The Binet equation for u (φ) can be solved numerically for nearly any central force F (1/ u). However, only a handful of forces result in formulae for u in terms of known functions. As derived above, the solution for φ can be expressed as an integral over u φ φ = φ φ 0 + L 2 m ∫ ∫ u d u E t o t − − U ( 1 / u ) − − L 2 u 2 2 m