Star Points for September 2010 by Curtis Roelle Original Global Positioning System Airplanes and ships have been traveling between the ports of the world for decades and centuries. The destinations are largely the same, but the technology used to navigate the airways and sea lanes have changed. Prior to today's global navigation satellite systems, pilots and mariners relied on the stars. As for ourselves, we used roadmaps, not GPS-based personal navigation equipment. The central problem in navigation has always been finding an answer to the question, "which way to go?" The answer of course is, "it depends" on where you want to be and your current location. Unless performing a rendezvous with a moving target, the destination is usually at a fixed location. When traveling, however, your own coordinates change with time requiring periodic checks of your position in order to confirm or recalculate the desired trajectory. The key to navigation is the precise determination of current position. It is a testament to human ingenuity that the stars have been pressed so uniquely into useful service for navigating the globe. When adrift in a vast and featureless ocean, the stars provide a reliable reference system that sailors have depended on for thousands of years. Positions on the earth's spherical surface are specified using a pair of Latitude and Longitude coordinates. Latitude is measured between equator and the poles. Each hemisphere is divided into 90 degrees measured either north (positive) or south (negative). The latitude at the equator is zero degrees. Longitude is measured from the Prime Meridian to the International Date Line. The Prime meridian is an imaginary arc stretching from pole to pole directly through the transit telescope located at the Royal Observatory at Greenwich, England. Longitudes range from 0 to 180 degrees, measured either east (negative) or west (positive) from Greenwich, whose longitude is zero degrees. How does one measure one's earthly position using the stars? Depending on method, several tools may be needed – in addition to a clear sky. Typically, required tools are 1) a measuring or sighting device, 2) an accurate clock or chronometer, and 3) an almanac with tables of stellar, lunar, solar, and planetary positions for various time throughout the year. Latitude is the easiest to determine. In the northern hemisphere the star Polaris marks the approximate position of the celestial pole. Measuring its position above the horizon gives the navigator's north Latitude. Near the equator Polaris lies on the horizon, so the Latitude is zero. On the other hand, at the North Pole Polaris occupies the zenith, 90 degrees from the horizon. Thus, it's Latitude is 90N. The instrument normally used to make this measurement is a sextant. It has two arms with sites, one for the horizon and the other for the celestial object. If the horizon isn't visible (it may be dark at sea), a bubble level presents an artificial method of determining the horizon. If an almanac with daily solar Declinations is handy, the sun can be used to determine Latitude in broad daylight. Declination is a coordinate axis in the sky similar to Latitude. During the course of the year the sun's Declination changes with the seasons. The sun's altitude angle above the horizon measured at local Noon (when the altitude reaches its highest point) can be used in conjunction with the solar Declination from the almanac to calculate Latitude. Notice that neither method for determining latitude requires a chronometer. The same cannot be said for all methods used to determine Longitude. Longitude is more problematic. Most techniques depend on having accurate time as well as precise angular measurements. With the earth rotating, an error of only five minutes translates to more than 80 miles at the equator. There are several techniques for determining Longitude. However, in the space remaining I will describe just one. It is called the "intercept method." Central to the intercept method is the fact that any given celestial body is, at some specified time, directly overhead at exactly one point somewhere on the earth. That location is the celestial object's sub point. If the object is visible from your location, you can measure its altitude angle above the horizon using your sextant. Your position on the earth will be somewhere along a circle, whose radius is a function of the altitude angle, around the object's sub point. Such a circle can easily be drawn on a globe using a compass after looking up the sub point in an almanac. Next, identify a second object above the horizon. The pair can be two stars or, a star and planet, or even the sun and moon during the day. There are 57 stars regularly used for navigation first collected in a list more than two centuries ago. Measure the second object's altitude and plot its visibility circle on the globe. Your position is where the two circles meet. Unfortunately, they will intersect in two places. One may be over dry land. Or they may be far apart, even in different hemispheres, thus ruling out one or the other. You may also notice that from one site the first object is left or right of the second, and vice versa at the other site. Simple common sense will rule out one of the two sites. Notice how this solution solves for both Latitude and Longitude. These days navigation on land, sea, air or in space depends on satellites. However, the old techniques are still being taught and learned. No one wants to be stuck in the middle of the sea or at 35,000 feet when some calamity, natural or otherwise, knocks the global satellite system offline. The old maps, compasses, and the like shouldn't be thrown out quite yet.