  It has been long proposed that, if all the terrestrial planets form within a
tiny ring of solid material at around 1 AU, the concentrated mass-distance
distribution of the current system can be reproduced. Recent planetesimal
formation models also support this idea. In this study, we revisit the ring
model by performing a number of high-resolution N-body simulations for 10 Myr
of a ring of self-interacting planetesimals, with various radial distributions
of the gas disc. We found that even if all the planetesimals form at ~1 AU in a
minimum mass solar nebula-like disc, the system tends to spread radially as
accretion proceeds, resulting in a system of planetary embryos lacking
mass-concentration at ~1 AU. Modifying the surface density of the gas disc into
a concave shape with a peak at ~1 AU helps to maintain mass concentrated at ~1
AU and solve the radial dispersion problem. We further propose that such a disc
should be short lived (<= 1 Myr) and with a shallower radial gradient in the
innermost region (< 1 AU) than previously proposed to prevent a too-rapid
growth of Earth. Future studies should extend to ~100 Myr the most promising
simulations and address in a self-consistent manner the evolution of the
asteroid belt and its role in the formation of the terrestrial planets.
