbit of psittaciform birds, describing known anatomical information but also bringing new information, mainly concerning species differences that might help not only veterinary anatomists but also zoologists, clinicians, researchers, and students of veterinary ophthalmology to better comprehend this order of birds.Results and conclusions: Variations in the anatomic conformation of the bony elements of the orbit were observed in different species of Psittaciformes. Based on these differences, Psittaciformes were classified into two different groups. The first group of Psittaciformes shows an enclosed (complete) bony orbit formed by the junction of the orbital with the postorbital processes, creating a suborbital arch. The second group of Psittaciformes essentially lacked a suborbital arch, presenting an open (incomplete) bony orbit, typical of most modern birds. In the latter group, orbital and postorbital processes are present.

Anatomical aspects of the lacrimal gland of the tufted capuchin (Cebus apella)

In the tufted capuchin (Cebus apella) the main lacrimal gland is composed of 2 distinct portions with an intraorbital and extraorbital localisation, interconnected by a bridge of glandular tissue which crosses the lateral orbital wall through the lateral orbital fissure located in the sphenozygomatic suture. The intraorbital lacrimal gland is flattened and extremely thin, with a variable outline. It lies on the upper and outer third of the globe of the eye, and the aponeurosis and the belly of the lateral rectus muscle, extending antero-posteriorly from the upper lateral angle of the orbit midway along the orbital cavity. The extraorbital lacrimal gland is compact, halfmoon-shaped, with 3 surfaces, 3 borders and 2 extremities. It lies in the temporal fossa between the temporalis muscle and the temporal surface of the zygomatic bone, fitting into a depression in this bone, and totally surrounded by adipose tissue. The secretory cells have a flocculent appearance and either low or high density. They possess a basal region containing the nucleus and rich in granular endoplasmic reticulum, and an apical region filled with secretory granules varying in size, form and density.

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.

Analytical attitude propagation with non-singular variables and gravity gradient torque for spin stabilized satellite

An analytical approach for the spin stabilized satellite attitude propagation is presented using the non-singular canonical variables to describe the rotational motion. Two sets of variables were introduced for Fukushima in 1994 by a canonical transformation and they are useful when the angle between z-satellite axis of a coordinate system fixed in artificial satellite and the rotational angular momentum vector is zero or when the angle between Z-equatorial axis and rotation angular momentum vector is zero. Analytical solutions for rotational motion equations and torque-free motion are discussed in terms of the elliptic functions and by the application of some simplification to get an approximated solution. These solutions are compared with a numerical solution and the results show a good agreement for many rotation periods. When the mean Hamiltonian associated with the gravity gradient torque is included, an analytical solution is obtained by the application of the successive approximations' method for the satellite in an elliptical orbit. These solutions show that the magnitude of the rotation angular moment is not affected by the gravity gradient torque but this torque causes linear and periodic variations in the angular variables, long and short periodic variations in Z-equatorial component of the rotation angular moment and short periodic variations in x-satellite component of the rotation angular moment. The goal of this analysis is to emphasize the geometrical and physical meaning of the non-singular variables and to validate the approximated analytical solution for the rotational motion without elliptic functions for a non-symmetrical satellite. The analysis can be applied for spin stabilized satellite and in this case the general solution and the approximated solution are coincidence. Then the results can be used in analysis of the space mission of the Brazilian Satellites. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

ESR STUDY OF CUCL2 ADSORBED ON A CHEMICALLY-MODIFIED SILICA-GEL SURFACE WITH BENZIMIDAZOLE MOLECULE

The ESR spectrum of CuCl2 adsorbed onto a silica gel surface chemically modified with the benzimidazole molecule showed that the surface complex has an octahedral symmetry with tetragonal distortion. The measured ESR parameters were g(parallel to) = 2.287, g(perpendicular to) = 2.062, A(parallel to) = 153 G and superhyperfine splitting A(N) = 15 G. The fit of the theoretical expressions to the experimental data was very reasonable. The effective spin orbit coupling constant for Cu2+ was reduced from its normal free ion value of lambda = -828 cm(-1) by as much as 30%. This reduction of lambda is normal in the solid state and in frozen solution complexes.

Resonance and chaos .1. First-order interior resonances

Analytical models for studying the dynamical behaviour of objects near interior, mean motion resonances are reviewed in the context of the planar, circular, restricted three-body problem. The predicted widths of the resonances are compared with the results of numerical integrations using Poincare surfaces of section with a mass ratio of 10(-3) (similar to the Jupiter-Sun case). It is shown that for very low eccentricities the phase space between the 2:1 and 3:2 resonances is predominantly regular, contrary to simple theoretical predictions based on overlapping resonance. A numerical study of the 'evolution' of the stable equilibrium point of the 3:2 resonance as a function of the Jacobi constant shows how apocentric libration at the 2:1 resonance arises; there is evidence of a similar mechanism being responsible for the centre of the 4:3 resonance evolving towards 3:2 apocentric libration. This effect is due to perturbations from other resonances and demonstrates that resonances cannot be considered in isolation. on theoretical grounds the maximum libration width of first-order resonances should increase as the orbit of the perturbing secondary is approached. However, in reality the width decreases due to the chaotic effect of nearby resonances.

Periodic collisions between the moon Prometheus and Saturn's F ring

Saturn's F ring, which lies 3,400 km beyond the edge of the main ring system, was discovered by the Pioneer 11 spacecraft(1) in 1979. It is a narrow, eccentric ring which shows an unusual 'braided' appearance in several Voyager 1 images' obtained in 1980, although it appears more regular in images from Voyager 2 obtained nine months later(3). The discovery of the moons Pandora and Prometheus orbiting on either side of the ring provided a partial explanation for some of the observed features(4). Recent observations of Prometheus(5,6) by the Hubble Space Telescope show, surprisingly, that it is lagging behind its expected position by similar to 20 degrees. By modelling the dynamical evolution of the entire Prometheus-F ring-Pandora system, we show here that Prometheus probably encountered the core of the F ring in 1994 and that it may still be entering parts of the ring once per orbit. Collisions with objects in the F ring provide a plausible explanation for the observed lag and imply that the mass of the F ring is probably less than 25% that of Prometheus.