Submitted by LoreCriticizer t3_z53aqr in askscience
phrankjones t1_ixvb757 wrote
Reply to comment by lacgibra in How would one calculate the gravity of a planet? by LoreCriticizer
Their question is more asking the line of: how do you get the mass of the earth?
lacgibra t1_ixvevls wrote
The comment above still fits, You can obtain mass of the earth by doing the simple pendulum method to obtain g from the equation √g = 2π√L/T
g = earth's gravity L = length of the pendulum T = time period
Note that simple pendulum give adequate answers for small angles only, if you swing the pendulum to wide you won't br arriving at the earth's gravity.
then equate it with g = GM/r²
Kered13 t1_ixy67ha wrote
It's actually very difficult, because we have to derive it from gravity, and measuring gravity is very difficult. Actually, measuring the acceleration due to gravity is quite easy, that's what /u/lacgibra described. The trouble is measuring the gravitational constant. Of all the fundamental physical constants, the gravitational constant is the one that is known to the least accuracy. The classic experiment for this is Cavendish's experiment, and indeed this was originally conducted in order to estimate the mass of the Earth. This is still basically the technique used, but with much more precise equipment.
Fun fact: We know the mass of the other planets as a ratio to the mass of the Earth much more precisely than we know their absolute mass. This is because the uncertainty in the gravitational constant is greater than the uncertainty in the acceleration due to the planets that we can measure.
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