Comment by kaapipo

1 year ago

If the length of a meter were defined as the length of a seconds pendulum [1], then g would equal exactly π². From the pendulum equation:

`T = 2π√(L/g)`

substitute T = 2 s and L = 1 m:

`2 s = 2π√(1 m / g)`

solve for g:

`g = π² m/s²`.

This holds up in any strength of gravity, but the length of a meter would be different depending on it.

[1]. This actually was proposed by Talleyrand in 1790. Imagine the world if this were true!

The article explains that Huygens proposed this in the 17th C, and gives the same derivation :)