Cobra Effect · Space

The planet found with pen and paper

How a planet straying off course led mathematicians to an unseen world.

7 cards, read aloud in 3:22, with a test and sources.

A telescope on a stand aimed up at a small round disc among stars

In 1781 William Herschel discovered a new planet, later named Uranus.

He spotted it while surveying the stars with a telescope he had built himself. It was the first planet found with a telescope. Astronomers used Newton’s theory of gravity to work out its path around the Sun. But over the following decades, Uranus kept straying from where it was predicted to be.

Something seemed to be pulling Uranus off course.

Some astronomers wondered whether Newton’s gravity might not work so far from the Sun. Others suspected an unseen planet, farther out, tugging on Uranus. Working backwards from the tugs to the planet causing them was a formidable calculation. In the 1840s, two mathematicians took it on, each unaware of the other.

In Cambridge, John Couch Adams worked out where an unseen planet might be.

Adams was a young mathematician at Cambridge University. By 1845 he had calculated a position for the planet. A search from Cambridge recorded the planet twice without recognising it, so his prediction played no part in the discovery. He is now credited with making an independent prediction.

In Paris, Urbain Le Verrier made his own prediction, and sent it to Berlin.

Le Verrier was a French mathematician who studied the motions of the planets. On the last day of August 1846, he presented his predicted position for the new planet. French astronomers were slow to search, so he wrote to Johann Galle at the Berlin Observatory. Galle and his colleagues began looking on the very evening the letter arrived, in September.

Within an hour, Galle and Heinrich d’Arrest found a star that was not on their chart.

D’Arrest suggested comparing the sky with a new, detailed star chart of that region. Galle called out the stars he could see, and d’Arrest checked each one against the chart. One point of light was missing from the chart, and it later moved against the stars, as a planet should. The new planet lay within about one degree of where Le Verrier had predicted.

The planet was named Neptune, and Le Verrier tried the same trick again.

Mercury’s orbit also slowly swung round a little more than Newton’s gravity predicted. Le Verrier suggested another unseen planet, closer to the Sun, which became known as Vulcan. Vulcan was never found. In 1915, Einstein’s general theory of relativity explained Mercury’s extra swing, with no extra planet needed.

So when something strays from its path, ask what unseen thing might be pulling on it.

Neptune was found by calculation, before anyone knew exactly where to look. The same reasoning failed for Vulcan, because that time the theory itself needed changing. Galileo’s notebooks show that he saw Neptune in 1612 and 1613, and took it for a star. Astronomers still hunt for unseen worlds from the tugs they leave behind.

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