Why is the velocity of a satellite in a circular orbit twice the orbital radius?

AI Thread Summary
The discussion centers on calculating the velocity of a satellite in a circular orbit at a distance of one Earth radius above the surface. The orbital radius is assumed to be twice the Earth's radius, leading to confusion in the calculations. One participant correctly notes that the formula for velocity should be v = √(GM/(2r_e)), where r_e is the Earth's radius. The calculations reveal that the correct velocity is approximately 5000 m/s, not the initially calculated 7913.048 m/s. The importance of using the correct orbital radius in the formula is emphasized throughout the discussion.
Maiia
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Homework Statement


A satellite is in a circular orbit about the Earth at a distance of one Earth radius above the surface. What is the velocity of the satellite?

The Attempt at a Solution


I assumed the orbital radius was twice the radius of the Earth so
GMearth/r= velocity
but that leaves me with a very small velocity...
 
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Can you show your answer and your work? If you do have a mistake, I can't find it without seeing both.
 
well since I assumed orbital radius was 2Eradius, then
(GMearth/r)^.5= v
I plugged in (6.67*10^-11(5.98*10^24)/6.37*10^6)6.5= 7913.048m/s
 
Maiia said:
well since I assumed orbital radius was 2Eradius, then
(GMearth/r)^.5= v
I plugged in (6.67*10^-11(5.98*10^24)/6.37*10^6)6.5= 7913.048m/s

Why are you multiplying by 6.5? Also, you never doubled the radius when you plugged in the numbers. According the the formula you give, which is correct, the velocity should be:

v=\sqrt{\frac{GM}{2r_e}}

Plugging in the numbers you give, I get an answer around 5000m/s.
 
why do you double the radius?
 
Maiia said:
why do you double the radius?

You said it yourself before. The orbital radius is twice the radius of Earth. In your formula, you used the radius of Earth, not double the radius of Earth.
 

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