To see this unstable behavior more quantitatively, consider the equations of motion for a fluid element mass in circular motion with an angular velocity formula_6 In general formula_4 will be a function of the distance from the rotation axis formula_5 and we assume that the orbital radius is formula_9 The centripetal acceleration required to keep the mass in orbit is formula_10 the minus sign indicates a direction toward the center. If this force is gravity from a point mass at the center, then the centripetal acceleration is simply formula_11 where formula_12 is the gravitational constant and formula_13 is the central mass.