The first generalization of Newton's theorem was discovered by Mahomed and Vawda in 2000. As Newton did, they assumed that the angular motion of the second particle was k times faster than that of the first particle, θ 2 = k θ 1. In contrast to Newton, however, Mahomed and Vawda did not require that the radial motion of the two particles be the same, r 1 = r 2. Rather, they required that the inverse radii be related by a linear equation