How did we find a planet before we saw it?

Neptune is so far away that you can’t see it with the naked eye. Yet in 1846 it was found almost exactly where a mathematician had calculated it would be. How can you find a planet by calculation?

Gravity pulls everything towards everything

Any two bodies attract each other, and the heavier they are and the closer together, the stronger the pull. Planets fly forwards, and without the Sun they would fly off in a straight line. But the Sun keeps pulling them in, so they go round and round.

Gravity lets you calculate the orbit

Isaac Newton described how gravity and motion work. If you know where a planet is and how fast it is moving, his laws tell you where it will be tomorrow, in a year or in a hundred years. Astronomers used them to draw up tables of where each planet would be in the sky.

Planets tug on each other too

It isn’t only the Sun that pulls on a planet; the other planets pull on it too, though more weakly – above all the giants Jupiter and Saturn. So its orbit bends a little and the calculation gets harder, but it can be done.

Uranus isn’t where it should be

In 1781 William Herschel discovered a new planet with his telescope: Uranus. Within a few decades it was clear that it wasn’t going where the calculation said, even with Jupiter and Saturn taken into account. The difference was much smaller than the Moon looks in the sky, but the calculation shouldn’t have been off by that much.

Something is pulling it

Until 1822 Uranus ran ahead of the calculation, and then it started to fall behind. That is exactly how it would behave if another, slower planet orbited further out from the Sun. While Uranus was catching up with it, that planet pulled it forwards, and once Uranus had overtaken it, the planet pulled it back.

Calculation instead of a telescope

The French mathematician Urbain Le Verrier worked out where an unknown planet would have to be to pull on Uranus in exactly this way. He calculated by hand for almost a year. In August 1846 he named a spot in the sky: all you had to do was aim a telescope there.

Found in a single night

Johann Galle at the Berlin Observatory received Le Verrier’s letter on 23 September 1846 and that same night aimed his telescope at the calculated spot. About two Moon-widths away he found a “star” that wasn’t on the star chart. Stars stay put, but this one had moved by the next night: it was a planet, Neptune.

The planet that didn’t exist

Mercury’s orbit didn’t match the calculation either. The whole orbit turns around the Sun a little faster than the calculations said it should. So Le Verrier predicted a planet called Vulcan even closer to the Sun, but nobody ever found it. It took Einstein to show that Newton’s laws aren’t quite exact, and that this shows up most near the Sun, where gravity is strongest.

So how did we find Neptune?

Newton’s laws tell you where the planets will be. When Uranus didn’t follow the calculation, Le Verrier used the difference to work out where the planet pulling on it had to be. Then a telescope found it almost exactly there.