The Clockwork of the Universe

The physics of the Foucault pendulum predict that the rate of the apparent rotation of the pendulum is only dependent on the latitude of the pivot point. If the pendulum is at the North or South pole, the pendulum rotates once every 24 hours (this was recently demonstrated at South Pole Station in 2001.) If the pendulum is on the equator, it does not rotate at all! In between, the pendulum rotates according to the equation:

where 23 hours, 56 minutes, 4 seconds is a sidereal day - the time a day would take if the Earth was standing still with respect to motion around the Sun - but still rotating.

Since the pendulum is in the Northern hemisphere, the pendulum's apparent rotation is clockwise. From the old photographs, looks like North is the compass rose point that is light, not one of the 3 dark ones. Schematics of the old Smithsonian museum show that the pendulum was towards the Northern wall, at the center of the building. Google Maps gives the latitude there as N 38.89129 degrees. From the equation, the period of the apparent rotation will be 38.1198 hours - the pendulum will travel 9.444 degrees per hour.

Even today, the Smithsonian opens at 10 am, so we can see the pendulum being started every day at that time. There is a ceremony to starting the pendulum off, since it is easy to force a direction that can impose an elliptical orbit effect on the pendulum motion, instead of being always in the plane - the way described on line for the LA pendulum is to tie the pendulum back with a thread, and then burn the thread to start the exhibit (and also allow time to reset the pegs from the day before).

The swing of the pendulum is constrained to keep the offset from going over 15 degrees, to allow the sin theta = theta approximation to keep the basic pendulum swing linear. There is an electromagnetic fixture at the top of the pendulum that imparts energy back into the swing, so modern pendulums do not have to be restarted every couple of hours.

From 1000 to 0133 gives us 15.55 hours. We have been told that the pendulum is started swinging in the North-South orientation (0 degrees). At 0133, the reference arm of the pendulum swing will point at 146.8 degrees.

We will work with that and a DC map - next time.