Physics 210Spring 2011
How to Derive Your Latitude & Longitude
First, you should figure out the latitude. That’s the easy one. If you have a sextant, you can use that to get the altitude of polaris. If you don’t have a sextant, get a protractor and a piece of string from the classroom. Tie the string to the center of the protractor and tie a weight to the other end of the string. Sight down the straight edge of the protractor at Polaris and see the angle reading where the string falls. The angle between the string and the straight edge of the protractor is your latitude plus 90 deg. So subtract 90 to get your latitude. Make sure to estimate a range of confidence! How far to either side of your reading would a number have to be before you would believe it to be different from what you measured?
For a consistency check, try to identify some circumpolar stars that are as close to the horizon as you can. The declination of these stars is related to your latitude. Look up their Dec values on a computer and average them. That will give you a lower bound on the latitude. See if you can also identify a star that is almost but not quite circumpolar. That will give you an upper bound. If the pole is at the zenith, your latitude is 90 deg and all the stars will be circumpolar, so the lowest stars will be at Dec=0. That means to get your latitude, subtract the lowest stars’ Dec from 90 deg. See if this range overlaps your range from the sextant.
Now, the longitude is a little trickier. You need to make a gnomon. This is essentially a vertical stick with a small ball on top (it’s easier to mark the center of a circle). Google it to find some images. You can get what you need at any craft store. It’s very important the stick be as vertical as you can make it. Once you have one, pick a bright, sunny day and do the measurements around noon. Pick some level ground and set up the gnomon. You could build a base or just shove the stick in the ground. Make sure it’s vertical. Use a plumb bob.
Mark the location of the ball’s shadow every five minutes or so for at least an hour before and after noon. Make a plot of the length of the shadow as a function of time in minutes before (-) or after (+) noon (according to your watch). You could also use the time-lapse feature on a smartphone (in fact, you could even use the phone/tripod as your gnomon, if you’re careful about how you set it up) to get a movie of the shadow in motion. See the sidereal time lab for more detailed instructions.
Estimate the time when the shadow is the shortest – this is when the sun crossed the meridian. You can eyeball it (make sure you estimate a range) or use a curve fitting program to get a more precise measurement. Talk to me about how to use the fit, if you want to try that.
Use the Equation of Time calculator ( at this writing) to figure out the difference between the apparent sun and the mean sun. Once you make this correction, you will know when the “mean sun” crossed the meridian. If we were in the middle of our time zone, at -75o longitude, this would be exactly noon. The difference between your mean sun and noon should be about +16 minutes. The more precise number you get will tell you how far west we are from the middle of the time zone. Since a day has 1440 minutes and 360 degrees, each minute of time delayed corresponds to 4 degrees west (360x4=1440).
How precise can you be? Remember, it’s not a single number you’re looking for, but a range of numbers. Use google maps (right click on the location and pick “what’s here”) to try to get a more precise measurement, or your own GPS device, if you have one. How does your gnomon measurement range compare?