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

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Homework Help Overview

The problem involves calculating the velocity of a satellite in a circular orbit at a distance of one Earth radius above the surface, which raises questions about the relationship between orbital radius and velocity.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use the formula for orbital velocity but questions the assumptions regarding the orbital radius. Some participants ask for clarification on the calculations and the reasoning behind using the radius of Earth versus double that radius.

Discussion Status

The discussion is ongoing, with participants providing feedback on each other's calculations and questioning the assumptions made about the orbital radius. There is no explicit consensus yet, but guidance is being offered regarding the correct application of the formula.

Contextual Notes

Participants are navigating the implications of using different values for the orbital radius and how that affects the calculated velocity. There is a focus on ensuring the correct interpretation of the problem statement and the formulas involved.

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:

[tex]v=\sqrt{\frac{GM}{2r_e}}[/tex]

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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