Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_177

3/177 Just after launch from the earth, the space-shuttle orbiter is in the \(37 \times 137\text{-mi}\) orbit shown. At the apogee point \(A\), its speed is \(17,290\text{ mi/hr}\). If nothing were done to modify the orbit, what would be its speed at the perigee \(P\)? Neglect aerodynamic drag. (Note that the normal practice is to add speed at \(A\), which raises the perigee altitude to a value that is well above the bulk of the atmosphere.)