Orbital Period of satellite in terms of v and r

[Cloud 9]

Homework Statement

"A satellite orbits the Earth in a circular orbit of radius r. If the orbital speed of the satellite is v, what is the orbital period T of the satellite in terms of v and r? You must explain how you derive the expression for the period."

Homework Equations

Speed = distance/time
a = v²/r

The Attempt at a Solution

Distance for 1 revolution of a circle is equal to the circumference. So distance = 2(pi)r
Time to travel 1 revolution = period T

So velocity = speed = 2(pi)r/T

a = v²/r

a = 2(pi)r/T * 1/T

a = 2(pi)r / T²

At this point I would solve for T, but I am not sure if this is valid, what I'm doing? I don't think we are supposed to have an acceleration in there, so I was wondering if there is another equation I could use that relates v and r. Btw this is not graded, it's just a sample test (that we're not turning in) to help us for the real test (on Tuesday). Thanks for any assistance.

 

[bossman27]

I don't think you even need to bother with the centripetal acceleration equation.

If we have an orbital radius of r, this gives an orbital path distance of 2∏r

T = d / v ---> T = (2∏r) / v

 

[voko]

If you know the distance per revolution, and you know the velocity, surely you can compute the time of one revolution.

 

[Cloud 9]

I don't think you even need to bother with the centripetal acceleration equation.

If we have an orbital radius of r, this gives an orbital path distance of 2∏r

T = d / v ---> T = (2∏r) / v

Oh thanks, so I could have stopped there and solved for T. I guess I made it too complicated. So that answers the question right?

 

[bossman27]

Oh thanks, so I could have stopped there and solved for T. I guess I made it too complicated. So that answers the question right?

Yup, in general you want to use the least amount of extra variables/equations possible.