The planet Uranus was discovered by William and Caroline Herschel in 1781. It was the first planet to be discovered (rather than simply being known since the dawn of history), and it was found simply by chance. Later that year Andrei Leksel calculated the orbit of Uranus and noticed it had some irregularities. He suggested there may be planets beyond Uranus, but made no clear predictions.
It wasn’t until the 1800s that Uranus’ orbit was determined well enough to calculate the nature of its orbital irregularities. By 1845 John Couch Adams became convinced that the orbit of Uranus indicated the existence of a more distant planet, and began calculating its location. Independently, Urbain Le Verrier began similar calculations. It turns out that Le Verrier’s calculations were more precise, and in the summer of 1846 Le Verrier wrote to Johanne Galle, who located what would eventually be named Neptune within a degree of Le Verrier’s prediction.
In the image below you can see the location of Neptune at the time of its discovery in comparison to the predictions of both Le Verrier and Adams. Of course this raises the question as to whom should get credit for Neptune’s discovery. This remains a matter of some debate, though the credit usually goes to Le Verrier and Galle.
Despite the controversy, the discovery of Neptune marks a huge step forward in the field of astrophysics. It was the first major discovery in which observations led to a prediction which was then confirmed. It reinforced the idea that astronomy was not simply a descriptive science, it could also be predictive. We can use our understanding of physics and chemistry to understand the mechanisms of the cosmos.
Sometimes we just need to listen to the cold equations.