Centripetal Acceleration Part II

AI Thread Summary
To find the time required for a satellite to complete one orbit at a radius of 6689 km and speed of 7723.55 m/s, the correct formula to use is v = 2πr/T. After substituting the values, the calculation yields T = 5221.57 seconds. This converts to approximately 1.51 hours. The discussion highlights the importance of using the correct radius in calculations and emphasizes the need for unit conversion.
BitterSuites
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[SOLVED] Centripetal Acceleration Part II

Homework Statement



(From previous question) In order for a satellite to move in a stable circular orbit of radius 6689 km at a constant speed, its centripetal acceleration must be inversely proportional to the square of the radius of the orbit.

What is the speed of the satellite? The G is 6.67259e-11 and the mass of the Earth is 5.98e24kg.

The answer to this was 7723.55 m/s.

Part II:

Find the time required to complete one orbit. Answer in units of h.

Homework Equations



The book only gives one equation for T referencing orbits, which is v=2pir/T

The Attempt at a Solution



v=2pi/T
7723.55 = 2pi/T
7723.55T = 2pi
T = 2pi/7723.55
T = .000814

I think the homework system even laughed at me when I entered that answer :)
 
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BitterSuites said:

Homework Equations



The book only gives one equation for T referencing orbits, which is v=2pir/T
Right.

The Attempt at a Solution



v=2pi/T
Wrong.

Compare the two equations. (You left off the r.)

And don't forget to convert your answer to the desired units.
 
*sigh* I keep making really silly mistakes.

So I input the correct equation but it came out correct.

v=2pir/t
7723.55 m/s = 2pi * 6689000m/T
7723.55T = 4.20282e7
T = 5221.57 seconds

Convert to hours

5221.57/60 = 90.6928 minutes
90.6928/60 = 1.51155 hours

Thank you so much.
 
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