Finding Neptune With Pencil and Paper
Uranus was found in 1781, and astronomers soon began to track its path around the sun. They used the laws of gravity to predict where it should be on any given date. But as the years went by, Uranus kept drifting away from the predictions. It was a little ahead in some years and a little behind in others.
Some scientists decided the planet was not to blame. They suspected that the pull of another, unseen planet was tugging on Uranus. If that was true, the new planet had to be farther out, and its gravity would be changing the way Uranus moved.
Two mathematicians, one in France and one in England, each worked on the problem separately. They had no telescope. They used pencils, paper and many long calculations to work backward from the odd motion of Uranus. Their goal was to find where a hidden planet would have to be to cause it.
In 1846, the French mathematician sent his answer to astronomers in Berlin. The observers pointed their telescope at the predicted place on the very first night they received the letter. Within about an hour, they spotted a faint point of light that was not on their star map. It was a new planet, now called Neptune, and it was very close to where the math said it would be.
Neptune is too dim to see with the unaided eye. Its discovery showed how powerful careful reasoning can be.