Calculating Satellite Orbit Time

In summary, the average speed of an orbiting satellite is 20,000 mph and it is orbiting 250 miles above the Earth's surface. It would take approximately 79.2 minutes (1.32 hours) for the satellite to orbit the Earth, with a total distance of 26457.84 miles. However, for more accurate measurements, it is recommended to use the exact value of 8426π miles (26471.0597 miles).
  • #1
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Homework Statement


The average speed of an orbiting satellite is 20,000 mph. How much time is required for the satellite to orbit Earth? (the satellite is orbiting 250 miles above the Earth’s surface, and remember that the Earth has a radius of 3,963 miles.)


Homework Equations


t=d/v
2∏(r)


The Attempt at a Solution


3963+250=4213

2∏(4213)
6.28(4213)
26457.84 miles

26457.64/20000
=1.32 hours*60mins
=79.2 mins

Did I do this correctly?
 
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  • #2
It looks OK.
 
  • #3
Thank you for the response.
 
  • #4
I don't see anything wrong. But, for the future; try to keep exact, or near exact answers throughout your problem, for example, when you multiplied ##6.28## by ##4213## you got ##26457.84##mi, whereas the exact answer was ##8426\pi##mi or ##26471.0597##mi. Besides that I don't see anything wrong with your solution.
 
  • #5


Your attempt at solving this problem using the given equations is correct. However, the final answer should be in hours, not minutes. So the correct answer would be 1.32 hours. Additionally, it is always good practice to include units in your final answer. So the final answer would be 1.32 hours or 79.2 minutes.
 

1. How is the orbit time of a satellite calculated?

The orbit time of a satellite is calculated using the formula T = 2π√(a^3/GM), where T is the orbit time, a is the semi-major axis of the orbit, G is the gravitational constant, and M is the mass of the central body (usually Earth).

2. What is the semi-major axis of an orbit?

The semi-major axis is the distance from the center of the orbit to the furthest point of the orbit. In other words, it is half of the longest diameter of the elliptical orbit.

3. How does the mass of the central body affect the orbit time of a satellite?

The mass of the central body (e.g. Earth) directly affects the orbit time of a satellite. The higher the mass of the central body, the stronger its gravitational pull, resulting in a shorter orbit time for the satellite.

4. Can the orbit time of a satellite be changed?

Yes, the orbit time of a satellite can be changed by altering its velocity or distance from the central body. This can be achieved through thrusters or gravitational assist maneuvers.

5. Are there any variables that can affect the accuracy of the calculated orbit time?

Yes, there are several factors that can affect the accuracy of the calculated orbit time, such as atmospheric drag, changes in the gravitational field, and irregularities in the shape of the central body. These variables must be taken into account for a more precise calculation of orbit time.

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