The Deorbit Burn

The Deorbit Burn

A space shuttle returning from the ISS 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 ∆v) required for a space shuttle to decrease its altitude to 60 miles when it’s orbiting with an apogee of 250 miles and a perigee of 208 miles above the surface
of Earth. Use the general rule that below an altitude of 500 miles, for every 2 feet per second (ft/s) change in the orbiting spacecraft’s velocity its altitude will
change by 1 mile. Make sure to show your work. Put your answer in units of feet per second.

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