Using a pendulum to find Planetary mass and radius

AI Thread Summary
To determine the mass (M) and radius (R) of a planet using a pendulum, the explorer measures the pendulum's period at two elevations: ground level (T1) and 2 km higher (T2). The gravitational force equation Fg = GM/R^2 and the pendulum period equation T = 2(pi)(sqrt(L/g)) are central to the calculations. The explorer realizes that they need an additional equation to relate the two periods and heights, as they currently have three variables but only two equations. The suggestion is to derive a second equation for the pendulum's period at the higher elevation. This approach will help solve for the unknowns effectively.
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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
 
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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.
 
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