Current Attempt in Progress

Just after launch from the earth, the space$-$shuttle orbiter is in the $26163-$ mi orbit shown. At the apogee point $A,$ its speed is

$17197m\frac{i}{h}r.$ If nothing were done to modify the orbit, what would its speed be 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.$)$ The radius of the earth is $3959$ mi $.$

Answer: $v_p=$

$m\frac{i}{h}r$