Because the stars, sun, and moon are available most of the time throughout the world, celestial navigation is a useful means to determine your position and crosscheck the accuracy of your GPS. Each celestial observation you take provides an LOP or line of position. During the day, when the sun may be the only visible body, this kind of navigation will mean using single LOPs. Fortunately, about half the time the moon is also visible during the day, and can provide a second LOP to give you a fix. At night there are numerous stars and planets available, but the horizon—a critical reference point when using the sextant—is not visible. For this reason, mariners must take their celestial observations during twilight (after sunset and before sunrise) when both the brightest bodies are available and the horizon can be seen. Although there are an infinite number of heavenly bodies in the universe, celestial navigation normally utilizes only 63 of them: the 57 brightest stars, four planets (Venus, Jupiter, Mars, and Saturn), the moon, and the sun. If you have any hesitancy in continuing after this introduction, I can certainly understand it. Why can't I just give you a cookbook series of steps that will enable you to use celestial without getting into all this theory? Well I could, but it would be just a series of meaningless instructions that you would need to refer to each and every time you took a celestial observation. Once you understand the concepts, you will be free to use celestial without referring to instructions. So relax, read slowly, and I will make this as painless as possible.

"The first assumption is that the Earth is a perfect sphere." 

To make celestial navigation more understandable, certain assumptions have been established that allow the navigator to use celestial bodies for navigation without requiring a detailed knowledge of celestial astronomy. These assumptions are not valid in light of modern astronomy, but do not affect the accuracy of your celestial observations.
The first assumption is that the Earth is a perfect sphere and the terrestrial sphere is the center of the universe, as proposed by Ptolemy in 127 AD, but long since disproved. The second assumption is that all celestial bodies are located on the inside surface of a celestial sphere that is located at an infinite distance from the earth and rotates at an equal rate from east to west. In actuality, the stars and planets are all at different distances from us and move at different rates and directions. The Earth's rotation from west to east makes the celestial bodies seem to rotate in the opposite direction.
Making these assumptions simplifies our calculations and makes celestial navigation easier to understand for three main reasons. Firstly, since the terrestrial and celestial spheres are geometrically similar and concentric, every point on the celestial sphere has a corresponding point on the terrestrial sphere and vice versa. By assuming concentric spheres, angular relationships between the two spheres remain constant. Secondly, by establishing an infinite radius, a body's location on the celestial sphere will also remain constant regardless of the observer's location since all light rays from the celestial body arrive in parallel rays. This means that the angle will be the same whether viewed at the Earth's center, upon the surface, or from an airplane.
Thirdly, all the relationships are valid for all bodies located on the celestial sphere. The moon, with its close proximity to the Earth, is treated as a special case and additional corrections must be made in order to get an accurate LOP.
Because the celestial and terrestrial spheres are concentric, every point on one has a corresponding point on the other. Each sphere contains an equator, north and south poles, meridians, and parallels of latitude. However, on the celestial sphere, parallels of latitude are known as declination. If a star has a declination of 45 degrees north, its corresponding point on the terrestrial sphere is 45 degrees north latitude. Consistent with the celestial sphere assumption, neither the Earth nor the celestial meridians rotate. All celestial bodies located on the inside surface of the celestial sphere (with the exception of the moon), rotate at a constant rate of 15 degrees per hour past the celestial meridians and the observer on the earth.



Two other relationships and terms need to be established to complete the picture. An observer on the Earth has a point directly overhead on the celestial sphere called the zenith. A celestial body has a corresponding point on the terrestrial sphere directly below it, which is referred to as its subpoint or geographical position. At its subpoint, the light rays from the body are perpendicular to the Earth's surface. If a celestial body is located directly overhead, at your zenith, you would be standing on its subpoint. At that moment in time, if you knew the body's declination and its meridian on the celestial sphere, its position would correspond exactly to your latitude and longitude on the earth. All you need to determine the body's subpoint are an accurate timepiece and the Nautical Almanac. For each day of the year and every second of time each day, all locations of navigational bodies on the celestial sphere are recorded in the Nautical Almanac. But since it's rare for celestial bodies to appear overhead, you need the ability to determine your position from them wherever they are in relation to your position. This is where the sextant comes into play, as it allows you to measure the body's angular distance above the observer's horizon. This measurement is used to determine your distance from the body's subpoint. But before I get into just how this is accomplished, I need to go a bit more into the celestial coordinate system. Celestial bodies and the observer's zenith are positioned on the celestial sphere using a coordinate system similar to that of the Earth's. Lines of latitude on Earth are projected onto the celestial sphere as parallels of declination. Lines of longitude establish the celestial meridians. And, of course, to complete the picture, both of the Earth's poles are also projected onto the celestial sphere. A line extended from the observer's zenith, through the observer, the center of the Earth and continuing into space, will intersect the celestial sphere at the observer's nadir.
The observer's celestial meridian is a great circle containing the zenith, nadir, and the two celestial poles. Celestial meridians are divided into two parts: the upper and the lower branch. The upper branch is the half of the celestial meridian, divided at the poles, containing the observer's zenith. The lower branch is the remaining part of the great circle that contains the nadir.
A second great circle on the celestial sphere is the hour circle. An hour circle is a great circle containing the celestial body and the celestial poles. Unlike the celestial meridians, which remain stationary, hour circles (because they contain the body) rotate at the standard rate of 15 degrees per hour, except for the moon. Like the observer's celestial meridian, hour circles also contain upper and lower branches. The upper branch contains the body and is the half divided at the celestial poles. The remaining half of the great circle is the lower branch. The location of any body on the celestial sphere can be described relative to the celestial equator and the celestial Greenwich meridian, just as any location on the Earth is found using latitude and longitude. Remember that longitude is either east or west in relationship to the Greenwich meridian. A body's location is recorded in the Nautical Almanac using declination and Greenwich hour angle (GHA.)
The declination of a celestial body is the angular distance the body is north or south of the celestial equator. Just like latitude, it ranges from 0 to 90 degrees.

"Remember that longitude is either east or west in relationship to the Greenwich meridian." 

The Greenwich Hour Angle of a body is the angular distance measured westward from the Greenwich celestial meridian to the upper branch of the body's hour circle. GHA ranges from 0 to 360 degrees, while longitude is measured 180 degrees both east and west from the Greenwich meridian. A GHA of 0 to 180 degrees will correspond with a west longitude subpoint, while a GHA of 180 to 360 will correspond with a east longitude subpoint. For example, a GHA of 200 degrees would correspond with a 160 degrees east longitude subpoint (360 degrees minus GHA.) Of course, we all know that the 0 and 180degree meridians of longitude are part of the same great circle on the Earth and are also called the Greenwich meridian and the International Date Line (IDL). In actuality, the IDL zigzags to avoid populated islands; but for the purposes of celestial navigation, the IDL and the 180degree meridian are the same.
The Nautical Almanac lists the GHA and declination of the sun, moon, four planets, and Aries. The first point of Aries, more commonly referred to as Aries, is the vernal equinox or first day of Spring. Aries is established as a point on the celestial equator and is used as the reference point to calculate the GHA of the 57 navigational stars. The GHA of Aries is used to save space. Just imagine how thick the Nautical Almanac would be if it also listed the GHA for each individual star for every hour of every day throughout the year.
So how do we calculate the GHA of a star from the GHA of Aries? It's very simple, as another hour circle called the Sidereal Hour Angle (SHA) is used along with the GHA of Aries to find the GHA of a particular star. As you may have already guessed, the SHA of a star is the angular measurement from the GHA of Aries to the hour circle of the star. By adding the SHA of the star to that of the GHA of Aries, we arrive at the GHA of the star. For each day in the Nautical Almanac, the SHA and declination for the 57 stars are listed along with the GHA of Aries for each hour of that day. A special table is used for the minutes and seconds after the whole hour for an additive value to the hourly GHA. There is one more important hour angle we need to know and that one is called Local Hour Angle (LHA.) LHA is the angular displacement measured from the observer's celestial meridian clockwise to the hour circle of the body. LHA is computed by applying longitude to the GHA of the body. In the Western Hemisphere, LHA = GHA minus West. longitude and in the Eastern Hemisphere, LHA = GHA plus East longitude.
Now that we have positioned the celestial body and the observer's zenith on the celestial sphere, the only remaining concepts left to explain are the celestial horizon and the horizon system of coordinates. This will be left until the next time, as it is almost as lengthy an explanation as what we have just been through.
I'd encourage you to study these concepts and become familiar with them so the next installation can build on these.