r ¨ ¨ 1 = − − G m 2 r 1 − − r 2 | r 1 − − r 2 | 3 − − G m 3 r 1 − − r 3 | r 1 − − r 3 | 3 , r ¨ ¨ 2 = − − G m 3 r 2 − − r 3 | r 2 − − r 3 | 3 − − G m 1 r 2 − − r 1 | r 2 − − r 1 | 3 , r ¨ ¨ 3 = − − G m 1 r 3 − − r 1 | r 3 − − r 1 | 3 − − G m 2 r 3 − − r 2 | r 3 − − r 2 | 3 . where G is the gravitational constant. This is a set of nine second-order differential equations. The problem can also be stated equivalently in the Hamiltonian formalism, in which case it is described by a set of 18 first-order differential equations, one for each component of the positions r i and momenta p i :