Summary: We consider a proto-ring nebula of a gas giant such as Neptune as a cloud of gas/dust particles whose behaviour is governed by the stochastic mechanics associated to the Kepler problem. This leads to a stochastic Burgers-Zeldovich type model for the formation of planetesimals involving a stochastic Burgers equation with vorticity which could help to explain the turbulent behaviour observed in ring systems. The Burgers fluid density and the distribution of the mass \(M(T)\) of a spherical planetesimal of radius {\(\delta\)} are computed for times \(T\). For circular orbits, sufficient conditions on certain time averages of \(\delta^2\) are given ensuring that \({\text Var} M(T) \sim 0\) as \(T \sim \infty\) . Some applications are given to the satellites of Jupiter and Saturn, in particular giving a possible explanation of the equal mass families of satellites.{
©2013 American Institute of Physics}