General Relativity: An Introduction for Physicists · Problem 10.2

Experimental tests of general relativity — Hobson, Efstathiou & Lasenby

Physics · newtonian-orbital-solution-ellipse

Problem

Show that the equation of motion in Exercise 10.1 has the solution

u = \frac{GM}{h^2}(1 + e\cos\phi),

and that this describes an ellipse. Show further that

a = \frac{h^2}{GM(1-e^2)},

where

r_1 = a(1-e)

and

r_2 = a(1+e)

are the distances of closest and furthest approach respectively.