Equitorial Coordinates

Latitude and Longitude

In order to pinpoint locations on the surface of the earth, a coordinate system which is termed latitude and longitude had been devised. Latitude is an angular measurement made from the earth's center, northward or southward from the equator, along a meridian circle to the location in question. Longitude is an angular measurement also made from the center of the earth, east or west from the Prime Meridian, along the equator to the meridian circle which contains the position. The range of longitude is from 0° to 180° east or west of the Prime Meridian, while the range of latitude is from 0° to 90°, north or south of the equator. In both cases the hemisphere of the position must be stated. For example, Allentown, PA is located at approximately 40° north latitude and 75° west longitude. Allentown is in the northern and western hemispheres.

The Equatorial System: Right Ascension and Declination

If you imagine the grid of latitude and longitude superimposed on a transparent sphere, which is surrounded by a larger sphere (the celestial sphere, which is really the sky), you are ready to understand how the equatorial coordinate system is formed. This system is used by astronomers to locate objects in the sky. If a flashcube were placed in the inner transparent sphere and fired, the light of the bulb would radiate outward to the celestial sphere, casting the shadows of latitude and longitude onto it. Where these shadows would fall, a new "equatorial" coordinate system would be formed called right ascension and declination. The circles of latitude would now correspond to declination. Instead of being measured north or south of the equator, they would be measured north or south of the celestial equator as either positive or negative angles respectively. Longitude would become meridians of right ascension measured eastward from the intersection of the celestial equator and the ecliptic. The ecliptic represents the path of the sun in the sky as the earth revolves around this star. The intersection position of the celestial equator and ecliptic is known as the vernal equinox, and it is the location of the sun at the first moment of spring. This is also the origin of the equatorial coordinate system. Right ascension is always measured along the celestial equator eastward from the vernal equinox. There is no westward component as in the terrestrial system of longitude.

Right Ascension and Sidereal Time

Right ascension positions are usually measured in hours, minutes, and seconds. The coordinates of the system form a sidereal (star) clock composed of 24 hours which is equal to the interval of one earth rotation. This time system is called sidereal time. Twenty-four hours of sidereal time (literally star time) is about four minutes less than the solar time measured by clocks throughout the world. In other words, one earth rotation equals 23 hours, 56 minutes of clock time. This 23 hour, 56 minute interval is divided into its own 24-hour system which is called a sidereal day.

THE EQUATORIAL COORDINATE SYSTEM

    We want to know where the individual objects of the universe are in space relative to each other, i.e., we want to discover the geometry of the universe, and the equatorial coordinate system will help us attain that objective. The equatorial coordinate system provides us with a system for measuring the universe as it is seen naturally from earth.
    As a system of measurement, the equatorial coordinate system represents a refinement over the ancient method of mapping the sky in terms of constellations. Through the use of constellation, the ancients were able to divide the night sky into broad areas (the north and south circumpolar regions, the equatorial region, and the zodiac) and into the 88 sub areas represented by the constellation figures themselves. But, given only the constellations, it is impossible to define the relative positions of the celestial bodies with any degree of precision. Whereas the constellations define the location of groups of stars, the equatorial coordinate system allows us to define the location of individual stars.
    Using the equatorial coordinate system, we can specify the position of the individual stars on the surface of the celestial sphere just as the earth's system of latitude and longitude enables us to specify an individual's position on the surface of the earth. On earth, we specify position by referring to a system of meridians of longitude, parallels of latitude, and poles. The equatorial coordinate system is composed of analogous features, although differently named.

The Equatorial Coordinate System

The essential features of the equatorial coordinate system are the celestial equator, celestial poles, parallels of declination, right ascension circles, the vernal equinox, and the ecliptic.

The Celestial Equator and Celestial Poles

The celestial equator is a projection of the earth's equatorial plane to the surface of the celestial sphere. The celestial equator could be formed by passing a plane (flat) surface through space which cuts both the earth and the celestial sphere exactly in half, at right angles to the earth's axis of rotation. The north and south celestial poles are the piercing points formed by an extension of the earth's axis of rotation to the surface of the celestial sphere.

Parallels of Declination

Lines drawn parallel to the earth's equator are called parallels of latitude, while lines drawn parallel to the celestial equator are called parallels of declination. Parallels are useful when considering displacement between the equator and the poles, i.e., when measuring north and south.

The Ecliptic and Vernal Equinox

The ecliptic helps us specify the exact position of the sun relative to the stars. As previously discussed, the ecliptic marks the path of the sun relative to the stars during the course of a year. The ecliptic, like the celestial equator, divides the celestial sphere exactly in half, but at an angle of 23 ½ ° to the celestial equator. The point of intersection between the ecliptic and the celestial equator is called the vernal equinox. The vernal equinox marks the celestial position of the sun on the first day of spring.

Hour Circles

Lines of right ascension, sometimes called hour circles, are used when measuring east or west on the surface of the celestial sphere. Right ascension circles extend from pole to pole on the surface of the celestial sphere in the manner of longitude circles on earth.

How the System Works

To aid us in specifying positions on the surface of the celestial sphere, in addition to the constellation, we now have the system of lines and points represented by the equatorial coordinate system. The system is simple to use since the apparent celestial position of any star can be specified by only two coordinates, one giving the position of the star north or south of the celestial equator, and another giving the star's position east of the zero right ascension circle. The star Vega in the constellation Lyra, for example, has a declination of +38°, and a right ascension of 18 hours 40 minutes. The diagram below illustrates the method of measurement on the celestial sphere.

Right ascension is almost always measured east of the vernal equinox in hours, minutes, and seconds. Each hour of right ascension corresponds to 15° of displacement on the celestial sphere; therefore, Vega is located 280° east of the zero hour circle (80° west).
Declination is always measured in positive (north) or negative (south) degrees, minutes, and seconds from the celestial equator. Vega, therefore, is located 38° north of the celestial equator, but it is written as +30°.

How We Link the Sky and Earth

We can locate the position of a star on the celestial sphere by specifying its equatorial coordinates. One can also specify positions on earth by using the earth? coordinate system. Now, how can we specify the positions of the stars relative to the surface of the earth. How, for example, can a person in San Francisco determine what is overhead, or in some other direction, at any given time? The system which has been devised to suit this purpose is called the horizon system of coordinates. The illustration to the right shows the simplicity of the system.

In the horizon system of coordinates known as altitude and azimuth, we specify the position of a star relative to the earth's surface by stating the star's place relative to our local horizon in terms of its altitude (elevation) and azimuth (direction). The altitude of a star is simply the angle between the star and the observer's horizon; and its azimuth is simply the angle between a point due north of the observer and the star, measured eastward along the horizon. Thus, to find a star whose altitude and azimuth are 30° and 135°, respectively, an observer should look 30° above the horizon in the southeast.
Note that altitude and azimuth are always dependent upon the observer's position on earth and the observer's local time since the celestial sphere and the earth are always in motion with respect to each other. At any given instant in time, and at any given point on the earth's surface, a given star can have only one altitude and azimuth. The horizon system of coordinates is, therefore, very useful to navigators. A navigator, knowing the local time, can determine his/her position on earth by measuring the altitude and azimuth of a star whose vertical position over the earth's surface can be obtained by a sextant or some other angle measuring device.