General Relativity: An Introduction for Physicists · Problem 10.3

Experimental tests of general relativity — Hobson, Efstathiou & Lasenby

Physics · gr-planetary-orbit-solution

Problem

Verify that the general-relativistic equation of motion for planetary orbits (10.3) has the solution

u = \frac{GM}{h^2}(1 + e\cos\phi) + \frac{3(GM)^2}{c^2 h^4}\left[1 + e^2\left(\frac{1}{2} - \frac{1}{6}\cos 2\phi\right) + e\phi\sin\phi\right],

to first order in the relativistic perturbation to the Newtonian solution.