Navigation consists of a) figuring out where you are and b) figuring out how to get form where you are to where you want to be. Navigation is now carried out with many high-tech improvements like satellites. However, for thousands of years people found their way around the globe and made fairly accurate maps using astronomical techniques based on the kinds of principles we have been studying.
As we have discussed in other units, "where you are" is described by your latitude and longitude. Given a good map, this will translate:
Ames, Iowa to 42
deg 02 min N, 93 deg 37 min W
In general, if you know the coordinates of a celestial object (RA and dec), the position of the object in the sky (altitude and azimuth), and the local sidereal time, then you can determine your latitude. The problem involves a little spherical trigonometry, but is otherwise pretty straightforward. There are many books that you may consult if you are interested in the general problem.
For our purposes, the meridian diagram is the basis of most simple methods for determining latitude. An example of a 3-D meridian is shown to the right, where the dark blue circle represents your local 360 deg horizon if you were standing in the middle of the "field" where the lines converge.
Measure the altitude of the star, look up its declination in a reference book, then you can fill in the angles in this diagram and find the altitude of the NCP (North Celestial Pole) which will equal your latitude.
For an observer in the Southern Hemisphere, the meridian diagram looks like this one on the left.
A couple of particularly useful special cases are as follows:
Zenith star: The islanders of the South Pacific Ocean used a version of this to determine when they were at the right latitude for the island they were seeking. At any given latitude, only those stars that have declination = latitude can pass through the zenith, thus they could associate islands and their latitudes with specific stars. By checking which star or stars passed through zenith, they could determine whether they had reached the right latitude for a specific island, for example, Hawaii. No math – all they had to do was to memorize which star went with which island! This works well with the method of sailing down the latitude, described below, which amounts to getting to the right latitude and then turning left or right towards your goal.
Pole Star: The altitude above the horizon of the pole star in the night sky is the same as your latitude on the planet. Sailors on the North Atlantic Ocean used this fact and is referred to in the Journals of Christopher Columbus.
Latitude from motions of stars near the horizon: Stars near the celestial equator make an angle equal to (90-latitude) with the horizon as they rise or set. The following diagrams illustrate the point. Here are some example of stars near the horizon and where they would appear in the sky for specific locations.
Left: Latitude 42N, Sunrise. Center: Latitude 33S, Sunrise. Right: Equator, Sunrise. The Sunset pictures would be similar, except that if we reverse the arrow (put the point at the other end without changing anything else) on the left hand picture it will show sunset for 42S while the middle one, with the arrow pointing to the ground, would be for 33N.
Use your "fist planetarium" on these: Which shows the motion as seen by an observer at the North Pole and which the South Pole? Answer: The sky motion corresponds to your left hand's fingers with your thumb pointing to the NCP, so the left hand picture here is a North Pole view and the right hand picture is a South Pole view.