Latitude Mystery Cache

For some reason celestial navigation is wrapped in a mystique that causes many to decide that it’s best left to our long forgotten ancestors. I’ll admit that the math surrounding most types of celestial navigation can be daunting. But when the stars line up, or in this case the sun, the math is reduced to simple addition and subtraction. The truth is that it’s not that hard to learn if you break it into small pieces.

We have designed a series of caches that lay out the basics. For those of you that already know celestial navigation, solve these puzzle caches in any order that you would like. For those that don’t we would suggest this order.

LATITUDE

The problem of latitude is much easier to solve than longitude. First, some basics. Latitude at the Equator is 0 degrees, latitude at the North Pole is 90 degrees north. Wisconsin lies about half way in between. Let's take the easiest case first. When the sun is directly over the equator (the Equinox), we can measure our latitude by simply measuring how high the sun is in the sky at its highest point (Local Apparent Noon). For example, if on that day the sun is 47 degrees above the horizon, our latitude is 43 degrees north. By the way, the height of the sun above the horizon is called the sun's altitude. You have to subtract your altitude from 90 degrees. Why subtract your answer from 90 degrees? Well let's think of the extreme. Suppose we are standing on the equator that day. The sun would be directly overhead at local apparent noon, or 90 degrees from the horizon. 90 minus 90 equals 0, the latitude at the equator.

Now for the wrinkle (there's always a wrinkle). The sun is only above the equator two days per year, the March Equinox and the September Equinox. Every other day we have to adjust our measurement of the sun's altitude for the Declination of the Sun. For example. Let's say that it's winter and we measured the sun's altitude at 34.05 degrees, that would mean our measured latitude is 55.95 degrees (90.00 degrees minus 34.05 degrees). Well we aren't really that far north because the sun is actually south of the equator. So, we look up the Declination of the Sun and adjust our measured latitude. On this day, the Declination of the Sun was -21.34 degrees. Therefore our corrected latitude is 34.61 degrees (55.95 minus 21.34).

Now it's time to find the cache. On this particular winter day I measured the altitude of the sun at local apparent noon at 27.8780 degrees north. I also noted from the Nautical Almanac that the Declination of the Sun that day was -19.0441 degrees. Oh, I almost forgot. The longitude coordinate in the cache listing is correct. Good Luck!