If A is the areal velocity of a planet of mass M , then its angular momentum is

Step-by-step solution

The areal velocity of a planet is defined as the rate at which the area is swept by the radius vector, given by dA dt = 1 2 r^2 d dt . The angular momentum L of a planet of mass M moving in an orbit is given by L = mvr = mr^2 , where = d dt . Substituting into the expression for angular momentum, we get L = M r^2 d dt . Comparing this with the expression for areal velocity A = 1 2 r^2 d dt , we see that r^2 d dt = 2A . Therefore, L = M(2A) = 2MA . Answer: 2 MA