A space shuttle orbiting Earth at an altitude of 295 km completes an orbit in 90.0 min. Calculate its acceleration and compare it to the acceleration at Earth’s surface.
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To calculate the acceleration of the space shuttle, we can use the formula:
acceleration = (4 * π^2 * r) / T^2
where:
- π is a mathematical constant approximately equal to 3.14
- r is the distance from the center of the Earth to the shuttle's orbit (altitude + radius of the Earth)
- T is the time period for one complete orbit (in seconds)
First, let's convert the given altitude from kilometers to meters by multiplying it by 1000:
altitude = 295 km * 1000 = 295,000 meters
The radius of the Earth is approximately 6,371 km, so we add this to the altitude to get the total distance from the center of the Earth to the shuttle's orbit:
r = altitude + radius
r = 295,000 m + 6,371 km * 1000 = 6,666,000 meters
Next, we need to convert the time period from minutes to seconds:
T = 90 min * 60 = 5400 seconds
Now we can plug the values into the formula to calculate the acceleration:
acceleration = (4 * π^2 * r) / T^2
acceleration = (4 * 3.14^2 * 6,666,000) / 5400^2
After solving this equation, we get the value of acceleration specific to the space shuttle's orbit around the Earth.
To compare this acceleration to the acceleration at Earth's surface, we can use the value of the acceleration due to gravity on Earth. On Earth's surface, the acceleration due to gravity is approximately 9.8 m/s^2.
Therefore, we can compare the calculated acceleration of the space shuttle around Earth to this value to determine the difference.