Mission 07
The Planet Found on Paper
Uranus would not keep to its timetable. For sixty years it ran ahead of where the tables said it should be, then fell behind, and by the 1840s the gap had grown to two arcminutes. In 1846 Le Verrier assumed an unseen planet was pulling on it, spent two years working out where that planet had to be, and posted the answer to an observatory in Berlin. They found Neptune the same night, less than a degree away.
Read the wobble
Each point is a year of observations: how far Uranus was from where a lone Uranus should have been, in arcseconds. The shape is the fingerprint of something pulling.
Place a planet
Set how far out it orbits and where in the sky it sits in 1846. Its pull on Uranus is worked out from Newton, live, every time you move a slider.
Point the telescope
When your line lies on the points, the direction you set is where to look. That is the whole of the method.
25.00 AU
a year there lasts 125 of ours
180.00° ecliptic longitude
Your line misses the observations by
66.5
arcseconds, on average
Le Verrier put the planet at 36 AU. It is at 30. He was wrong about the distance and right about the direction to within a degree, because the observations pin down the pull far better than they pin down what is doing the pulling.
The orbits here are flattened into one plane, both are within about a degree of it anyway; Jupiter and Saturn are left out because their effects were already in the tables Uranus was being compared against; and the trial planet is given Neptune's mass, which Le Verrier had to solve for as well.