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

Neate, Andrew and Truman, Aubrey (2013). A stochastic Burgers-Zeldovich model for the formation of planetary ring systems and the satellites of Jupiter and Saturn. Journal of Mathematical Physics, 54(3), article no. 033512.

DOI: https://doi.org/10.1063/1.4794514

Abstract

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 δ are computed for times T. For circular orbits, sufficient conditions on certain time averages of δ2 are given ensuring that VarM(T) ∼ 0 as T ∼ ∞. Some applications are given to the satellites of Jupiter and Saturn, in particular giving a possible explanation of the equal mass families of satellites.

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