What is the Radius of a Satellite's Circular Orbit Around Earth?

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To calculate the radius of a satellite's circular orbit around Earth with a period of 22.0 hours, the correct formula T^2 = (4π^2/GM) * r^3 should be used. It's crucial to convert the period from hours to seconds to ensure all units are in SI. A participant initially calculated the radius as 1.84x10^8 m but was informed that the expected result should be around 40,000 km. The discussion emphasizes the importance of unit conversion and careful application of the formula to arrive at the correct answer. Proper calculations lead to a more accurate determination of the satellite's orbital radius.
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Homework Statement


A satellite is in a circular orbit around the earth. The period of the satellite is 22.0 hr. Calculate the radius of the orbit of the satellite. Data: Mass of the Earth = 5.98·1024 kg.



Homework Equations


I thought I could use...
T^2 = (4pi^2/GM) * r^3
but I am not getting the right answer, can someone give me a start on this?
 
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This is the correct formula. Did you convert the period from hours to seconds? If not, you are going to get the incorrect answer. You have to make sure everything is in SI units.
 
I also assume you mean the mass of the Earth = 5.98*10^24 kg.
 
yes I converted it to seconds and got 1.84x10^8 m, but its wrong.
 
Show your work. You made a mistake somewhere, as you should have about 40000 km had you applied the equation properly.
 

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