Determining the mass of a planet in a pendulum system?

Question

An astronaut arrives at a new planet, and gets out his simple device to determine the gravitational acceleration there. Prior to this arrival, he noted that the radius of the planet was 6140 km. If his 0.600-m-long pendulum has a period of 1.0 s, what is the mass of the planet?

____ kg

Answer 1

R=6140 km

L=0.6m

T=1 s

γ=6.673e-11 m3/kg s2

M=mass of the planet

T=2π√(L/g) ==> g=L(2π/T)^2

On the other hand g=γM/R^2

L(2π/T)^2=γM/R^2 ==>

M=(L/γ)*(2πR/T)^2=13.388e24 kg

Answer 2

The time period of a simple pendulum is given by :

T = 2 * pi * sqrt.[l / g]

or

g = 4 pi^2 l / T^2

Here l = 0.6 and T = 1

So g = 23.69 m/s^2

Now g = GM / R^2

So M = 1.34 * 10^24 kg

Hope this helps.

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