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How did unusual motions in Uranus’s orbit lead to the discovery of Neptune?

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Clouds in Neptune's atmosphere — Neptune A photograph of clouds in Neptune's atmosphere, taken by Voyager 2 in August 1989. The view is from below the planet's equator, and north is up. The Great Dark Spot (center left) is 13,000 km (8,100 miles)—about the diameter of Earth—in its longer dimension. Accompanying it are bright, wispy clouds thought to comprise methane ice crystals. At higher southern latitudes lies a smaller, eye-shaped dark spot with a light core (bottom left). Just above that spot is a bright cloud dubbed Scooter. Each of these cloud features was seen to travel eastward but at a different rate, the Great Dark Spot moving the slowest.

Following the discovery of Uranus in 1781, astronomers observed that the planet was not following the path predicted by Newton’s laws of motion and the gravitational influence of the Sun and other known planets. Furthermore, recorded prediscovery sightings of Uranus dating back to 1690 consistently disagreed with its calculated positions.1

These anomalies led scientists to hypothesize that the gravitational attraction of an undiscovered, more distant planet was perturbing the orbit of Uranus. In the 1840s, mathematicians John Couch Adams and Urbain-Jean-Joseph Le Verrier independently calculated the potential position of this unseen body based on these orbital irregularities.123

In 1846, acting on Le Verrier’s calculations, German astronomer Johann Gottfried Galle searched the predicted area of the sky and successfully identified Neptune. This discovery served as a significant confirmation of Newtonian gravitational theory.132