Classical Mechanics (Kibble & Berkshire) · Problem 7.12
Non-linear oscillations and phase space — T.W.B. Kibble, F.H. Berkshire
Physics — Mechanics · nearly-circular-orbits
Problem
Suppose the solar system is embedded in a dust cloud of uniform density ρ. Find an approximation to the 'annual' advance of the perihelion of a planet moving in a nearly circular orbit of radius a. (For convenience, let ρ=ϵM/a3, where M is the solar mass and ϵ is small.)