Dust particle which are initially distributed homogeneously in the solar nebula aggregate and settle towards the equatorial plane. As a result, the solar nebula separate into three layers: and equatorial thin dust-gas layer and two residual gas layers. We study gravitational instabilities in the dust-gas layer on the assumption of axial symmetry, taking account of motions perpendicular to as well as parallel to the equatorial plane and also making use of proper boundary conditions between the dust-gas layer and the gas layers. As far as radii of dust particles are sufficiently small (&Isim;1 cm at 1 au), a dust fluid and a gas fluid are firmly coupled owing to the drag force; consequently, they behave like one fluid. It is also found that the dust-gas layer behaves like an incompressible fluid owing to high pressure of the gas layers exerted on the dust-gas layer. Taking these conditions into account, a mode of gravitational instability accompanied with a motion perpendicular to the equatorial plane is newly found. If unstable wavelengths of the largest growing rate for non-axisymmetric and axisymmetric perturbations are the same, typical masses of planetesimals are 4×10^<17> g at the Earth orbit, 3×10^<20> g at the Jupiter orbit and 4×10^<21> g at the Neptune orbit.
Minoru, SEKIYA., & Department, O. P. K. U. (1983). Gravitational Instabilities in a Dust-Gas Layer and Formation of Planetesimals in the Solar Nebula. Progress of Theoretical Physics, 69(4), 1116-1130. https://doi.org/10.1143/PTP.69.1116