On the dynamics of some resonances of Phobos in the future

A probable capture of Phobos into an interesting resonance was presented in our previous work. With a simple model, considering Mars in a Keplerian and circular orbit, it was shown that once captured in the resonance, the inclination of the satellite reaches very high values. Here, the integrations are extended to much longer times and escape situations are analyzed. These escapes are due to the interaction of new additional resonances, which appear as the inclination starts to increase reaching some specific values. Compared to classical capture in mean motion resonances, we see some interesting differences in this problem. We also include the effect of Mars' eccentricity in the process of the capture. The role played by this eccentricity becomes important, particularly when Phobos encounters a double resonance at a approximate to 2.619R(M). Planetary perturbations acting on Mars and variation of its equator are also included. In general, some possible scenarios of the future of Phobos are presented.

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.

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.

Moonlets wandering on a leash-ring

Since the Voyager flybys, embedded moonlets have been proposed to explain some of the surprising structures observed in Saturn's narrow F ring. Experiments conducted with the Cassini spacecraft support this suggestion. Images of the F ring show bright compact spots, and seven occultations of stars by the F ring, monitored by ultraviolet and infrared experiments, revealed nine events of high optical depth. These results point to a large number of such objects, but it is not clear whether they are solid moonlets or rather loose particle aggregates. Subsequent images suggested an irregular motion of these objects so that a determination of their orbits consistent with the F ring failed. Some of these features seem to cross the whole ring. Here we show that these observations are explained by chaos in the F ring driven mainly by the 'shepherd' moons Prometheus and Pandora. It is characterized by a rather short Lyapunov time of about a few hundred orbital periods. Despite this chaotic diffusion, more than 93 per cent of the F-ring bodies remain confined within the F ring because of the shepherding, but also because of a weak radial mobility contrasted by an effective longitudinal diffusion. This chaotic stirring of all bodies involved prevents the formation of 'propellers' typical of moonlets, but their frequent ring crossings explain the multiple radial 'streaks' seen in the F ring. The related 'thermal' motion causes more frequent collisions between all bodies which steadily replenish F-ring dust and allow for ongoing fragmentation and re-accretion processes (ring recycling).

Postsurgical stability of oropharyngeal airway changes following counter-clockwise maxillo-mandibular advancement surgery

Purpose: This study evaluated oropharyngeal airway changes and stability following surgical counter-clockwise rotation and advancement of the maxillo-mandibular complex.Methods and Patients: Fifty-six adults (48 females, 8 males), between 15 and 51 years of age, were treated with Le Fort I osteotomies and bilateral mandibular ramus sagittal split osteotomies to advance the maxillo-mandibular complex with a counter-clockwise rotation. The average postsurgical follow-up was 34 months. Each patient's lateral cephalograms were traced, digitized twice, and averaged to estimate Surgical changes (T2-T1) and Postsurgical changes (T3-T2).Results: During surgery, the occlusal plane angle decreased significantly (8.6 +/- 5.8 degrees) and the maxillo-mandibular complex advanced and rotated counter-clock-wise. The maxilla moved forward (2.4 +/- 2.7 mm) at ANS and the mandible was advanced 13.1 +/- 5.1 min at menton, 10 +/- 4.4 mm at point B, and 6.9 +/- 3.7 mm at lower incisor edge. Postsurgical hard tissue changes were not statistically significant. While the upper oropharyngeal airway decreased significantly (4.2 +/- 3.4 min) immediately after surgery, the narrowest retropalatal, lowest retropalatal airway, and the narrowest retroglossal airway measurements increased 2.9 +/- 2.7, 3.7 +/- 3.2, and 4.4 +/- 4.4 mm, respectively. Over the average 34 months Postsurgical period, upper retropalatal airway increased 3.9 +/- 3.7 mm, while narrowest retropalatal, lowest retropalatal airway, and narrowest retroglossal airway remained stable. Head posture showed flexure immediately after Surgery (4.8 +/- 5.9 degrees) and extension postsurgically (1.6 +/- 5.6 degrees).Conclusion: Maxillo-mandibular advancement with counter-clockwise rotation produces immediate increases in middle and lower oropharyngeal airway dimensions, which were constrained by changes in head posture but remain stable over the postsurgical period. The upper oropharyngeal airway space increased only on the longest follow-up. (C) 2006 American Association of Oral and Maxillofacial Surgeons.