Discovery of Neptune (1846)
Astronomers predicted Neptune's existence by analyzing Uranus's orbital wobbles, then found it exactly where math said it would be. The discovery proved Newton's laws worked beyond the known solar system and showed invisible objects could be detected through gravitational effects. It was astronomy's first major planet found by calculation rather than accident.
Confirmed mathematical astronomy's predictive power and expanded the known solar system.
Established the technique of inferring unseen bodies from gravitational perturbations—the same method used 150 years later to find the first exoplanets.
Mayor and Queloz used radial velocity measurements (detecting stellar wobbles) to infer 51 Pegasi b's existence, reprising the Neptune strategy on an interstellar scale.