A stochastic Burgers-Zeldovich model for the formation of planetary ring systems and the satellites of Jupiter and Saturn

作者：Neate Andrew^*; Truman Aubrey

来源：Journal of Mathematical Physics, 2013, 54(3): 033512.

DOI：10.1063/1.4794514

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 VarM(T) similar to 0 as T similar to infinity. Some applications are given to the satellites of Jupiter and Saturn, in particular giving a possible explanation of the equal mass families of satellites.

• 出版日期2013-3