Celestial Navigation
Learning to steer by the stars
At the risk of detracting from the importance of using the entire star pattern, this discussion focuses on three parts of the pattern: The North Star, the constellation Orion, and overhead stars.
The North Star
Polaris is not located exactly at the north celestial pole, but it's so close that you can use it for steering purposes without making any corrections. It's a convenient directional reference point because it's virtually motionless during the night and through the seasons. It's easier to use when you're at lower latitudes because it doesn't appear high in the sky from such latitudes.
Polaris doesn't stand out when you're looking for it because it isn't a first magnitude star. To find it, locate the two pointer stars at the Big Dipper's cup end. Extend a line from these stars to a distance five times the distance between the pointers — and there's Polaris. You can use the angles subtended by your fingers at the ends of your fully extended arms to measure these and other angular distances.
When clouds cover the Big Dipper you can find Polaris by using the constellation Cassiopeia, which is on the opposite side of Polaris from the Big Dipper.
Because Polaris can be so important to your directional orientation, you may want to use it even when it's obscured by clouds. You can locate the cloud-covered Polaris by using the Big Dipper when it's still visible. To do this, you'll need a stick, string, and small weight. Mark the stick with five segments, each equal in length to the distance between the Big Dipper's two pointer stars when you hold the stick up to them at arm's length. When you align the stick with the pointers, as shown in the figure, its end marks the location of Polaris behind the cloud cover. The weighted string tied to the stick's end brings the direction of Polaris down vertically to your horizon. Bringing the direction down is a particularly useful thing to do when Polaris, or any other body, is high in the sky. You might want to use this jury-rigged device for this purpose even when a body is visible.
Ways to Find Polaris
Many navigators are familiar with the technique of finding Polaris by using the two "pointer stars" on the outer edge of the Big Dipper (Ursa Major) to first establish the distance "X," and then point to Polaris five "X" lengths from the dipper. This illustration shows that relationship as well as five other constellations that point in some manner to Polaris. Note that the "X" distances vary from constellation to constellation, and in the cases of Auriga and Cygnus, the 5X distance is modified slightly. (See Fig. 1.) Finding polaris behind clouds can be a problem, see diagram for further explanation of how to do this. (See Fig. 2.)
Orion
Mintaka is the leading star in Orion's belt; the other two stars in the belt follow it as the constellation appears to move across the sky from east to west. Mintaka circles westward right above the equator and, because of this, its direction is exactly east when rising and west when setting.
Unless you're located on the equator, Mintaka doesn't remain directly east of you after rising and isn't directly west before setting. That is, it doesn't move in a plane vertical to your horizon. The angle its path makes with your horizon depends on your latitude. When you're closer to the equator, the path is more vertical; when you're farther away from the equator, the path is inclined more toward your horizon.
You can use even a rough knowledge of your latitude to describe the path of Mintaka's ascent and descent. And, in doing so, you can estimate how far from east or west Mintaka is at times after rising and before setting and use it for steering over a several-hour period. One approach is to visualize Mintaka's path by tracing it back to the horizon after rising, or forward to the horizon before setting. To do this, hold a stick (again) up to Mintaka and incline it to the horizon at an angle equal to 90 degrees minus your latitude. You use that formula because the angle varies inversely with latitude, as explained above. East or west is located where the inclined stick meets your horizon.
In midlatitudes or higher, you can use this method only up to about three hours after Mintaka rises or before it sets because its path curves markedly when its direction departs substantially from east or west, as shown in the illustration.
Overhead Stars
Any star passing directly overhead (through your zenith) is moving west as it does so. You can tell directions, then, by closely watching the movement of a star passing overhead. A weighted string suspended from a stick (again) can provide you with the needed point of reference. Sight up along the string to the tip of the stick held above your head. The tip indicates your zenith. With patience and practice, you can track a star's direction as it moves through your zenith.
A star that passes directly overhead won't stay on an east-west path throughout the night, though, unless you're looking at it from the equator. Only stars with zero declination, like Mintaka, rise at 090 degrees and set at 270 degrees. And those stars pass directly over your head only if you're at latitude 0 degrees.
Using Orion's Belt to Find East
This illustration shows east being determined when you are approximately 35 degrees north and Mintaka, the leading star of Orion's Belt, has risen about 2 hours. The stick is held at 55 degrees(90 degrees to 35 degrees). Best results are obtained up to three hours after rising. The dotted line shows how a sighting at 3 hours yields a bearing almost 10 degrees in error. (See Fig. 3.)
Stars that pass overhead have declinations equal to your latitude, so you can estimate an overhead star's declination when you have only a rough idea of your latitude. And, a star's declination is one determinant of how far north or south of the east-west line it rises and sets. If you're in the Northern Hemisphere you know that a star passing directly overhead is heading for a point on the horizon that's north of west.
Here's a rule you can use to estimate the direction of an overhead star long after it has passed overhead — it's called the half-latitude rule. When the star descends to an altitude that equals your latitude, it is displaced from west by one-half your latitude. Therefore, when you're at latitude 30 degrees north, for example, an overhead star is 15 degrees north of west when its altitude is 30 degrees. A way of gauging when the star's altitude equals your latitude is to compare its height with that of Polaris, whose altitude always equals your latitude.
When you're anywhere in the tropics, it's easier to get direction from overhead stars because they appear, from those latitudes, to rise and set north or south of the east-west line by an amount equal to your latitude. For example, an overhead star rises and sets 15 degrees to the north of east-west when your latitude is 15 degrees N. (This convenient relationship in the tropics may be one of the reasons the ancient Polynesians could make successful long distance passages.)