Solutions ( q , p ) of the n -body problem q ˙ ˙ = M − − 1 p , p ˙ ˙ = ∇ ∇ U ( q ) (where M are the masses and U denotes the gravitational potential) are said to have a singularity if there is a sequence of times t n converging to a finite t ∗ ∗ where ∇ ∇ U ( q ( t n ) ) → → ∞ ∞ . That is, the forces and accelerations become infinite at some finite point in time.