Dynamical Models of Terrestrial Planet Formation
  We review the problem of the formation of terrestrial planets, with
particular emphasis on the interaction of dynamical and geochemical models. The
lifetime of gas around stars in the process of formation is limited to a few
million years based on astronomical observations, while isotopic dating of
meteorites and the Earth-Moon system suggest that perhaps 50-100 million years
were required for the assembly of the Earth. Therefore, much of the growth of
the terrestrial planets in our own system is presumed to have taken place under
largely gas-free conditions, and the physics of terrestrial planet formation is
dominated by gravitational interactions and collisions. The earliest phase of
terrestrial-planet formation involve the growth of km-sized or larger
planetesimals from dust grains, followed by the accumulations of these
planetesimals into ~100 lunar- to Mars-mass bodies that are initially
gravitationally isolated from one-another in a swarm of smaller planetesimals,
but eventually grow to the point of significantly perturbing one-another. The
mutual perturbations between the embryos, combined with gravitational stirring
by Jupiter, lead to orbital crossings and collisions that drive the growth to
Earth-sized planets on a timescale of 10-100 million years. Numerical treatment
of this process has focussed on the use of symplectic integrators which can
rapidly integrate the thousands of gravitationally-interacting bodies necessary
to accurately model planetary growth. While the general nature of the
terrestrial planets--their sizes and orbital parameters--seem to be broadly
reproduced by the models, there are still some outstanding dynamical issues.
One of these is the presence of an embryo-sized body, Mars, in our system in
place of the more massive objects that simulations tend to yield. [Abridged]
