4 ms·

By 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.

imrehg 5mo ago
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#Derivation_of_G_and_the_Earth's_mass https://en.wikipedia.org/wiki/Cavendish_experiment#Derivatio...
- UncleSlacky 5mo ago
  It's also a notoriously difficult experiment to perform. When I did it at university, the value of G I got was out by an order of magnitude - and that was considered a good result!
phh 5mo ago
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.
alkonaut 5mo ago
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?
- ricksunny 5mo ago
  Several years back when I first learned about the Cavendish experiment, I was indeed surprised that he was able to measure anything related to gravity without using a planetary-scale mass as one of experimental masses.
  - recursivecaveat 5mo ago
    Clever experiments to measure tiny values are probably my favorite kind of science. Millikan found the charge of an electron by looking for a common integer multiple of charge in tiny oil droplets. Or LIGO measures gravitational waves by watching the interference pattern generated over time by two light beams taking different paths.
- ricksunny 5mo ago
  Y’know, I went and looked at the current Wikipedia page for the Cavendish experiment. There’s apparently more nuance than my simple outline offers, particularly as G wasn’t treated as an isolated quantity till decades after his experiment. Linking directly to section anchor: https://en.wikipedia.org/wiki/Cavendish_experiment#Reformulation_of_Cavendish's_result_to_G https://en.wikipedia.org/wiki/Cavendish_experiment#Reformula... There is less description than I would like, but I am happy to have been made aware of the discrepancy at all.

imrehg 5mo ago

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#Derivation_of_G_and_the_Earth's_mass https://en.wikipedia.org/wiki/Cavendish_experiment#Derivatio...

UncleSlacky 5mo ago
It's also a notoriously difficult experiment to perform. When I did it at university, the value of G I got was out by an order of magnitude - and that was considered a good result!

phh 5mo ago

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.

alkonaut 5mo ago

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?

ricksunny 5mo ago
Several years back when I first learned about the Cavendish experiment, I was indeed surprised that he was able to measure anything related to gravity without using a planetary-scale mass as one of experimental masses.
- recursivecaveat 5mo ago
  Clever experiments to measure tiny values are probably my favorite kind of science. Millikan found the charge of an electron by looking for a common integer multiple of charge in tiny oil droplets. Or LIGO measures gravitational waves by watching the interference pattern generated over time by two light beams taking different paths.
ricksunny 5mo ago
Y’know, I went and looked at the current Wikipedia page for the Cavendish experiment. There’s apparently more nuance than my simple outline offers, particularly as G wasn’t treated as an isolated quantity till decades after his experiment. Linking directly to section anchor: https://en.wikipedia.org/wiki/Cavendish_experiment#Reformulation_of_Cavendish's_result_to_G https://en.wikipedia.org/wiki/Cavendish_experiment#Reformula... There is less description than I would like, but I am happy to have been made aware of the discrepancy at all.