Comment by thaumasiotes
1 year ago
g is related to the radius of the earth; the meter is related to the circumference of the earth; and pi is the relationship between the radius and the circumference.
1 year ago
g is related to the radius of the earth; the meter is related to the circumference of the earth; and pi is the relationship between the radius and the circumference.
Aside from the fact that the post already explained what the actual historical connection is, your explanation requires some serious hand-waving about the mass of the Earth and the gravitational constant, neither of which were known when the meter was first defined.
Reasonably accurate values for both M_earth and G were known at the time the SI meter was defined.
Also it's not too hard to extend this. M_earth is a function of Earth's radius which goes into the definition of the meter. G is a function of earth's orbital period, which goes into the definition of the second. Further our definition of mass is based on the density of water, which is chosen because it is a stable liquid at this particular orbital distance from a star of our sun's mass.
As far as I can tell, the most recent experiment to measure the mass of the Earth by 1790, when they decided on the definition of the meter, was the 1772 Schiehallion experiment, which gave a value 20% below the actual value. So if pi^2 were to somehow fall out of that it would likely be so far off as to be unrecognizable.
But even that doesn’t matter, because the mass of the Earth didn’t play a direct role in the definition of the meter. If you take out the whole thing about the meter’s definition targeting half a toise, then all you have is “related to the circumference of the Earth”, and it would be a monumental coincidence if the mass of the earth and gravitational constant just conspired to somehow drop an unadulterated pi^2 out of the math.
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