Finding planet radius from satellite orbit using Kepler's third law

[brett812718]

[SOLVED] need help with keplers 3rd law of periods problem

Homework Statement

A 20 kg satellite has a circular orbit with a period of 2.6 h and a radius of 9.4E6 m around a planet of unknown mass. If the magnitude of the gravitational acceleration on the surface of the planet is 8.6 m/s2, what is the radius of the planet?

Homework Equations

T^2=((4pi^2)/(GM))r^3

a gravity=(GM)/r^2

The Attempt at a Solution

I used the law of periods to find the mass and then used the second equation to find the radius of the planet but I got a really small number

 

[hage567]

Can you show your calculations in more detail? Note that r in your first equation is not the same as r in the second (in case you forgot that).