Mercury's Perihelion Precession
In 1859, Urbain Le Verrier was the first to report that the slow precession of Mercury's orbit around the Sun could not be completely explained by Newtonian Mechanics and perturbations by the known planets. He suggested that it was possible another planet, or series of minor planets (asteroids) might exist in an orbit even closer to the Sun, perturbing Mercury.
This was significant, because Le Verrier had basically discovered Neptune the same way. Back in the 1840's Le Verrier was studying small but systematic discrepancies between Uranus's observed orbit and the one predicted by Newtonian gravity. He engaged for months in complex calculations and on August 31st, 1846 he predicted the location of a planet that could be responsible for perturbing Uranus' orbit. Johann Galle of the Berlin Observatory found the predicted planet, Neptune, within 1 degree or where Le Verrier predicted it should be. So, yeah, it was a big deal when Le Verrier predicted a planet closer to the sun than Mercury a decade later.
In 1860, Le Verrier, after a meeting with an amateur astronomer who detailed a transit he had observed that he thought might be Le Verrier's hypothetical planet, Le Verrier announced the discovery of a previously unknown planet, Vulcan, to a meeting of the Academie des Sciences in Paris. The amateur astronomer, Lescarbault, was awarded the Legion d'honneur and invited to appear before numerous learned societies.
In 1877 Le Verrier died, convinced of having discovered another planet, although it was never convincingly confirmed. It in fact remained a possibility until 1915. That year, Einstein's theory of relativity showed that Mercury's perihelion precession should be slightly faster than Newtonian gravity predicted, thus eliminating the need for a perturbing planet inside Mercury's orbit. Still, astronomers have persisted, though never found, a planet inside of Mercury's orbit.
Something to keep in mind when you read this:
http://www.sciencemag.org/news/2016/01/feature-astronomers-say-neptune-sized-planet-lurks-unseen-solar-system
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