Finding planet radius from satellite orbit and surface gravity

[fiestytig]

Here's my problem:

A 23.0-kg satellite has a circular orbit with a period of 2.35 h and a radius of 8.90×106 m around a planet of unknown mass. If the magnitude of the gravitational acceleration on the surface of the planet is 8.90 m/s2, what is the radius of the planet?

I got to say, I have no idea where to start since I don't have the mass of the planet. Any help? Pretty please? Due tonight at 10 pm EST... thanks!

 

[DizzyGillespie]

The force acting on the satellite is also the centripetal force. F-mv^2/R and F-G(M*m)/r^2. that should help you find the mass of the planet. right?

 

[Janus]

First question: Do you know how to find the period of a satellite if you know the planet's mass and the Radius of its orbit?

Second question: If you do, can't you use this method to find the Planet's mass when you know the period and radius of the orbit?

 

[fiestytig]

I'm afraid I still don't follow, even with those suggestions... All I really know is T^2=4 Pi^2 r^3 /G M. But I don't really have the r either, do I?

 

[Janus]

I'm afraid I still don't follow, even with those suggestions... All I really know is T^2=4 Pi^2 r^3 /G M. But I don't really have the r either, do I?

Then what is this?

A 23.0-kg satellite has a circular orbit with a period of 2.35 h and a radius of 8.90×106 m around a planet of unknown mass.

 

[fiestytig]

So then how do I find the radius of the planet? (I got confused by the radiuses there for a minute.)

 

[fiestytig]

Aha! I figured it out! Thanks. Had to use a formula to find mass and then use g = G+M/R^2 to find R. :)