Using a pendulum to find Planetary mass and radius

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SUMMARY

The discussion focuses on calculating planetary mass (M) and radius (R) using a pendulum of length (L) and its periods (T1 and T2) at different elevations. The gravitational force equation (Fg = GMm/R^2) and the pendulum period equation (T = 2π√(L/g)) are central to the analysis. The user seeks an additional equation to relate the pendulum's period at an elevation of 2 km, indicating a need for a third equation to solve the problem definitively. The assumption of a spherical planet is critical for the calculations.

PREREQUISITES
  • Understanding of gravitational force equations (Fg = GMm/R^2)
  • Knowledge of pendulum mechanics (T = 2π√(L/g))
  • Familiarity with concepts of elevation and its effect on gravitational acceleration
  • Basic algebraic manipulation skills for solving equations
NEXT STEPS
  • Research how to derive gravitational acceleration at different elevations
  • Learn about the concept of center of mass (CoM) in planetary physics
  • Explore the effects of altitude on pendulum motion and period
  • Investigate additional equations related to gravitational potential energy
USEFUL FOR

Students in physics, educators teaching gravitational concepts, and anyone interested in planetary science and mechanics will benefit from this discussion.

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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
 
Physics news on Phys.org
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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