# How is orbital precession calculated in Newtonian gravity?

So one of the big test successes of General Relativity over Newtonian gravity was the precession of Mercury's orbit. Mercury's orbit precesses 5600 arcseconds/century, but Newton's laws only accounted for 5557 arcseconds, and Relativity came up with the remaining 43 arcseconds. But where do you find precession from the Newtonian formula F = GMm/r^2?

### 3 Answers

- Anonymous6 months ago
Yes, just ignore bummer answers like user quantumclaustrophobe, he will break your heart

- DixonLv 76 months ago
The actual orbits have to be measured and there isn't a special law for precession as such, you just deduce it from the position of planets over time, like any other time dependent trig / calculus problem. The point is that Einstein's Relativity included time dilation for Mercury relative to the Earth, due to its proximity to the sun.

Regarding orbits and F = GMm/r^2, you find the net force of gravity and centrifugal force acting on a mass, and from that look for a stable solution. The general case solution is an ellipse. This was already know from Kepler's laws but Newton was able to deduce Kepler's laws from his own laws of motion and gravity. Part of Newton solving the equations required him to invent calculus, so he did.