Equinox
Noon Sun

Yesterday was the Spring Equinox (2014). My friend and I brought the sextant to a nearby beach to shoot the noon sun.

There is just something appealing about deducing one’s latitude simply and directly, merely by observing the height of the sun at or near the time it crosses the celestial equator. No complicated math is needed—no calculators or tables. The calculation is as simple as subtracting the sun’s observed height from 90°.

In centuries past mariners depended upon the noon sun for latitude. An accurate timepiece was not needed because only the sun’s height matters for the noon latitude, not the time at which it reaches maximum height. It is necessary, however, to correct for the sun’s declination (angular distance north or south of the celestial equator).

The March 20, 2014 equinox occurred at
4:57 PM universal time (AKA Greenwich mean time), which corresponds to
a
few minutes before
1:00 PM EDT, where I
live in Charleston, South Carolina.
At the time of the
equinox the sun’s
declination is zero (by definition).
Charleston lies about 5°
west of the 75° meridian.
Solar noon
yesterday, the
time that the sun reached its maximum height, was about a half hour
after the equinox. By then the sun was less than a minute
north of the equator. The exact time of solar noon for any
location, as well as other interesting times, may be calculated at this NOAA
page, from
which the following table is reproduced.

Because solar noon occurred at nearly the same time as the equinox, declination can be ignored when computing latitude from yesterday’s noon sun. The simplicity of this situation is summarized in the sketch below.

The above diagram should be self-explanatory. As we learned in school, earth’s equator is 90° from the pole—the same holds for the celestial poles and equator. Similarly the horizon is 90° from the observer’s zenith, an imaginary point directly overhead in the sky.

When shooting sights yesterday, we did not know (or pretended not to know) exactly when the sun would reach its maximum height. We began taking sights at about ten minutes before 1 PM EDT and shot the last sight at about five past two. This allowed us to plot a curve as the sun rose to its maximum height and then began to descend. In the following graph, the horizontal axis is time in minutes past noon EDT and the vertical axis is sextant height (Hs) in degrees. (Sextant height is uncorrected.)

The DIP correction refers to the height of the observer’s eye. The formula is 1.76 multiplied by the squareroot of height in meters. Lastly, the sextant zero point (where the reflected horizon makes a continuous line with the actual horizon) is a fraction of a minute below the zero mark on the scale.

This brings us to the moment of truth, so-to-speak. Subtracting 57° 22’ from 90° gives a latitude of 32° 38’. Our actual latitude by the park bench method