Celestial navigation, like piloting, involves plotting lines of position to establish a fix. These "lines" are really sections of huge distance off circles whose radii would range between 900 and 4500 miles. Small pieces of the circumference of a circle would be straight lines for all practical purposes. Each celestial object can be thought of for that instant of time, it stands directly over one spot on the earth. This is called the geographical position (GP) of the sun for that short time period. The Nautical Almanac lists positions (with coordinates similar to latitude and longitude) of the sun, moon, four brightest planets, and the stars which can be seen in twilight. These positions or GPs can be figured for any day, hour, minute and second of the year with accuracy of one tenth of a minute of arc (compard to one tenth of a mile or less). If you were lost and happened to observe a celestial body overhead, you would note the exact time of observation, enter the Nautical Almanac and find the "latitude" and l0ngitude" of the body. This position would be exactly yours on the earth. This sounds like a good way of navigating if the sky is clear but, there aren't enough bright celestial objects to mark every place on earth for every instant of time. Stars also can be identified as to location, their sky coordinates being listed in the Nautical Almanac. The purpose of obtaining distance accurately, the sextant was invented. This instrument measures the height (altitude) of celestial bodies above the horizon. Our overhead point is 90° above the horizon. The distance between a star and our overhead point would be 90° minus the star's altitude. You aren't really measuring a distance in the sky but an angle. However, one degree or sixty minutes of altitude (angle) in the sky equals sixty nautical miles (distance) on the earth's surface.
90° - Altitude 15° = 75° x 60 = 4500 n.m.
90 - Altitude 57° = 33° x 60 = 1980 n.m.
90 - Altitude 40° = 50° x 60 = 3000 n.m.
The coordinates of our overhead point can be found from bright celestial objects that are in the surrounding sky. Our geographical position would be directly under this overhead point and have the same coordinates.
The sight reduction tables have been published by the United States Government, they come in several forms with titles like H.O. 249, and H.O. 229. I use 229 by entering it with numbers based on our DR position and the position of the celestial body sighted, we can get information as to the corrected sextant altitude and bearing of the body from a place only a few miles from our real position. The difference between the sextant altitude at that place and the altitude that we obtain with our sextant gives us a distance off from that place. With a distance and a bearing, we then plot our lines of position.
