Basic Celestial Concepts

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.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.

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 180-degree 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 180-degree 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.