The theory of Schwarzschild geodesics is revisited. Basing on a result by
Weierstrass and Biermann, we derive a formula describing all non radial,
timelike and null trajectories in terms of Weierstrass elliptic functions.
Quite remarkably, a single formula works for an entire geodesic trajectory,
even if it passes through turning points. Using this formula, we derive
expressions for the proper and coordinate time along the geodesic.
