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How did Urbain-Jean-Joseph Le Verrier predict Neptune’s location?

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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.

Urbain-Jean-Joseph Le Verrier predicted the location of Neptune by mathematically analyzing the irregular orbit of Uranus.1

Astronomers had observed that Uranus was not following the path predicted by Newton’s laws of motion and the gravitational influence of the known planets. Le Verrier hypothesized that these orbital perturbations were caused by the gravitational pull of an undiscovered planet.21

In 1845, he began a study to calculate the size and position of this unknown body. By mid-1846, he had successfully computed its probable location. He communicated these results to the German astronomer Johann Gottfried Galle at the Berlin Observatory, who, with the help of detailed star maps, identified the planet on September 23, 1846, within one degree of the position Le Verrier had calculated.123