The shuttle must reduce its velocity at a pre-calculated point in its orbit in order to return to Earth. For this maneuver, the shuttle is turned into an attitude with the Orbital Maneuvering System (OMS) nozzles pointing into the direction of the shuttle's velocity. The shuttle must perform the burn to change its orbit so that the perigee, the point in the orbit that is closest to Earth, is inside earth’s atmosphere. The opposite of perigee is apogee.
De-orbit maneuvers are usually done to lower the perigee of the orbit to 60 miles (or less). The shuttle is captured and re-enters as it passes into the atmosphere at this altitude. There is a change of 1 mile for every 2 feet per second (fps) change in velocity when you are below a 500 mile altitude above the Earth.
Calculate the minimum change in velocity (delta V or ∆V) required for the Space Shuttle to decrease its altitude to 60 miles if it’s orbiting with an apogee of 236 miles and a perigee of 220 miles above the surface of Earth. Put your answer in units of feet per second.
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To calculate the minimum change in velocity (ΔV) required for the Space Shuttle to decrease its altitude to 60 miles, we need to find the difference in velocity between the current perigee (220 miles) and the desired altitude of 60 miles.
Given:
Current perigee = 220 miles
Desired altitude = 60 miles
Step 1: Convert miles to feet.
1 mile = 5280 feet
Current perigee in feet = 220 miles * 5280 feet/mile = 1,159,200 feet
Desired altitude in feet = 60 miles * 5280 feet/mile = 316,800 feet
Step 2: Calculate the change in altitude.
Change in altitude = Current perigee - Desired altitude
Change in altitude = 1,159,200 feet - 316,800 feet = 842,400 feet
Step 3: Use the conversion factor of 1 mile = 2 feet per second (fps) below 500 mile altitude.
Change in velocity (ΔV) = Change in altitude * 2 fps/feet
ΔV = 842,400 feet * 2 fps/feet = 1,684,800 fps
Therefore, the minimum change in velocity (ΔV) required for the Space Shuttle to decrease its altitude to 60 miles is 1,684,800 feet per second (fps).