How did scientists predict the position of Uranus after its discovery?

The prediction of Uranus's position after its discovery primarily involved the application of Kepler's laws of planetary motion. Kepler's laws provide a framework for understanding the orbital mechanics of planets, detailing how they move around the sun, including their elliptical orbits and the relationship between a planet's orbital period and its distance from the sun.

In the case of Uranus, astronomers observed deviations in its orbit that could not be accounted for solely by the gravitational effects of known planets. This led them to infer the presence of another, as-yet-unseen planet influencing its trajectory. By applying Kepler's laws along with Newton's law of universal gravitation, scientists were able to create predictions about where this additional planet might be located in the solar system.

The successful prediction of Uranus's position confirmed the power of gravitational theory and observational astronomy in finding new celestial bodies based solely on the influences they exert on known objects. This method marked a significant moment in astrophysics, demonstrating how mathematics and observed behavior in the sky can lead to groundbreaking discoveries.