How did unexplained changes in Uranus’s orbit lead to the discovery of Neptune?

The discovery of Neptune is a landmark achievement in celestial mechanics, resulting from the application of Newtonian physics to explain observed irregularities in the orbit of Uranus.12

By the early 19th century, astronomers noted that Uranus was not following the path predicted by Newton’s laws of motion and the known gravitational influences of the Sun and other planets. Furthermore, historical prediscovery sightings of Uranus dating back to 1690 consistently disagreed with its calculated positions. Astronomers hypothesized that these deviations, or perturbations, were caused by the gravitational pull of an undiscovered, more distant planet.13

In the 1840s, mathematicians John Couch Adams and Urbain-Jean-Joseph Le Verrier independently calculated the predicted location of this hypothetical body. Following Le Verrier’s calculations, German astronomer Johann Gottfried Galle identified Neptune on September 23, 1846, within one degree of the predicted position. This success confirmed that the "unexplained" motions of Uranus were, in fact, the result of gravitational interactions with a previously unknown planet.145