Simple precession calculation for Mercury: a linearization approach

The additional precession of Mercury due to general relativity can be calculated by a method that is no more difficult than solving for the Newtonian orbit. The method relies on linearizing the relativistic orbit equation, is simpler than standard textbook methods, and is closely related to Newton's theorem on revolving orbits. The main result is accurate to all orders in $\tfrac{1}{c}$ for near-circular orbits.