Radius of Satellite Orbit - 2.1 Days Period

[talaroue]

Homework Statement

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

Homework Equations

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 (Gm_s/r)? For some reason gravity has got me confused

 

[LowlyPion]

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

 

[talaroue]

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

 

[Cyosis]

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

 

[talaroue]

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]

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?

 

[talaroue]

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?

 

[talaroue]

here is another one of my questions. I feel bad seeing as I have posted 3 questions in a row. But I think I am starting the grasp the concept of where anwsers are coming from.
https://www.physicsforums.com/showthread.php?t=318215"