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 ≈ 0.4895 (1.0000 − 1.0305e P − 0.2738e sat ). In the case of retrograde satellites, it is given by a E ≈ 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.

Reproducing the large Earth/Mars mass ratio requires a strong mass depletion in solids within the protoplanetary disk between 1 and 3 AU. The Grand Tack model invokes a specific migration history of the giant planets to remove most of the mass initially beyond 1 AU and to dynamically excite the asteroid belt. However, one could also invoke a steep density gradient created by inward drift and pile-up of small particles induced by gas-drag, as has been proposed to explain the formation of closein super Earths. Here we show that the asteroid belt's orbital excitation provides a crucial constraint against this scenario for the Solar System. We performed a series of simulations of terrestrial planet formation and asteroid belt evolution starting from disks of planetesimals and planetary embryos with various radial density gradients and including Jupiter and Saturn on nearly circular and coplanar orbits. Disks with shallow density gradients reproduce the dynamical excitation of the asteroid belt by gravitational self-stirring but form Mars analogs significantly more massive than the real planet. In contrast, a disk with a surface density gradient proportional to r −5.5 reproduces the Earth/Mars mass ratio but leaves the asteroid belt in a dynamical state that is far colder than the real belt. We conclude that no disk profile can simultaneously explain the structure of the terrestrial planets and asteroid belt. The asteroid belt must have been depleted and dynamically excited by a different mechanism such as, for instance, in the Grand Tack scenario.

Models of terrestrial planet formation for our solar system have been successful in producing planets with masses and orbits similar to those of Venus and Earth. However, these models have generally failed to produce Mars-sized objects around 1.5 AU. The body that is usually formed around Mars' semimajor axis is, in general, much more massive than Mars. Only when Jupiter and Saturn are assumed to have initially very eccentric orbits (e ∼ 0.1), which seems fairly unlikely for the solar system, or alternately, if the protoplanetary disk is truncated at 1.0 AU, simulations have been able to produce Mars-like bodies in the correct location. In this paper, we examine an alternative scenario for the -2formation of Mars in which a local depletion in the density of the protosolar nebula results in a non-uniform formation of planetary embryos and ultimately the formation of Mars-sized planets around 1.5 AU. We have carried out extensive numerical simulations of the formation of terrestrial planets in such a disk for different scales of the local density depletion, and for different orbital configurations of the giant planets. Our simulations point to the possibility of the formation of Mars-sized bodies around 1.5 AU, specifically when the scale of the disk local mass-depletion is moderately high (50-75%) and Jupiter and Saturn are initially in their current orbits. In these systems, Mars-analogs are formed from the protoplanetary materials that originate in the regions of disk interior or exterior to the local mass-depletion. Results also indicate that Earth-sized planets can form around 1 AU with a substantial amount of water accreted via primitive water-rich planetesimals and planetary embryos. We present the results of our study and discuss their implications for the formation of terrestrial planets in our solar system. Subject headings: Planets and satellites: formation; Methods: numericalA planet-forming disk is a complex and dynamic environment. During the course of

Abstract. In this work we study the basic aspects concerning the stability of the outer satellites of Jupiter. Including the effects of the four giant planets and the Sun we study a large grid of initial conditions. Some important regions where satellites cannot survive are found. Basically these regions are due to Kozai and other resonances. We give an analytical explanation for the libration of the pericenters − J . Another different center is also found. The period and amplitude of these librations are quite sensitive to initial conditions, so that precise observational data are needed for Pasiphae and Sinope. The effect of Jupiter's mass variation is briefly presented. This effect can be responsible for satellite capture and also for locking − J in temporary libration.

The rotational fission of asteroids has been studied previously with simplified models restricted to planar motion. However, the observed physical configuration of contact binaries leads one to conclude that most of them are not in a planar configuration and hence would not be restricted to planar motion once they undergo rotational fission. This motivated a study of the evolution of initially non-planar binaries created by fission. Using a two-ellipsoid model, we performed simulations taking only gravitational interactions between components into account. We simulate 91 different initial inclinations of the equator of the secondary body for 19 different mass ratios. After disruption, the binary system dynamics are chaotic, as predicted from theory. Starting the system in a non-planar configuration leads to a larger energy and enhanced coupling between the rotation state of the smaller fissioned body and the evolving orbital system, and enables re-impact to occur. This leads to differences with previous planar studies, with collisions and secondary spin fission occurring for all mass ratios with inclinations θ 0 ≥ 40 o , and mimics a Lidov-Kozai mechanism. Out of 1729 studied cases, we found that ∼14 per cent result in secondary fission, ∼25 per cent result in collisions and ∼6 per cent have lifetimes longer than 200 yr. In Jacobson & Scheeres stable binaries only formed in cases with mass ratios q < 0.20. Our results indicate that it should be possible to obtain a stable binary with the same mechanisms for cases with mass ratios larger than this limit, but that the system should start in a non-planar configuration.

One of the most important subjects of debate in the formation of the solar system is the origin of Earth's water. Comets have long been considered as the most likely source of the delivery of water to Earth. However, elemental and isotopic arguments suggest a very small contribution from these objects. Other sources have also been proposed, among which, local adsorption of water vapor onto dust grains in the primordial nebula and delivery through planetesimals and planetary embryos have become more prominent. However, no sole source of water provides a satisfactory explanation for Earth's water as a whole. In view of that, using numerical simulations, we have developed a compound model incorporating both the principal endogenous and exogenous theories, and investigating their implications for terrestrial planet formation and water-delivery. Comets are also considered in the final analysis, as it is likely that at least some of Earth's water has cometary origin. We analyze our results comparing two different water distribution models, and complement our study using D/H ratio, finding possible relative contributions from each source, focusing on planets formed in the habitable zone. We find that the compound model play an important role by showing more advantage in the amount and time of water-delivery in Earth-like planets.

The Centaur population is composed by minor bodies wandering between the giant planets and that frequently perform close gravitational encounters with these planets, which leads to a chaotic orbital evolution. Recently, the discovery of two well-defined narrow rings was announced around the Centaur 10199 Chariklo. The rings are assumed to be in the equatorial plane of Chariklo and to have circular orbits. The existence a well-defined system of rings around a body in such perturbed orbital region poses an interesting new problem. Are the rings of Chariklo stable when perturbed by close gravitational encounters with the giant planets? Our approach to address this question consisted of forward and backward numerical simulations of 729 clones of Chariklo, with similar initial orbits, for a period of 100 Myrs. We found, on average, that each clone suffers along its lifetime more than 150 close encounters with the giant planets within one Hill radius of the planet in question. We identified some extreme close encounters able to significantly disrupt or to disturb the rings of Chariklo. About 3 % of the clones lose the rings and about 4 % of the clones have the ring significantly disturbed. Therefore, our results show that in most of the cases (more than 90 %) the close encounters with the giant planets do not affect the stability of the rings in Chariklo-like systems. Thus, if there is an efficient mechanism that creates the rings, then these structures may be common among these kinds of Centaurs.Subject headings: minor planets: individual (10199 Chariklo), planets and satellites: rings, planets and satellites: dynamical evolution and stability

Space missions are an excellent way to increase our knowledge of asteroids. Near‐Earth asteroids (NEAs) are good targets for such missions, as they periodically approach the orbit of the Earth. Thus, an increasing number of missions to NEAs are being planned worldwide. Recently, NEA (153591) 2001 SN263 was chosen as the target of the ASTER MISSION – the First Brazilian Deep Space Mission, with launch planned for 2015. NEA (153591) 2001 SN263 was discovered in 2001. In 2008 February, radio astronomers from Arecibo‐Puerto Rico concluded that (153591) 2001 SN263 is actually a triple system. The announcement of ASTER MISSION has motivated the development of the present work, whose goal is to characterize regions of stability and instability of the triple system (153591) 2001 SN263. Understanding and characterizing the stability of such a system is an important component in the design of the mission aiming to explore it. The method adopted consisted of dividing the region around the system into four distinct regions (three of them internal to the system and one external). We performed numerical integrations of systems composed of seven bodies, namely the Sun, Earth, Mars, Jupiter and the three components of the asteroid system (Alpha, the most massive body; Beta the second most massive body; and Gamma, the least massive body), and of thousands of particles randomly distributed within the demarcated regions, for the planar and inclined prograde cases. The results are displayed as diagrams of semi‐major axis versus eccentricity that show the percentage of particles that survive for each set of initial conditions. The regions where 100 per cent of the particles survive are defined as stable regions. We found that the stable regions are in the neighbourhood of Alpha and Beta, and in the external region. Resonant motion of the particles with Beta and Gamma was identified in the internal regions, leading to instability. For particles with I > 45° in the internal region, where I is the inclination with respect to Alpha’s equator, there is no stable region, except for particles placed very close to Alpha. The stability in the external region is not affected by the variation of inclination. We also present a discussion of the long‐term stability in the internal region, for the planar and circular case, with comparisons with the short‐term stability.