In Newton’s theory of gravity, orbits make perfect ellipses when they occur around single, large masses. However, in General Relativity, there is an additional precession effect due to the curvature of spacetime, and this causes the orbit to shift over time, in a fashion that is sometimes measurable. Mercury precesses at a rate of 43" (where 1" is 1/3600th of one degree) per century; the smaller black hole in OJ 287 precesses at a rate of 39 degrees per 12-year orbit. (NCSA, UCLA / KECK, A. GHEZ GROUP; VISUALIZATION: S. LEVY AND R. PATTERSON / UIUC)

This Is Why Scientists Will Never Exactly Solve General Relativity

Even extremely simple configurations in General Relativity cannot be solved exactly. Here’s the science of why.

It’s difficult to appreciate how revolutionary of a transformation it is to consider the Universe from Einstein’s, rather than Newton’s, point of view. According to Newtonian mechanics and Newtonian gravity, the Universe is a perfectly deterministic system. If you were to give a scientist who understood the masses, positions, and momenta of each and every particle in the Universe, they could determine for you where any particle would be and what it would be doing at any point in the future.

In theory, Einstein’s equations are deterministic as well, so you can imagine something similar would occur: if you could only know the mass, position, and momentum of each particle in the Universe, you could compute anything as far into the future as you were willing to look. But whereas you can write down the equations that would govern how these particles would behave in a Newtonian Universe, we can’t practically achieve even that step in a Universe governed by General Relativity. Here’s why.