I’m currently working on the tests of general relativity portion of the astrophysics book, and have been calculating the path of Mercury this afternoon. The orientation of Mercury’s orbit shifts over time, commonly referred to as the “advance of the perihelion” in general relativity. It is one of the classic tests of the theory. Once you get the equations in the right form (and with good astrophysical data regarding Mercury’s orbit) you can solve Einstein’s relativity equations numerically to determine Mercury’s orbit.
So here are two basic plots. The first picture is one orbit of Mercury around the sun (axes are in AU), and it looks just like Newton predicted. The second is a plot of 500 orbits. Since Mercury’s orbit shifts by a tiny bit each time, the 500 orbits look smeared out. This is because each orbit shifts by such a tiny amount you can’t see each individual orbits.
The next challenge is to use these calculations to determine the rate of perihelion advance. Anyone interested in seeing how it’s done?