  We develop the idea proposed by Barge & Sommeria (1995) and Tanga et al.
(1996) that large-scale vortices present in the solar nebula can concentrate
dust particles and facilitate the formation of planetesimals and planets. We
introduce an exact vortex solution of the incompressible 2D Euler equation and
study the motion of dust particles in that vortex. In particular, we derive
analytical expressions for the capture time and the mass capture rate as a
function of the friction parameter. Then, we study how small-scale turbulent
fluctuations affect the motion of the particles in the vortex and determine
their rate of escape by solving a problem of quantum mechanics. We apply these
results to the solar nebula and find that the capture is optimum near Jupiter's
orbit (as noticed already by Barge & Sommeria 1995) but also in the Earth
region. This second optimum corresponds to the transition between the Epstein
and the Stokes regime which takes place, for relevant particles, at the
separation between telluric and giant planets (i.e near the asteroid belt). At
these locations, the particles are efficiently captured and concentrated by the
vortices and can undergo gravitational collapse to form the planetesimals.
