The Space Shuttle does not directly inject into its prescribed mission orbit. Rather, themain engine shutdown occurs at the apogee of an elliptical orbit with 100-km altitudeand the external tank is discarded. Perigee of this orbit is at 30-km altitude. After thetank is released, the Shuttle uses its orbital maneuvering system (OMS) to maneuverinto an elliptical orbit with perigee at 100-km altitude and apogee at 250-km altitude.This is called the OMS-1 burn. At the new apogee, the Shuttle performs the OMS-2burn to circularize into the 250-km altitude mission orbit. Calculate:
(a) the burnout speed at apogee in the external tank disposal orbit;(b) the ΔV required for the OMS-1 maneuver;(c) the ΔVrequired for the OMS-2 maneuver;(d) if launching from the Kennedy Space Center, without a plane change maneuver,what is the range of inclinations possible for the Shuttle mission orbit? Why?