Chaotic diffusion caused by close encounters with several massive asteroids The (4) Vesta case

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Mean motion resonances and the stability of a circumbinary disk in a triple stellar system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An analysis of the region of the Phocaea dynamical family

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

Nebular gas drag and co-orbital system dynamics

Aims. We study trajectories of planetesimals whose orbits decay due to gas drag in a primordial solar nebula and are perturbed by the gravity of the secondary body on an eccentric orbit whose mass ratio takes values from mu(2) = 10(-7) to mu(2) = 10(-3) increasing ten times at each step. Each planetesimal ultimately suffers one of the three possible fates: (1) trapping in a mean motion resonance with the secondary body; (2) collision with the secondary body and consequent increase of its mass; or (3) diffusion after crossing the orbit of the secondary body.Methods. We take the Burlirsh-Stoer numerical algorithm in order to integrate the Newtonian equations of the planar, elliptical restricted three-body problem with the secondary body and the planetesimal orbiting the primary. It is assumed that there is no interaction among planetesimals, and also that the gas does not affect the orbit of the secondary body.Results. The results show that the optimal value of the gas drag constant k for the 1: 1 resonance is between 0.9 and 1.25, representing a meter size planetesimal for each AU of orbital radius. In this study, the conditions of the gas drag are such that in theory, L4 no longer exists in the circular case for a critical value of k that defines a limit size of the planetesimal, but for a secondary body with an eccentricity larger than 0.05 when mu(2) = 10(-6), it reappears. The decrease of the cutoff collision radius increase the difusions but does not affect the distribution of trapping. The contribution to the mass accretion of the secondary body is over 40% with a collision radius 0.05R(Hill) and less than 15% with 0.005R(Hill) for mu(2) = 10(-7). The trappings no longer occur when the drag constant k reachs 30. That means that the size limit of planetesimal trapping is 0.2 m per AU of orbital radius. In most cases, this accretion occurs for a weak gas drag and small secondary eccentricity. The diffusions represent most of the simulations showing that gas drag is an efficient process in scattering planetesimals and that the trapping of planetesimals in the 1: 1 resonance is a less probable fate. These results depend on the specific drag force chosen.

Dynamics of two satellites in the 2/1 Mean-Motion resonance: application to the case of Enceladus and Dione

The dynamics of a pair of satellites similar to Enceladus-Dione is investigated with a two-degrees-of-freedom model written in the domain of the planar general three-body problem. Using surfaces of section and spectral analysis methods, we study the phase space of the system in terms of several parameters, including the most recent data. A detailed study of the main possible regimes of motion is presented, and in particular we show that, besides the two separated resonances, the phase space is replete of secondary resonances.

On the V-type asteroids outside the Vesta family - II. Is (21238) 1995 WV7 a fragment of the long-lost basaltic crust of (15) Eunomia?

Context. The V-type asteroids are associated with basaltic composition. Apart from ( 1459) Magnya, an asteroid that is clearly dynamically and mineralogically unconnected to the Vesta family, all currently known V-type asteroids are either members of the Vesta family, or are hypothesized to be former members of the dynamical family that migrated to their current orbital positions. The recent identification of ( 21238) 1995 WV7 as a V-type asteroid introduces the possibility that a second basaltic asteroid not connected with the Vesta family exists. This asteroid is on the opposite side of the 3: 1 mean motion resonance with respect to Vesta, and it would be very unlikely that a member of the Vesta family of its size (D > 5km) migrating via either the Yarkovsky effect or repeated close encounters with Vesta survived the passage through such a resonance.Aims. In this work we investigate the possibility that ( 21238) 1995 WV7 originated as a fragment of the parent body of the Eunomia family and then migrated via the interplay of the Yarkovsky effect and some powerful nonlinear secular resonances, such as the (s - s(6)) - ( g(5) - g(6)). If (15) Eunomia is, as claimed, a differentiated object whose originally pyroxene-enriched crust layer was lost in a collision that either created the Eunomia family or preceded its formation, can (21238) be a fragment of its long-lost basaltic crust that migrated to the current position?Methods. We mapped the phase space around (21238) and determined which of the nonlinear secular resonances that we identified are stronger and more capable of having caused the current difference in proper i between (21238) and members of the Eunomia family. We simulated the Yarkovsky effect by using the SWIFT-RMVSY integrator.Results. Our results suggest that it is possible to migrate from the Eunomia dynamical family to the current orbital location of ( 21238) via the interplay of the Yarkovsky effect and the (s - s6) - (g5 - g6) nonlinear secular resonance, on time-scales of at least 2.6 Gyr.Conclusions. (15) Eunomia might be the third currently known parent body for V-type asteroids.

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.

Stable satellites around extrasolar giant planets

In this work, we study the stability of hypothetical satellites of extrasolar planets. Through numerical simulations of the restricted elliptic three-body problem we found the borders of the stable regions around the secondary body. From the empirical results, we derived analytical expressions of the critical semimajor axis beyond which the satellites would not remain stable. The expressions are given as a function of the eccentricities of the planet, e(P), and of the satellite, e(sat). In the case of prograde, satellites, the critical semimajor axis, in the units of Hill's radius, is given by a(E) approximate to 0.4895 (1.0000 - 1.0305e(P) - 0.2738e(sat)). In the case of retrograde satellites, it is given by a(E) approximate to 0.9309 (1.0000 - 1.0764e(P) - 0.9812e(sat)). We also computed the satellite stability region (a(E)) for a set of extrasolar planets. The results indicate that extrasolar planets in the habitable zone could harbour the Earth-like satellites.

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 exploration of resonant dynamics in the system of Saturnian major satellites

We numerically investigate the long-term dynamics of the Saturnian system by analyzing the Fourier spectra of ensembles of orbits taken around the current orbits of Mimas, Enceladus, Tethys, Rhea and Hyperion. We construct dynamical maps around the current position of these satellites in their respective phase spaces. The maps are the result of a great deal of numerical simulations where we adopt dense sets of initial conditions and different satellite configurations. Several structures associated to the current two-body mean-motion resonances, unstable regions associated to close approaches between the satellites, and three-body mean-motion resonances in the system, are identified in the map. (C) 2010 Elsevier Ltd. All rights reserved.

Instability zones for satellites of asteroids: The example of the (87) Sylvia system

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

Distant stable direct orbits around the Moon

In the present work we explore regions of distant direct stable orbits around the Moon. First, the location and size of apparently stable regions are searched for numerically, adopting the approach of temporary capture time presented in Vieira Neto & Winter (2001). The study is made in the framework of the planar, circular, restricted three-body problem, Earth-Moon-particle. Regions of the initial condition space whose trajectories are apparently stable are determined. The criterion adopted was that the trajectories do not escape from the Moon during an integration period of 10(4) days. Using Poincare surface of sections the reason for the existence of the two stable regions found is studied. The stability of such regions proved to be due to two families of simple periodic orbits, h1 and h2, and the associated quasi-periodic orbits that oscillate around them. The robustness of the stability of the larger region, h2, is tested with the inclusion of the solar perturbation. The size of the region decreases, but it is still significant in size and can be useful in spacecraft missions.

EXPANSION OF THE DISTURBING FUNCTION FOR HIGH ECCENTRICITY AND LARGE-AMPLITUDE OF LIBRATION

Following some ideas, developed by Woltjer (1928), Message (1989), Yokoyama (1988, 1989) and Duriez (1990) an expansion of the disturbing function is given for high values of the eccentricity and large amplitude of libration. The classical expansion can be obtained as a particular case of the present model. Several asteroids with high eccentricity and large amplitude of libration are tested and the results are much better than those obtained from the classical theory.