The Central Force Problem — Herbert Goldstein, Charles Poole, John Safko
Physics — Mechanics · hodograph-kepler-motion
Problem
If all the momentum vectors of a particle along its trajectory are translated so as to start from the center of force, then the heads of the vectors trace out the particle's hodograph, a locus curve of considerable antiquity in the history of mechanics, with something of a revival in connection with space vehicle dynamics. By taking the cross product of L with the Laplace--Runge--Lenz vector A, show that the hodograph for elliptical Kepler motion is a circle of radius mk/l with origin on the y axis displaced a distance A/l from the center of force.