In stellar dynamics, a massive body (star, black hole, etc.) can experience Brownian motion as it responds to gravitational forces from surrounding stars. The rms velocity V of the massive object, of mass M, is related to the rms velocity v ⋆ ⋆ of the background stars by M V 2 ≈ ≈ m v ⋆ ⋆ 2 where m ≪ ≪ M is the mass of the background stars. The gravitational force from the massive object causes nearby stars to move faster than they otherwise would, increasing both v ⋆ ⋆ and V. The Brownian velocity of Sgr A*, the supermassive black hole at the center of the Milky Way galaxy, is predicted from this formula to be less than 1 km s.