Can calculation find the place of an unseen planet?

That time, that place

After Herschel found Uranus in 1781, astronomers computed its orbit by Newtonian mechanics.

The actual positions kept drifting from the calculation. The discrepancy was small, but it would not go away, and it grew.

Two explanations were possible. Either Newton's law of gravity differs slightly at that distance, or an unknown planet lies beyond Uranus, pulling on it.

Why this question

Le Verrier calculated on the second.

What makes the problem hard is that it runs backwards. Normally you know a planet's mass and position and compute its effects. Here only the effects were given, and the mass, orbit and present position of whatever produced them had to be found.

He solved for the unknown planet that would account for every part of Uranus's deviation, and named the place in the sky where it must now be.

The Paris observatory showed little interest. He wrote to Galle at the Berlin observatory.

What was found

Galle turned the telescope that way the night the letter arrived. Within an hour, less than a degree from the named position, he found an object missing from the star charts. Neptune.

It was the first planet found by calculation, and a demonstration of how far Newtonian mechanics could be trusted.

A young mathematician in England had done the same calculation at about the same time but never got it published. Today both are credited.

Le Verrier applied the same method to Mercury, whose orbit also showed an unexplained deviation. He proposed a planet closer to the sun and named it Vulcan. Several people claimed sightings; none was confirmed.

This time the first explanation was the right one. In 1915 general relativity accounted for Mercury's deviation exactly. The same method once found a new planet and once demanded new physics.