What Does Pi Have To Do With Gravity?
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Re: What Does Pi Have To Do With Gravity?
#2Wouldn'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...
Re: What Does Pi Have To Do With Gravity?
#3Wouldn'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...
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.
Re: What Does Pi Have To Do With Gravity?
#4Wouldn'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...
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.
Re: What Does Pi Have To Do With Gravity?
#5Wouldn'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...
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.
Re: What Does Pi Have To Do With Gravity?
#6I spent $3.14 (USD) on a latte this morning.
Re: What Does Pi Have To Do With Gravity?
#7Was hoping to see some relation with the big G, but the author instead used small g, which depends on all kinds of things and cannot be treated as a constant.
Re: What Does Pi Have To Do With Gravity?
#8Earlier quoted context omitted.
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.
Re: What Does Pi Have To Do With Gravity?
#9Was hoping to see some relation with the big G, but the author instead used small g, which depends on all kinds of things and cannot be treated as a constant.
It wasn't up to the author! He's just relaying a historical point.
Re: What Does Pi Have To Do With Gravity?
#10For anyone hoping for some deeper fundamental connection, you should read about natural units[1] to understand why that couldn't happen.
Given a dimensional constant, it can only be related to some more fundamental mathematical constant in a particular set of units. So the connection will be entirely due to how the units are defined, as is the case here.