Mercury's orbit Mercury has a weird orbit. It's elliptical orbit rotates around an axis, but for no readily apparent reason. My question is why? What is causing this?
 A: The actual amount of the precession for Mercury is about 574 arcsec/century so your figure is ten times too big. This is mostly due to tugs from other planets. Oblateness of Sun has an effect but too small to measure. About 43 arcsec/century is an effect of general relativity.
This table from Wikipedia gives the figures.

A: There are two reasons.
The first is due to the other planets. The other planets exert an average central inverse-square force ($\frac{\beta}{r^2}$) on Mercury. (If you average out the force over their full rotation). The standard keplerian elliptical orbit is of the form $r=\frac{p}{1+e\cos \theta}$.a With this term, the equation changes to$r=\frac{p'}{1+e'\cos\gamma\theta}, \gamma=\sqrt{\frac{m^2+\beta}{m^2}}\lesssim 1$. This is almost an ellipse, but the $\gamma$ means that the motion repeats after slightly less than a full revolution around the sun, causing precession.
The second reason is that General Relativity forbids perfectly elliptical orbits (one can have a circular orbit if one neglects dissipation, but not an elliptical one). Instead, we have Rosetta orbits

The image shown is a bit to the extreme end, for Mercury this rosetta has a much smaller precession.
Both effects contribute to the precession of Mercury.
