Physics

Problem

A satellite follows an elliptical orbit with perigee (closest approach) distance

r_{p}

and apogee (farthest distance)

r_{a}

from the planet’s center. Derive an expression for the ratio

\dfrac{v_{p}}{v_{a}}

of its speed at perigee to its speed at apogee in terms of

r_{p}

and

r_{a}

. State the final simplified ratio.