Isaac Newton's Law of Universal Gravitation was used to predict the position of planets based on their mutual force of gravity. From about 1820 it was noticed that the predicted position of was different than the actual position. Some astronomers correctly thought that an unknown planet was the cause of the difference, allowing for the discovery of .

From about 1820 it was noticed that the predicted position of Uranus was different than the actual position. Some astronomers correctly thought that an unknown planet was the cause of the difference, allowing for the discovery of Neptune.

Explanation:

Uranus was discovered by William Herschel in 1781. In the early 19th century odd perturbations in the orbit of Uranus led to astronomers to speculate with the existence of an unknown planet located farther away whose gravitational tug affected Uranus orbit. The observations made of the position  of Uranus did not agree with those predicted by Newton's Law of Gravitation.

In September of 1846 the astronomer Urbain Le Verrier made calculations based on the data available and predicted the position of this hypothetical planet. Then on September 23 of that year Neptune was observed for the first time by Johann Galle at the Berlin observatory.