3/177 Just after launch from the earth, the space-shuttle orbiter is in the 37 x 137-mi orbit shown. At the apogee point A, its speed 1s 17,290 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.) 17,290 mi/hr 37 mi PROBLEM 3/177 (a) Calculate the angular momentum per unit mass and solve for the speed of the orbiter as it passes through the perigee P. (b) Calculate the energy per unit mass E /m for the elliptical orbit. () Calculate (h/m). and (E /m) for the circular orbit. (d) Evaluate the increment of velocity Av that is needed to circularize the elliptical orbit at the apogee A of the elliptical orbit. (e) Use the impulse-momentum equation Fe, At =mAve, to solve for the burn duration At