The De-orbit Burn

The Shuttle must reduce its velocity at a pre-calculated point in its orbit in order to return
to Earth. In order to reduce the velocity and change the orbit of the Shuttle, a maneuver
called the de-orbit burn is performed. For this maneuver, the Shuttle is turned in a
direction such that the Orbital Maneuvering System (OMS) nozzles point in the direction
of the Shuttle's velocity back toward Earth. The OMS engines fire and give the Shuttle a
velocity in the opposite direction, thus slowing the spacecraft.

The Shuttle must perform the de-orbit burn to change its orbit so that the perigee, the
point in the orbit closest to Earth, is inside of Earth's atmosphere. De-orbit maneuvers
are done to lower the perigee of the orbit to 60 miles (or less). An altitude of 60 miles is
important because this is where the orbiting spacecraft is recaptured by Earth's gravity
and re-enters Earth's atmosphere.

Calculate the minimum change in velocity (delta V or AV) required for the Space Shuttle
to decrease its altitude to 111190 m if it's orbiting with an apogee of 437.35 km and a
perigee of 379.9 km above the surface of Earth.
Use the rule of thumb that below an altitude of 500 miles, for every .6096m per second
(m/s) change in the orbiting spacecraft's velocity its altitude will change by 1 mile.

Answer in feet per second. Show all work neatly on a separate sheet of paper.