The discovery of Neptune is widely regarded as a dramatic validation of celestial mechanics, and is one of the most remarkable moments of 19th-century science.

He was able to derive some important limits on the motions of the system, but due to the inaccurately-known masses of the planets, his results were tentative.

Encouraged by physicist Arago,[5] Director of the Paris Observatory, Le Verrier was intensely engaged for months in complex calculations to explain small but systematic discrepancies between Uranus's observed orbit and the one predicted from the laws of gravity of Newton.

At the same time, but unknown to Le Verrier, similar calculations were made by John Couch Adams in England.

The letter arrived five days later, and the planet was found with the Berlin Fraunhofer refractor that same evening, 23 September 1846, by Galle and Heinrich d'Arrest within 1° of the predicted location near the boundary between Capricorn and Aquarius.

Not even the briefest account of Adams's predicted orbital elements was published until more than a month after Berlin's visual confirmation.

Adams made full public acknowledgement of Le Verrier's priority and credit (not forgetting to mention the role of Galle) when he gave his paper to the Royal Astronomical Society in November 1846:[6] I mention these dates merely to show that my results were arrived at independently, and previously to the publication of those of M. Le Verrier, and not with the intention of interfering with his just claims to the honours of the discovery; for there is no doubt that his researches were first published to the world, and led to the actual discovery of the planet by Dr. Galle, so that the facts stated above cannot detract, in the slightest degree, from the credit due to M. Le Verrier.Early in the 19th century, the methods of predicting the motions of the planets were somewhat scattered, having been developed over decades by many different researchers.

[4] In 1859, 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, among possible explanations, that another planet (or perhaps, instead, a series of smaller 'corpuscules') might exist in an orbit even closer to the Sun than that of Mercury, to account for this perturbation.

The success of the search for Neptune based on its perturbations of the orbit of Uranus led astronomers to place some faith in this possible explanation, and the hypothetical planet was even named Vulcan.