E. Vieira Neto

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 (H enon 1970; Huang & Innanen 1983). Their results are reviewed using Poincar e surface of sections. The stable non-planar retrograde trajectories, 110 o i< 180 o , are found to be tridimensional quasi-periodic orbits around the same family of periodic orbits found for the planar case (i = 180 o ). 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 =6 0 o . Trajectories in such region are found to behave as quasi-periodic orbits evolving similarly to the stable retrograde trajectories that occurs at i = 120 o .

Effect of Jupiter's mass growth on satellite capture The prograde case

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 ≤ a ≤ 400R 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 0.85RHill (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 0.45RHill 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.

A statistical model of aggregate fragmentation

A statistical model of fragmentation of aggregates is proposed, based on the stochastic propagation of cracks through the body. The propagation rules are formulated on a lattice and mimic two important features of the process—a crack moves against the stress gradient while dissipating energy during its growth. We perform numerical simulations of the model for two-dimensional lattice and reveal that the mass distribution for small- and intermediate-size fragments obeys a power law, F(m) / m 3/2 , in agreement with experimental observations. We develop an analytical theory which explains the detected power law and demonstrate that the overall fragment mass distribution in our model agrees qualitatively with that one observed in experiments.

Orbital maneuvers using gravitational capture times

Abstract 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.

Growth and evolution of satellites in a Jovian massive disc

The formation of satellite systems in circum-planetary discs is considered to be similar to the formation of rocky planets in a proto-planetary disc, especially Super-Earths. Thus, it is possible to use systems with large satellites to test formation theories that are also applicable to extrasolar planets. Furthermore, a better understanding of the origin of satellites might yield important information about the environment near the growing planet during the last stages of planet formation. In this work we investigate the formation and migration of the Jovian satellites through N-body simulations. We simulated a massive, static, low viscosity, circum-planetary disc in agreement with the minimum mass sub-nebula model prescriptions for its total mass. In hydrodynamic simulations we found no signs of gaps, therefore type II migration is not expected. Hence, we used analytic prescriptions for type I migration, eccentricity and inclination damping, and performed N-body simulations with damping forces added. Detailed parameter studies showed that the number of final satellites is strong influenced by the initial distribution of embryos, the disc temperature, and the initial gas density profile. For steeper initial density profiles it is possible to form systems with multiple satellites in resonance while a flatter profile favours the formation of satellites close to the region of the Galilean satellites. We show that the formation of massive satellites such as Ganymede and Callisto can be achieved for hotter discs with an aspect ratio of H/r ~ 0.15 for which the ice line was located around 30 R_J.