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 215 miles above the surface of Earth.

Use the rule of thumb that below an altitude of 500 miles, for every 2 feet per second (fps) change in the orbiting space craft’s velocity its altitude will change by 1 mile.

To calculate the minimum change in velocity (∆V) required for the Space Shuttle to decrease its altitude to 60 miles, we can follow these steps:

1. Find the current altitude of the Space Shuttle:
Altitude = (apogee + perigee)/2 - radius of Earth
Given: Apogee = 236 miles, Perigee = 215 miles, and radius of Earth = 3959 miles
Altitude = (236 + 215)/2 - 3959 = 72 miles

2. Calculate the change in altitude required:
Change in altitude = Current altitude - Final altitude
Change in altitude = 72 - 60 = 12 miles

3. Determine the change in velocity (∆V) required using the rule of thumb:
For every 2 fps change in the spacecraft's velocity, the altitude changes by 1 mile.

Change in velocity = Change in altitude / (1 mile / (2 fps))
Change in velocity = 12 / (1/2) = 12 * 2 = 24 fps (∆V)

Therefore, the minimum change in velocity (∆V) required for the Space Shuttle to decrease its altitude to 60 miles is 24 feet per second (fps).

To calculate the minimum change in velocity (∆V) required for the Space Shuttle to decrease its altitude to 60 miles, we can use the given rule of thumb.

Step 1: Determine the difference in altitudes between the current orbit and the desired altitude.
Difference in Altitude = Current Altitude - Desired Altitude

In this case:
Current Altitude = Apogee - Earth's Surface = 236 miles - 0 miles = 236 miles
Desired Altitude = 60 miles

Difference in Altitude = 236 miles - 60 miles = 176 miles

Step 2: Convert the difference in altitude from miles to feet.
Difference in Altitude (in feet) = Difference in Altitude (in miles) * 5,280 feet/mile

Difference in Altitude (in feet) = 176 miles * 5,280 feet/mile = 927,680 feet

Step 3: Determine the required change in velocity (∆V) using the rule of thumb.
Required ∆V = Change in Altitude (in feet) / 2 feet per second (fps)

Required ∆V = 927,680 feet / 2 fps = 463,840 fps

Therefore, the minimum change in velocity (∆V) required for the Space Shuttle to decrease its altitude to 60 miles is 463,840 feet per second (fps).