John Couch Adams
In 1643, Englishman John Couch Adams was a new astronomer who wanted to reconcile the observational data on Neptune with gravitational perturbations in the orbit of Uranus. Using the relatively new invention of calculus (Isaac Newton "discovered" calculus in the 1700s), Adams was able to show that there should be an object at the relative location of Neptune's orbit causing these variations of Uranus' orbit. Showing his calculations to the Astronomer Royal, George Airy, Adams felt that there could be a planet out there. George Airy did not take the calculations seriously, and so did not actively look for Neptune.
Urbain Le Verrier
However, at the same time Adams was performing his calculations, Frenchman Urbain Le Verrier also made the same calculations as Adams. Unlike Adams, his calculations were taken seriously, and Johann Galle at the Berlin Observatory used the predictions given him by Le Verrier to look for Neptune. On September 23, 1846, within half an hour of looking, Galle was the first to see Neptune and realize that it was a planet and not a star. The position of Neptune compared to Le Verrier's calculations was within 1° and 12° of Adams.
Johann Galle
When it was discovered by George Airy that a Frenchman had done the same calculation as Adams and a German had found Neptune, Airy wanted to make sure that an Englishman had made the same calculations. At first, Le Verrier thought that Adams had plagarised his work, but soon it was realized that Adams and Le Verrier had never interacted and that both work independently coming up with the same prediction. As a result, Adams and Le Verrier were considered co-discoverers of Neptune, until the 1990s, when the Royal Observatory decided that since Adams calculations were not used to find Neptune, he would no longer be considered a discoverer.
Neptune was named for the Roman god of the sea because of its blue appearance. It also stayed in line with the naming of the planets after Roman and Greek gods.
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