Classical Mechanics (Kibble & Berkshire) · Problem 7.13

Non-linear oscillations and phase space — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · nearly-circular-orbits

Problem

Orbits in general relativity In the theory of general relativity, the path equation for a planet moving in the gravitational field of the Sun is, in the standard notation, d2udθ2+u=MGL2+(3MGc2)u2,\frac{d^2u}{d\theta^2} + u = \frac{MG}{L^2} + \left(\frac{3MG}{c^2}\right)u^2, where cc is the speed of light. Find an approximation to the 'annual' advance of the perihelion of a planet moving in a nearly circular orbit of radius aa.

Related theory

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