Everything But the Magnetic Sink

I was looking at some of the environmental data supplied by our PUC this week, and I had a thought on the magnetometer reading:

A magnetometer measures the direction and strength of the local magnetic field, similar to a compass. A significant difference though is that a compass only measures the horizontal direction of the field, while this reading shows all 3 dimensions. What's interesting about that is that we can see the field here has a significant z (vertical) component.

The Earth's magnetic field is approximately a dipole, with an offset of 11° from the rotational axis. We can plot the field lines over the surface:

The red line shows the rotational axis, and the magenta line shows the axis of the magnetic field. Notice that the lines come out of the South pole (a source), and go into the North pole (a sink). One of the strange quirks of how we define our magnetic poles is that because the North pole of a compass points toward the North geographic pole, this must be the South pole of the Earth's magnetic field. Using this plot, we can plot the relationship between the vertical angle of the magnetic field relative to the surface and your latitude on Earth:

The two curves represent the two halves of the Earth in the plot above: the right side, closer to the North pole, and the left side opposite it. The PUC gives us the horizontal dotted line, and we can look up our latitude here in Michigan for the vertical line (or "look up" to the North Star if you want to be fancy). In theory, we could measure our longitude by interpolating between the blue and green lines to the point where the red lines cross. Trying that out gives a position of -37.84°, while our true longitude is -83.86°. Maybe I'll stick to using GPS for now!