Show that the vector C = p × l − mkê_r is a conserved quantity for the motion in a central potential U(r) = −k/r. Here p is the linear momentum, and l is the angular momentum.

Question

Note: C, p, and l are supposed to have arrows on top to indicate they are vectors; ê_r is a unit vector in the direction of r.

Answer 1

C = p × l − mkê_r is the Laplace-Runge-Lenz (LRL) vector.