Problems for Intermediate Methods in Theoretical Physics Edward F. Redish

we considered the radial motion of a planet in orbit around a star. After eliminating the angular variables, the equation of motion for the radial distance involves an effective radial potential,

where m is the mass of the planet, M is the mass of the star, G is Newton's universal gravitational constant, and L is the planet's orbital angular momentum. It was then claimed that this equation could be reduced to the dimensionally more convenient form

where ε is an energy and σ is a distance. Show that this is the case by finding the explicit form of ε and σ expressed in terms of the original parameters of the problem.

Last revision 14. October, 2004.