Stereographic projection of Hopf field on the 3-sphere into Euclidean 3-space is used as a model of 3D steady flow of ideal compressible fluid in MHD. In such case, flow lines are Villarceau circles lying on tori corresponding to the levels of Bernoulli function. Existence of an optimal torus with minimal relative surface free energy is shown. Beat of oscillations with wave numbers corresponding to structural radii of optimal torus leads to scaling of optimal tori. Spatial intersection of homothetic tori within one torus result in formation of cluster with the size depending on scaling factor. Optimal tori are considered as precursors of planetary orbits. We found that scaling factor of solar system precisely corresponds to an optimal torus. Scaling factors of satellite systems have deviations depending on central body axial tilt and local ratio of semi-major axes of neighbor planets.
At least two stages of toroidal flow development have been determined in nebula. At first stage, nebula was uniform, and tori separation brought about linear dependence of logarithm of relative volumes of planets on logarithm of relative semi-major axes. All regular satellites of giant planets with increasing volumes at increasing semi-major axes have distribution approximated by linear dependence with high degree of correlation. In suggestion on absence of dissipation of particles involved in toroidal flow around planets, high correlation confirms that density of particles in all satellite systems was similar. Moon has close parameters to concerned distribution, thereby suggesting that its formation has been processed by common mechanism. Triton's parameters fit well the distribution of regular Neptune's satellites. This means that formation of Triton and regular Neptune's satellites was simultaneous. At second stage, main stream of flow was located on tori thus resulting in formation of paired planets with neighbor orbits and equal volumes. We found that number of pairs in a system depends on cluster size.