Foucault’s Pendulum

Over on the Astronomy Stack Exchange site, (obviously I follow the “new questions” feed in my RSS reader,) someone asked if it was possible, without knowing the date, to determine one’s latitude only by observing the sun. These are the sorts of random questions that grab me by the lapels and shake me until an idea falls out.

So my first thought was: Well if you’re in the arctic or antarctic polar circles you could get a good idea… when you don’t see the sun for a few days. Also, COLD. But that feels like cheating and doesn’t give a specific value. Which left me with this vague feeling that it would take me several months of observations. I could measure the highest position of the sun over the passing days and months and figure out what season I was in…

…wait, actually, I should be able to use knowledge of the Coriolis Force—our old friend that makes water circle drains different in the northern and southern hemispheres, and is the reason that computers [people who compute] were first tasked with complex trigonometry problems when early artillery missed its targets because ballistics “appear” to curve to do this mysterious force because actually the ground rotates . . . where was I?

Coriolis Force, right. But wait! I don’t need the sun at all! All I need is a Foucault Pendulum and some trigonometry… Here I went to Wikipedia and looked it up—which saved me the I’m-afraid-to-actually-try-it hours of trying to derive it in spherical trig… anyway. A Foucault Pendulum exhibits rotation of the plane of the pendulum’s swing. Museums have these multi-story pendulums where the hanging weight knocks over little dominos as it rotates around. Cut to the chase: You only need to be able to estimate the sine function, and enough hours to measure the rotation rate of the swing-plane and you have it all; northern versus southern hemisphere and latitude.