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 ∆V) required for the Space Shuttle to decrease its altitude to 60 miles if it’s orbiting with an apogee of 260 miles and a perigee of 220 miles above the surface of Earth.
Use the rule of thumb that below an altitude of 500 miles, for every 2 feet per second (ft/s) change in the orbiting space craft’s velocity its altitude will change by 1 mile.
and I have to answer in feet per second
Here's what I have-
change of altitude: 220-60=160
rule of thumb: 160mi.*2ft/sec=320ft/sec.
I don't know what to do from there
To calculate the minimum change in velocity (ΔV) required for the Space Shuttle to decrease its altitude to 60 miles, we need to use the rule of thumb provided.
According to the rule of thumb, for every 2 feet per second (ft/s) change in the orbiting spacecraft's velocity, its altitude will change by 1 mile.
You've correctly calculated the change in altitude as 160 miles. Now, to convert this change in altitude from miles to feet, we multiply it by the conversion factor of 5280 feet per mile:
Change in altitude (in feet) = 160 miles * 5280 feet/mile = 844,800 feet
So, to change the altitude by 844,800 feet, we need to calculate the corresponding change in velocity using the provided rule of thumb.
Change in velocity = Change in altitude / (2 ft/s per 1 mile) = 844,800 feet / (2 ft/s per 1 mile)
Now, if we simplify the calculation, we get:
Change in velocity = 844,800 / 2 = 422,400 ft/s
Therefore, the minimum change in velocity (ΔV) required for the Space Shuttle to decrease its altitude to 60 miles is 422,400 ft/s.
To calculate the required change in velocity (ΔV) in feet per second, you first need to convert the change in altitude from miles to feet. Since there are 5,280 feet in a mile, the change in altitude of 160 miles is equal to 160 x 5280 = 844,800 feet.
Next, you can use the provided rule of thumb, which states that for every 2 feet per second change in velocity, the altitude changes by 1 mile. In other words, for every 2 ft/s change, the altitude changes by 5280 feet.
To find the required change in velocity (ΔV) in feet per second, you need to divide the change in altitude (844,800 feet) by the conversion factor of 5280 feet per mile. This gives:
ΔV = 844,800 feet / 5280 feet per mile = 160 ft/s.
Therefore, the minimum change in velocity required for the Space Shuttle to decrease its altitude to 60 miles is 160 feet per second (ft/s).