Gravitational scattering is the deflection of the paths of particles passing near a massive body. For small angle scattering, the change in velocity is given by
where F is the gravitational force and m is the mass of the scattering particle. The perpendicular component of the speed change is then given by
where is the angle with respect to the initial unperturbed trajectory. Using
where is perpendicular offset gives
where b is the so-called impact parameter and r is the distance from the central mass.
