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It's a long story, and to answer it, we have to go all the way back to when Uranus, the planet before Neptune, was discovered.

Uranus was discovered in 1781, and astronomers started calculating the orbit it should be following around the Sun. However, within a few years, astronomers started noticing the planet wasn't quite following the orbit they'd assigned it; it was slightly out of place. No matter how hard they tried, the mathematicians couldn't manage to calculate an orbit for Uranus that fit the facts.

In 1845, two astronomers, John Couch Adams in England and Urbain LeVerrier in France, working independently of each other, came to the conclusion that there must be another planet beyond Uranus, pulling on it with its gravity and affecting its orbit. They used the discrepancies in Uranus' orbit to calculate where the new planet should be, but couldn't get anyone interested for a long time. It wasn't until 1846 that a German astronomer, Johann Gottfried Galle, using LeVerrier's calculations, decided to look at the spot in the sky LeVerrier had predicted the planet should be - and lo and behold, there was Neptune! So Neptune was discovered by Adams and LeVerrier, writing down their calculations with a pen, before astronomers had ever actually seen it. That's why Neptune was "discovered by pen."

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