Uniform circular motion with unknown mass

[Emil Zapotec]

Homework Statement

A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.7x10^4 m/s and the radius is 5.25x10^6 meters. A second satellite also has a circular orbit around the same planet and has an orbit radius of 8.6x10^6 meters. What is the orbital speed of the second satellite?

The Attempt at a Solution

I was wondering if I have to find the centripetal acceleration of the first satellite. If so I know the acceleration is 55.05 m/s^2. But I'm stuck on what to do with there because I don't even know if that acceleration is relevance and how you work it into mv^2/r

 

[Archduke]

What force is causing the satellite to be in circular orbit? Do you know any equations for this force?

 

[Emil Zapotec]

The only force would be the gravitational force of the unknown planet. But there's no information about the planet, only that a satellite rotates around it, so I'm assuming there's a formula that I need to derive where a mass needs to cancel?

 

[Archduke]

As the gravitational force is the only force, how about equating it to the centripetal force?

 

[Emil Zapotec]

Oh, so just find the centripetal force of the first one, find out what it is and equate it to the centripetal force of the satellite with the unknown velocity? I guess I made it a lot harder than I thought, thanks a lot.

 

[Archduke]

Well, the centripetal force of the first satellite isn't the same as the centripetal force on the second satellite. But, once you've equated the centripetal force and gravitational forces together, can you re-write the expression so one side of the equation has only constants, and the other side has the variables. Now, as one side has only constants, you can equate the variables of the two satellites. I guess I'm saying use proportionality, but in a really round-about way!