The Titius–Bode law is a formulaic prediction of spacing between planets in any given planetary system. The formula suggests that, extending outward, each planet should be approximately twice as far from the Sun as the one before. The hypothesis correctly anticipated the orbits of Ceres and Uranus, but failed as a predictor of Neptune's orbit. It is named after Johann Daniel Titius and Johann Elert Bode.

The planet Neptune was mathematically predicted before it was directly observed. With a prediction by Urbain Le Verrier, telescopic observations confirming the existence of a major planet were made on the night of September 23–24, 1846, at the Berlin Observatory, by astronomer Johann Gottfried Galle, working from Le Verrier's calculations. It was a sensational moment of 19th-century science, and dramatic confirmation of Newtonian gravitational theory. In François Arago's apt phrase, Le Verrier had discovered a planet "with the point of his pen".