alt Hacker NewsBy ascertaining an approxiamte value of G , perhaps? After that, you know M_earth, and already knowing Earth’s geometry, one arrives at average density rho.
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Yup, that's exactly it:
- get the gravitational constant with these two known masses
- then can deduct the mass of the unknown Earth by its interaction with other masses (say the "g" gravitational acceleration value)
- then from the mass and the otherwise measured size of Earth the density pops out
More details in good ol' Wikipedia: https://en.wikipedia.org/wiki/Cavendish_experiment#Derivatio...
Oh so the earth density is merely the motivation for the experiment? I read it as the earth mass actually being used somewhere in the formulas within the setup itself which was what confused me.
He uses his experiment to calculate G based only on the test masses and spring and then the _result_ of the calculation was just used as a final step to calculate the mass of the earth, and then from that the density?
Laying out the math (assuming earth is an homogeneous sphere) just in case it's not clear:
F_gravitational = G m1 m2 /r^2
g = G Mass_earth / r_earth^2
Mass_earth = r_earth^2 * g/G
Density_earth = r_earth^2 * g/G / V_earth
Density_earth = 3*g / (4*Pi*G*r_earth)
Prior to Cavendish we already new g and r_earth, just missing G.