Chapter 12.3, Problem 12.97P

A particle of mass m describes the parabola y = x²/4r₀ under a central force F directed toward the center of force C. Using Eq. (12.35) and Eq. (12.37′) with ε = 1, show that F is inversely proportional to the square of the distance r from the particle to the center of force and that the angular momentum per unit mass $h=\sqrt{2GM{r}_0}$.

Fig. P12.97