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Comment by PankajGhosh | Hacker News Reader

Wouldn't this relationship only exist on earth (to be exact on surface of earth)? Unless we redefine 1 meter of length depending on gravitational field on every surface of planet/star...

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Yes, the definition of ‘1 metre’ s.t. a pendulum of this length has a period of 2 seconds (with some other, not length-related definition of seconds) only works in uniform gravity. But this wasn’t really a problem at the time these definitions were first made, as few people wanted to build metre sticks on the moon and the variations of g on the surface of Earth are likely to small to be measured given the usual experimental errors in the 19th century.

Nervertheless, the correct constant should be τ[0] anyways.

[0] http://tauday.com/

You are underestimating early 19th century science, and even 17th century science. http://en.wikipedia.org/wiki/History_of_the_metre: "However, it was soon discovered that the length of a seconds pendulum varies from place to place: French astronomer Jean Richer had measured the 0.3% difference in length between Cayenne (in French Guiana) and Paris."

Richer discovered that while in French Guyana, between 1671 and 1673 (http://en.wikipedia.org/wiki/Jean_richer)

Yup. So - the answer to the question "What Does Pi Have To Do With Gravity" is pretty much - nothing.

The article also notes that it does not work it you use feet instead of meters, hence basically already answering the question.

No, the answer is that our units were constructed so that pi has something to do with gravity.

Exactly. I found this article sorely lacking of punch, however. It's like saying what does the meter have to do with the mass of the H2O molecule? Well 1 Kg is defined as the weight of 1 cubic meter of water at 1 atm.

1000 cubic centimetres - a cubic decimetre. Not a cubic meter. A cubic meter of water ways a ton.

If you think of π as the relation between the circumference of a circle and its diameter, then it does have something to do with gravity (and dimensions) - in a one-dimensional world, for example, the force of gravity would not fall of with distance, as it is the gravitational flux that is conserved. If there is only one dimension, there's no way for it to disperse away from a body, hence it is constant.

If you then add another dimension (a flat world of two spatial dimensions), you suddenly get a 1/r relation for the force (log(r) for the potential) as the gravitational flux can now disperse in two dimensions. Naturally, a constant comes in here, which is a function of π. The argument naturally extends to three dimensions to give you 1/r² and a more complicated coefficient.

Naturally, this also applies to other classical forces, viz. electromagnetism.

That depends on how you pick the gravitational constant. It's trivial to make e show up in gravitational equations but with the right g you can avoid pi in a our world. At which point you can play around with a different number of dimensions, but that's just math and has nothing to do with physics.

Pi relates to SI units, but not gravity.

Unless you wanna be esoteric and go herp derp g=(GMm)/((orbital circumference)/2pi)^2 at which point tada QED!

Also tidal forces, lots of pi when your cranking those out. And keplers laws of planetary motion, which last I checked are all about gravity.

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