It is desired to stabilize a near-Earth spacecraft against random disturbance torques using gravity-gradient?

It is desired to stabilize a near-Earth spacecraft against random disturbance torques using gravity-gradient stabilization. This is accomplished by attaching a long m less boom to the spacecraft bus, at the end of which is a proof m. If the spacecraft bus (except boom) is spherical with a m of 200kg and a radius of 1m and the m is 5kg, the random disturbance torques are ~ 10^-4 Nm, how long must the boom be to maintain a constant attitude with 10, 1 and 0.1 degrees? Does the result depend on the radius of the spacecraft bus?