Effect of Jupiter's mass growth on satellite capture

We study the effects of Jupiter mass growth in order to permanently capture prograde satellites. Adopting the restricted three-body problem, Sun-Jupiter-Particle, we performed numerical simulations backward in time while considering the decrease in Jupiter's mass. We considered the particle's initial conditions to be prograde, at pericenter, in the region 100R(4) <= a <= 400R(4) and 0 <= e <= 0.5. The results give Jupiter's mass at the moment when the particle escapes from the planet. Such values give an indication of the conditions that are necessary for capture. An analysis of these results shows that prograde satellite capture is more complex than a retrograde one. It occurs in a two-step process. First, when the particles get inside about 0.85R(Hill) (Hills' radius), they become weakly bound to Jupiter. Then, they keep migrating toward the planet with a strong decrease in eccentricity, while the planet is growing. The radial oscillation of the particles reduces significantly when they reach a radial distance that is less than about 0.45R(Hill) from the planet. Three-dimensional simulations for the known prograde satellites of Jupiter were performed. The results indicate that Leda, Himalia, Lysithea, and Elara could have been permanently captured when Jupiter had between 50% and 60% of its present mass.

Possible effects of secular resonances in Phobos and Triton

Due to the tides, the orbits of Phobos and Triton are contracting. While their semi major axes are decreasing, several possibilities of secular resonances involving node, argument of the pericenter and mean motion of the Sun will take place. In the case of Mars, if the obliquity (epsilon), during the passage through some resonances, is not so small, very significant variations of the inclination will appear. In one case, capture is almost certain provided that epsilon greater than or equal to 20degrees. For Triton there are also similar situations, but capture seems to be not possible, mainly because in S-1 state, Triton's orbit is sufficiently inclined (far) with respect to the Neptune's equator. Following Chyba et al. (Astron. Astrophys. 219 (1989) 123), a simplified equation that gives the evolution of the inclination versus the semi major axis, is derived. The time needed for Triton crash onto Neptune is longer than that one obtained by these authors, but the main difference is due to the new data used here. In general, even in the case of non-capture passages, some significant jumps in inclination and in eccentricities are possible. (C) 2002 Elsevier B.V. Ltd. All rights reserved.

The effect of Jupiter's mass growth on satellite capture - Retrograde case

Gravitational capture can be used to explain the existence of the irregular satellites of giants planets. However, it is only the first step since the gravitational capture is temporary. Therefore, some kind of non-conservative effect is necessary to to turn the temporary capture into a permanent one. In the present work we study the effects of Jupiter mass growth for the permanent capture of retrograde satellites. An analysis of the zero velocity curves at the Lagrangian point L-1 indicates that mass accretion provides an increase of the confinement region ( delimited by the zero velocity curve, where particles cannot escape from the planet) favoring permanent captures. Adopting the restricted three-body problem, Sun-Jupiter-Particle, we performed numerical simulations backward in time considering the decrease of M-4. We considered initial conditions of the particles to be retrograde, at pericenter, in the region 100 R-4 less than or equal to a less than or equal to 400 R-4 and 0 less than or equal to e < 0.5. The results give Jupiter's mass at the moment when the particle escapes from the planet. Such values are an indication of the necessary conditions that could provide capture. An analysis of these results shows that retrograde satellites would be captured as soon as they get inside the Hills' radius and after that they keep migrating toward the planet while it is growing. For the region where the orbits of the four old retrograde satellites of Jupiter ( Ananke, Carme, Pasiphae and Sinope) are located we found that such satellites could have been permanently captured when Jupiter had between 62% and 93% of its present mass.

Dynamics of two planets in the 3/2 mean-motion resonance: Application to the planetary system of the pulsar PSR B1257+12

This paper considers the dynamics of two planets, as the planets B and C of the pulsar PSR B1257+12, near a 3/2 mean-motion resonance. A two-degrees-of-freedom model, in the framework of the general three-body planar problem, is used and the solutions are analyzed through surfaces of section and Fourier techniques in the full phase space of the system.

Dynamics of Enceladus and Dione inside the 2:1 mean-motion resonance under tidal dissipation

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

Numerical study about natural escape and capture routes by the Moon via Lagrangian points L1 and L2

The lunar sphere of influence, whose radius is some 66,300 km, has regions of stable orbits around the Moon and also regions that contain trajectories which, after spending some time around the Moon, escape and are later recaptured by lunar gravity. Both the escape and the capture occur along the Lagrangian equilibrium points L1 and L2. In this study, we mapped out the region of lunar influence considering the restricted three-body Earth-Moon-particle problem and the four-body Sun-Earth-Moon-particle (probe) problem. We identified the stable trajectories, and the escape and capture trajectories through the L I and L2 in plots of the eccentricity versus the semi-major axis as a function of the time that the energy of the osculating lunar trajectory in the two-body Moon-particle problem remains negative. We also investigated the properties of these routes, giving special attention to the fact that they supply a natural mechanism for performing low-energy transfers between the Earth and the Moon, and can thus be useful on a great number of future missions. (C) 2007 Published by Elsevier Ltd on behalf of COSPAR.

Determination of pesticide residues in coconut water by liquid-liquid extraction and gas chromatography with electron-capture plus thermionic specific detection and solid-phase extraction and high-performance liquid chromatography with ultraviolet detection

Two simple methods were developed to determine, 11 pesticides in coconut water, a natural isotonic drink rich in salts, sugars and vitamins consumed by the people and athletes. The first procedure involves solid-phase extraction using Sep-Pak Vac C-18 disposable cartridges with methanol for elution. Isocratic analysis was carried out by means of high-performance liquid chromatography with ultraviolet detection at 254 nm to analyse captan, chlorothalonil, carbendazim, lufenuron and diafenthiuron. The other procedure is based on liquid-liquid extraction with hexane-dichloromethane (1:1, v/v), followed by gas chromatographic analysis with effluent splitting to electron-capture detection for determination of endosulfan, captan, tetradifon and trichlorfon and thermionic specific detection for determination of malathion, parathion-methyl and monocrotophos. The methods were validated with fortified samples at different concentration levels (0.01-12.0 mg/kg). Average recoveries ranged from 75 to 104% with relative standard deviations between 1.4 and 11.5%. Each recovery analysis was repeated at least five times. Limits of detection ranged from 0.002 to 2.0 mg/kg. The analytical procedures were applied to 15 samples and no detectable amounts of the pesticides were found in any samples under the conditions described. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Temperature-dependent vortex motion in a square mesoscopic superconducting cylinder: Ginzburg-Landau calculations

In this work we investigate the dynamics of vortices in a square mesoscopic superconductor. As time evolves we show how the vortices are nucleated into the sample to form a multivortex, single vortex, and giant vortex states. We illustrate how the vortices move around at the transition fields before they accommodate into an equilibrium configuration. We also calculate the magnetization and the free energy as functions of the applied magnetic field for several values of temperature. In addition, we evaluate the upper critical field.

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.

Intra-articular pressure profiles of the cadaveric equine fetlock joint in motion

The study of the influence of motion and initial intra-articular pressure (IAP) on intra-articular pressure profiles in equine cadaver metatarsophalangeal (MTP) joints was undertaken as a prelude to in vivo studies, Eleven equine cadaver MTP joints were submitted to 2 motion frequencies of 5 and 10 cycles/min of flexion and extension, simulating the condition of lower and higher (double) rates of passive motion. These frequencies were applied and pressure profiles generated with initial normal intra-articular pressure (-5 mmHg) and subsequently 30 mmHg intra-articular pressure obtained by injection of previously harvested synovial fluid.The 4 trials performed were 1) normal IAP; 5 cyles/min; 2) normal IAP; 10 cycles/min; 3) IAP at 30 mmHg; 5 cycles/min and 4) IAP at 30 mmHg; 10 cycles/min. The range of joint motion applied (mean +/- s.e.) was 67.6 +/- 1.61 degrees with an excursion from 12.2 +/- 1.2 degrees in extension to 56.2 +/- 2.6 degrees in flexion, Mean pressure recorded in mmHg for the first and last min of each trial, respectively, were 1) -5.7 +/- 0.9 and -6.3 +/- 1.1; 2) -5.3 +/- 1.1 and -6.2 +/- 1.1; 3) 58.8 +/- 8.0 and 42.3 +/- 7.2; 4) 56.6 +/- 3.7 and 40.3 +/- 4.6. Statistical analyses showed a trend for difference between the values for the first and last minute in trial 3 (0.05>P<0.1) with P = 0.1 and significant difference (P = 0.02) between the mean IAP of the first and last min in trial 4. The loss of intra-articular pressure associated with time and motion was 10.5, 16.9, 28.1 and 28.9% for trials 1-4, respectively. As initial intraarticular pressure and motion increased, the percent loss of intra-articular pressure increased.The angle of lowest pressure was 12.2 +/- 1.2 (mean +/- s.e.) in extension in trials 1 and 2, In trials 3 and 4, the lowest pressures were obtained in flexion with the joints at 18.5 +/- 2.0 degrees (mean +/- s.e.). This demonstrated that the joint angle of least pressure changed as the initial intra-articular pressure changed and there would not be a single angle of least pressure for a given joint.The volume of synovial fluid recovered from the MTP joints in trial 3 compared to 4 (trials in which fluid was injected to attain IAP of 30 mmHg) was not significantly different, supporting a soft tissue compliance change as a cause for the significant loss of intra-articular pressure during the 15 min of trial 4.The pressure profiles generated correlate well with in vivo values and demonstrated consistent pressure profiles. Our conclusions are summarised as follows:1. Clinically normal equine MTP joints which were frozen and then later thawed were found to have mostly negative baseline intra-articular pressures, as would be expected in living subjects,2. Alternate pressure profiles of the dorsal and plantar pouch at baseline intra-articular pressure document the presence of pressure forces that would support 'back and forth' fluid movement between joint compartments. This should result in movement of joint fluid during motion, assisting in lubrication and nutrition of articular cartilage,3. If joint pressure was initially greater than normal (30 mmHg), as occurs in diseased equine MTP joints, joint motion further increased joint capsule relaxation (compliance) and, therefore, reduced intra-articular pressure.4. Peak intra-articular pressures reached extremely high values (often >100 mmHg) in flexion when initial pressure was 30 mmHg. Joint effusion pressures recorded for clinical MCP joints are frequently 30 mmHg. These IAP values are expected to produce intermittent synovial ischaemia in clinical cases during joint flexion.5, Additional in vivo studies are necessary to confirm our conclusions from this study and to identify the contributions of fluid absorption and the presence of ischaemia in a vascularised joint.

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.

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.