Such approximations are unnecessary, however. Newton's laws of motion allow any classical two-body problem to be converted into a corresponding exact one-body problem. To demonstrate this, let x 1 and x 2 be the positions of the two particles, and let r = x 1 − x 2 be their relative position. Then, by Newton's second law, r ¨ ¨ = x ¨ ¨ 1 − − x ¨ ¨ 2 = ( F 21 m 1 − − F 12 m 2 ) = ( 1 m 1 + 1 m 2 ) F 21