Using a pendulum to find Planetary mass and radius

[boardaddict]

Long Time reader, first time caller

Homework Statement

An explorer wants to find planetary mass M and radius R using a pendulum of length L. The average elevation of the planet is R. At this elevation the pendulum has period T1. He then climbs up 2km where the pendulum has period t2. Express M and R interms of other variables need to calculate. Assume the planet is spherical

Homework Equations

Fg= GMm/R^2

T=2(pi)(sqrt(v/g)

The Attempt at a Solution

g = 4pi^2 L/T^2= GMm/R^2

I know I need another equation, I was hoping someone could point one out or tell me what I am missing. Obviously this could be solved one of ther variable but at the moment I have 3 var. and 2 equations. I thought about CoM but or CoE but then that brings in a lot more variables.

any thoughts

 

[ideasrule]

4pi^2 L/T^2= GM/R^2 (note: NOT GMm/R^2) is for ground level. Write another equation that says the pendulum has period t2 2km up.