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A hybrid symplectic integrator that permits close encounters between massive bodies
Mixed-variable symplectic integrators exhibit no long-term accumulation of energy error, beyond that owing to round-off, and they are substantially faster than conventional N-body algorithms. ThisExpand
Making More Terrestrial Planets
The results of 16 new 3D N-body simulations of the final stage of the formation of the terrestrial planets are presented. These Nbody integrations begin with 150‐160 lunar-to-Mars size planetaryExpand
Source regions and timescales for the delivery of water to the Earth
— 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 investigateExpand
The Stability of Multi-Planet Systems
A system of two small planets orbiting the Sun on low-eccentricity, low-inclination orbits is stable with respect to close encounters if the initial semi-major axis difference, Δ, measured in mutualExpand
Making the Terrestrial Planets: N-Body Integrations of Planetary Embryos in Three Dimensions
We simulate the late stages of terrestrial-planet formation using N-body integrations, in three dimensions, of disks of up to 56 initially isolated, nearly coplanar planetary embryos, plus JupiterExpand
Planetary accretion in the inner Solar System
Abstract Unlike gas-giant planets, we lack examples of terrestrial planets orbiting other Sun-like stars to help us understand how they formed. We can draw hints from elsewhere though. AstronomicalExpand
We describe an analytic model for the evolution of a protoplanetary disk heated by viscous accretion and radiation from the central star. The disk is assumed to be flared and viscosity is assumed toExpand
Late-stage planetary accretion including hit-and-run collisions and fragmentation
Abstract To date, most simulations of the final accretion of the terrestrial planets have assumed that all collisions lead to mergers. Recent hydrodynamic simulations of impacts between planetaryExpand
A semi-analytic model for oligarchic growth
Abstract A new semi-analytic model for the oligarchic growth phase of planetary accretion is developed. The model explicitly calculates damping and excitation of planetesimal eccentricities e andExpand
The origin of water on Mars
Abstract This paper considers the origin of water on Mars, in the context of a dynamical model that accounts for most of the Earth's water as a product of collisions between the growing Earth andExpand