 Keplerian disk

A Keplerian disk is an astrophysical disk whose orbital motion is governed mainly by a central point mass. Balancing radial gravitational acceleration with circular motion gives $r{\Omega }_K^2=GM/r^2$, hence ${\Omega }_K=\sqrt{GM/r^3}$ and orbital speed $v_K=\sqrt{GM/r}$. Inner rings rotate faster than outer rings: this differential rotation supplies the shear on which many disk stresses act. The approximation requires small corrections from pressure gradients, disk self-gravity and relativistic gravity.