Chapter 12.3, Problem 12.118P

A satellite describes an elliptic orbit about a planet. Denoting by r₀ and r₁ the distances corresponding, respectively, to the perigee and apogee of the orbit, show that the curvature of the orbit at each of these two points can be expressed as

$\frac{1}{\rho }=\frac{1}{2}\left(\frac{1}{r_0}+\frac{1}{r_1}\right)$

Fig. P12.118 and P12.119