Math and the Missing Planet

With apologies to Pluto, there are eight planets in our Solar System. We discovered Earth by, well, just being here — that one was easy. Of the other seven, five — Mercury, Venus, Mars, Jupiter, and Saturn — were discovered simply by looking at the night sky and noticing that some of the stars were moving. (Yes, I’m oversimplifying.) We’ve known about those five for millennia. But it took a long time for humans to discover the existence of the sixth planet, Uranus. Uranus was so small and so far away that it was very dim and didn’t seem to move, at least not to the naked eye. For centuries, the leading minds thought it was most likely a star, or maybe some sort of comet. But on March 13, 1781, a British astronomer named William Herschel was mapping out the stars using a telescope and noticed that one didn’t quite look the same. Over the next few years, he and other scientists kept an eye on this odd heavenly body — again, using a telescope to help — and realized that it was, in fact, orbiting the sun. It was a planet, dubbed “Uranus,” much to the glee of generations of children since.

But as our understanding of science and math improved, we realized that there was a problem with Uranus.

Uranus, like all of the other planets (including Earth), orbits the Sun, and in 1846, Uranus completed its first solar orbit since its discovery in 1781. At that point in human history, we understood the science and could predict where Uranus would be in the sky. But there was a problem — Uranus wasn’t quite where it was supposed to be. There were only a few possible explanations: virtually every astronomer in the world had made a math mistake, the universe was broken, the science wasn’t all that well understood, or something was interfering with Uranus’s orbit. The first seemed unlikely, the second was a problem beyond human capacity to solve, and the third was something few people wanted to admit as possible. (Again, I’m oversimplifying.) That last one, though, was interesting.

Planetary orbits are a function of gravity — and specifically, the gravitational pull of the Sun. But anything massive enough could have an impact on the orbital path. Typically, though, there aren’t a lot of things out in the solar system that are large enough to have a meaningful impact on a planet’s orbit, with one exception: other planets. But in Uranus’s case, there was no other planet — at least, not one we had yet found. 

And then, the scientific community realized something was broken. But in a good way, because it led us to Neptune.

Like Uranus, Neptune can’t be seen from Earth with the naked eye — it’s simply too dim. Finding it by accident would have been difficult. First, you’d have to happen across it while peering at the heavens through a telescope, and the odds of you coming across a tiny dot in an ocean of stars are vanishingly small. And that did actually happen a few times; for example, it was recorded in drawings made by famed polymath Galileo Galilei in late 1612 and again in early 1613. But in both of those cases, and in a few others throughout history, Neptune was written off as yet another star. As no one was looking for an 8th planet, no one found one.

But that changed after the scientific community realized that Uranus’ orbit was “broken” in 1781. The theory that another, yet undiscovered planet was impacting Uranus took hold and spread. For the next half-century or so, various astronomers began running all sorts of mathematical models to determine where that planet could be. And eventually, one such scientist got it right — or, close enough. In August of 1846, a French astronomer named Urbain Le Verrier “calculated the approximate location of [a previously undiscovered] planet by studying gravity-induced disturbances in the motions of Uranus, according to Le Verrier’s calculations were close enough to correct, and on the night of September 23-24, 1846, a German astronomer named Johann Gottfried Galle looked through a telescope and found Neptune, not too far from where Le Verrier thought it would be. As Wikipedia’s editors summarize, Galle’s search took “less than an hour of searching and [was] less than 1 degree from the position Le Verrier had predicted, a remarkable match.” Math had made a discovery that our eyes had, collectively, dismissed.

Bonus fact: The word “planet” shows how confused the ancient Greeks were about the true nature of planets. “Planet” comes from the Greek word “planetes,” which means “wanderer.” The Greeks looked at the night sky and saw that most of the stars were in the same place (relative to the other stars), but a few seemed to move around a bit — that is, they wandered. The Greeks thought the planets were “wandering stars,” giving them the name “planetes.” 

From the Archives: The Swedish Solar System: Sweden is also a scale model of our cosmic neighborhood.