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Jupiter and Saturn formed in a few million years (ref. 1) from a gas-dominated protoplanetary disk, and were susceptible to gas-driven migration of their orbits on timescales of only ∼100,000 years (ref. 2). Hydrodynamic simulations show that these giant planets can undergo a two-stage, inward-then-outward, migration. The terrestrial planets finished accreting much later, and their characteristics, including Mars' small mass, are best reproduced by starting from a planetesimal disk with an outer edge at about one astronomical unit from the Sun (1 au is the Earth-Sun distance). Here we report simulations of the early Solar System that show how the inward migration of Jupiter to 1.5 au, and its subsequent outward migration, lead to a planetesimal disk truncated at 1 au; the terrestrial planets then form from this disk over the next 30-50 million years, with an Earth/Mars mass ratio consistent with observations. Scattering by Jupiter initially empties but then repopulates the asteroid belt, with inner-belt bodies originating between 1 and 3 au and outer-belt bodies originating between and beyond the giant planets. This explains the significant compositional differences across the asteroid belt. The key aspect missing from previous models of terrestrial planet formation is the substantial radial migration of the giant planets, which suggests that their behaviour is more similar to that inferred for extrasolar planets than previously thought.

Planetary formation theories suggest that the giant planets formed on circular and coplanar orbits. The eccentricities of Jupiter, Saturn and Uranus, however, reach values of 6 per cent, 9 per cent and 8 per cent, respectively. In addition, the inclinations of the orbital planes of Saturn, Uranus and Neptune take maximum values of approximately 2 degrees with respect to the mean orbital plane of Jupiter. Existing models for the excitation of the eccentricity of extrasolar giant planets have not been successfully applied to the Solar System. Here we show that a planetary system with initial quasi-circular, coplanar orbits would have evolved to the current orbital configuration, provided that Jupiter and Saturn crossed their 1:2 orbital resonance. We show that this resonance crossing could have occurred as the giant planets migrated owing to their interaction with a disk of planetesimals. Our model reproduces all the important characteristics of the giant planets' orbits, namely their final semimajor axes, eccentricities and mutual inclinations.

Jupiter's Trojans are asteroids that follow essentially the same orbit as Jupiter, but lead or trail the planet by an angular distance of approximately 60 degrees (co-orbital motion). They are hypothesized to be planetesimals that formed near Jupiter and were captured onto their current orbits while Jupiter was growing, possibly with the help of gas drag and/or collisions. This idea, however, cannot explain some basic properties of the Trojan population, in particular its broad orbital inclination distribution, which ranges up to approximately 40 degrees (ref. 8). Here we show that the Trojans could have formed in more distant regions and been subsequently captured into co-orbital motion with Jupiter during the time when the giant planets migrated by removing neighbouring planetesimals. The capture was possible during a short period of time, just after Jupiter and Saturn crossed their mutual 1:2 resonance, when the dynamics of the Trojan region were completely chaotic. Our simulations of this process satisfactorily reproduce the orbital distribution of the Trojans and their total mass.

Although it is well known that a massive planet opens a gap in a proto-planetary gaseous disk, there is no analytic description of the surface density profile in and near the gap. The simplest approach, which is based upon the balance between the torques due to the viscosity and the gravity of the planet and assumes local damping, leads to gaps with overestimated width, especially at low viscosity. Here, we take into account the fraction of the gravity torque that is evacuated by pressure supported waves. With a novel approach, which consists of following the fluid elements along their trajectories, we show that the flux of angular momentum carried by the waves corresponds to a pressure torque. The equilibrium profile of the disk is then set by the balance between gravity, viscous and pressure torques. We check that this balance is satisfied in numerical simulations, with a planet on a fixed circular orbit. We then use a reference numerical simulation to get an ansatz for the pressure torque, that yields gap profiles for any value of the disk viscosity, pressure scale height and planet to primary mass ratio. Those are in good agreement with profiles obtained in numerical simulations over a wide range of parameters. Finally, we provide a gap opening criterion that simultaneously involves the planet mass, the disk viscosity and the aspect ratio.

Abstract-In the primordial solar system, the most plausible sources of the water accreted by the Earth were in the outer asteroid belt, in the giant planet regions, and in the Kuiper Belt. We investigate the implications on the origin of Earth's water of dynamical models of primordial evolution of solar system bodies and check them with respect to chemical constraints. We find that it is plausible that the Earth accreted water all along its formation, from the early phases when the solar nebula was still present to the late stages of gas-free sweepup of scattered planetesimals. Asteroids and the comets from the Jupiter-Saturn region were the first water deliverers, when the Earth was less than half its present mass. The bulk of the water presently on Earth was carried by a few planetary embryos, originally formed in the outer asteroid belt and accreted by the Earth at the final stage of its formation. Finally, a late veneer, accounting for at most 10% of the present water mass, occurred due to comets from the Uranus-Neptune region and from the Kuiper Belt. The net result of accretion from these several reservoirs is that the water on Earth had essentially the D/H ratio typical of the water condensed in the outer asteroid belt. This is in agreement with the observation that the D/H ratio in the oceans is very close to the mean value of the D/H ratio of the water inclusions in carbonaceous chondrites.

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Icarus, 204, pp. 558-573 (2009)International audienc