## Homework Statement

A satellite orbits the sun with a period of 2.1 day. What is the radius of its orbit?

T=2pi*r/V

## The Attempt at a Solution

If the time is given in days I have to convert to seconds right? Also how would I find velocity would I use V=square root (Gms/r)? For some reason gravity has got me confused

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LowlyPion
Homework Helper
If the time is given in days I have to convert to seconds right?
That would be useful, as the units of G involve seconds.

Recognize that

v = 2πr/T

and m*v2/r = GMm/r2 or as you have written

v2 = GM/r

Combine with

v2 = (2πr/T)2 = GM/r

so that actually gets rid of the actual speed of the object as far as usefulness in the equation.

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Cyosis
Homework Helper
Alternatively you could also use $m \omega^2 r$ as the centripetal force.

That is an awesome way to check yourself since he wants the work done by using the gravity equations but just to double check myself I can use that! Thats a big help also thank you!

LowlyPion
Homework Helper
so that actually gets rid of the actual speed of the object as far as usefulness in the equation.
Well ... yes. They only ask you for the radius. Were you invested in wanting to find the speed?

No, but I just didn't even think about using the equations that deal with velocity. So I was getting lost. Is there another way to go about this problem?

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