Coordinate systems used in astronomy

Type of physical science: Astronomy; Astrophysics

Field of study: Observational techniques

There are several astronomical coordinate systems that are in common usage. In each system, the position of an object in the sky, or on the celestial sphere, is denoted by two angles: the reference plane and a reference direction.

Overview

An astronomical coordinate system is a way for locating the position of an object in the sky, or on the celestial sphere, as denoted by two angles. There are several astronomical coordinate systems, and each system uses the measurement of two angles: the reference plane, which contains the observer, and the reference direction, which is the direction from the observer to some arbitrary point lying in the reference plane. The intersection of the plane and the celestial sphere is a great circle defining the equator of the coordinate system. The celestial poles, each 90 degrees from the equator, are imaginary points around which the celestial sphere appears to rotate; they are the poles of the coordinate system. Great circles passing through these poles intersect the equator of the system at right angles.

One of the two angular coordinates of each coordinate system is measured from the equator of the system to the object along the great circle passing through it and the poles. Angles on one side of the equator are considered positive; those on the opposite side are negative. The other angular coordinate is measured along the equator from the reference direction to the intersection of the equator, with the great circle passing through the object and the poles.

In addition to a reference plane and reference direction, each system uses a "latitude" coordinate with a range as well as a "longitude" coordinate with a range. The range of the latitude for four commonly used systems is from 0 to 90 degrees, with positive degrees located north of the equator and negative toward the south. On the other hand, the longitude coordinates are measured to the east and range from 0 to 360 degrees, or, equivalently, from 0 to 24 hours.

The latitude and longitude of each system can be compared with the terrestrial latitude and longitude. On Earth, the plane of the equator is the fundamental plane and the earth's equator is the equator of the system. The North and South terrestrial poles are the poles of the system. One coordinate--the latitude--is either positive (north) or negative (south) of the equator. Longitude is measured along the equator to the intersection of the equator and the Greenwich meridian.

Terrestrial longitude is either east or west, depending upon whichever is less. On the other hand, the corresponding coordinate in the celestial system is generally in one direction to the east, from 0 to 360 degrees, or 0 to 24 hours.

Four astronomical coordinate systems are commonly used: horizon, equator, ecliptic, and galactic. The horizon system has as its reference plane the horizon plane, which is a great circle on the celestial sphere 90 degrees from the zenith. Its reference direction is the north point and its latitude coordinate is defined by its altitude (h) being positive toward the zenith and negative toward the nadir. Its range is plus or minus 90 degrees. The longitude coordinate has its azimuth (A) measured to the east along the horizon from the north point; its range is 0 to 360 degrees. The equator system uses the plane of the celestial equator as its reference plane, with the reference direction the vernal equinox. The latitude coordinate has a declination that is positive toward the north celestial pole and negative toward the south celestial pole with a range of 0 to 90 degrees. The longitude coordinate has a right ascension measured to the east along the celestial equator from the vernal equinox and has a range of 0 to 24 hours.

In the ecliptic system, the reference plane is the plane of the earth's orbit, which is ecliptic, and its reference direction is the vernal equinox. The latitude is the celestial latitude toward the north ecliptic pole and is positive; toward the south ecliptic pole, the latitude is negative and the range is 0 to 90 degrees. The longitude coordinate is the celestial longitude measured to the east along the ecliptic from the vernal equinox, and it has a range from 0 to 360 degrees. The fourth coordinate system is the galactic system, which has a reference plane that is the mean plane of the Milky Way with a direction to the galactic center. The latitude coordinate is the north galactic pole, which is positive, and toward the south galactic pole, it is negative. Its range is plus or minus 90 degrees. The longitude is the galactic longitude measured along the galactic equator to the east from the galactic center and with a range of 0 to 360 degrees.

The coordinates of the stars are not completely fixed, since the phenomenon of precession alters the frame of reference. Precession is the slow circular motion of the earth's axis in space. The proper motion of the stars themselves slowly causes the coordinates to change, as do other slight influences. Star positions are updated periodically to allow for these changes. At present, most star catalogs and charts use the positions of the stars in 1950 as a basis for comparison. Astronomical atlases often give formulas for working out up-to-date coordinates from those of the standard reference. The three motions of the earth can be illustrated by likening the earth to a spinning top placed on the edge of a merry-go-round. The top's spinning represents the rotation of the earth on its axis, and the top's motion around the center of the merry-go-round represents the revolution of the earth around the sun. This top is not spinning upright; its axis of rotation is tipped from the perpendicular to the floor of the merry-go-round, with the result that the axis of rotation itself rotates around the perpendicular (as all tops do, especially as their spinning slows down). This motion is precession.

The positions of the celestial poles and celestial equator do not remain fixed on the celestial sphere. They wander in a predictable way as a result of precession. The celestial poles, for example, describe a circle on the celestial sphere, which repeats itself every 25,800 years.

Because of precession, the equinoxes are wandering westward so that gradually the seasons are changing. The vernal equinox, now in Pisces (March 21), occurs about a month earlier than it did two thousand years ago, when it was in Aries. Polaris will eventually cease to be the pole star. At the time of the building of the Great Pyramid in Egypt, more than forty-five hundred years ago, Thuban in Draco was the pole star. The builders lined up the pyramid's main passages with the star. In about ten thousand years, Vega in Lyra will be the pole star. Understanding precession is important to the coordinate system, since its effect must be allowed in accurate observational astronomy. It is the main factor in the periodic updating of star positions in star catalogs and almanacs.

Applications

An application of the coordinate system is shown by star maps, which show the position of the stars on the celestial sphere. Like all maps, these maps slightly distort what they represent, since they show a curved surface on flat paper. The maps are crisscrossed with a reference grid, which shows the equatorial coordinates of right ascension and declination. The coordinates relate to epoch 1950.

The sky is divided into six equatorial segments and northern and southern circumpolar regions. Stars are included down to the fourth magnitude of brightness. Many of the best-known stars are named. Others accompanying the maps are identified by Greek letters according to the Bayer system, which classifies the stars in a constellation in order of their brightness. Magnitude can be apparent, which is brightness of a body as it appears to an observer on Earth, or absolute, which is the brightness it would appear from a distance of 32.6 light-years. A light-year is the distance light travels in a year. Also included on the maps are the brighter star clusters, galactic nebulas, and external galaxies. They are identified by their Messier (M) numbers or by their NEW GENERAL CATALOGUE (NGC) numbers. Star brightness is measured on a scale based on stars visible to the naked eye. On this scale, brightness is divided into six categories of brightness, denoted as first, second, third, fourth, fifth, and sixth magnitude. The brightest stars in the sky are of the first magnitude (mag 1); those just visible are of the sixth magnitude (mag 6). A first magnitude star is 2.5 times brighter than one of the second magnitude, which is 2.5 times brighter than one of the third magnitude, until the comparison of a mag 1 star, which is one hundred times brighter than a mag 6 star. A typical star from each of the equatorial segments and the northern and southern circumpolar regions is identified by its right ascension range in the following table:

Since hour circles are to stars in the sky what meridians are to cities on Earth, the hour circle must rise and set with the stars. The hour circle chosen as the reference is the one that passes through the vernal equinox. A star's position with reference to this prime hour circle is given as right ascension and is measured only to the east in hours instead of in degrees (24 hours equals 360 degrees). An important distinction between solar and sidereal time is that stars set four minutes earlier each day according to solar time, therefore, the clocks set to "sidereal time" (star time) must run four minutes faster each day. The solar day begins at midnight when a point in the sky exactly opposite the sun crosses the meridian of a given locality (or in actual practice crosses the midpoint of a time zone). The sidereal "day" begins when the vernal equinox crosses the meridian of a particular locality (time zones are not being used or are not of any use in this case).

The vertical axis is declination and is measured in number of degrees north (+) or south (-) of the celestial equator; as a result, the celestial equator has 0 degrees declination, the north celestial pole is positive 90 degrees, and the south celestial pole has a declination of negative 90 degrees. The scale of right of ascension is fixed arbitrarily by assuming a particular line to be zero. The zero point, which is zero hour, is the vernal equinox. The equinoxes are the two points where the celestial equator crosses the ecliptic, which is the path the sun follows across the sky in the course of the year. The vernal equinox is one of these points that the sun crosses on its way north each year; the other point is the autumnal equinox.

To find a star's celestial coordinates, one can measure the number of hours around the celestial equator to its hour circle and the number of degrees north or south of the celestial equator to its declination. A star's right ascension is equal to the length of time that elapses after the vernal equinox crosses the meridian until the star crosses the same meridian. The interval is measured in sidereal time. The stars are essentially fixed in the sky, therefore, their right ascension and declination do not change measurably over short periods of time. The sun, Moon, and planets, though, wander through the sky with respect to the stars; their right ascension and declination change during the course of a year. An example of how a star's location is described by its coordinates is shown in the Messier Catalog description for the Crab nebula: One of the brightest stars in the sky is Sirius; it is identified by its coordinates, as follows:

Context

The earliest references to measurements and locations of stars stem from Hellenistic astronomy. The strength of Hellenistic culture was caused by a great extent to the merging of Greek and Asian elements. In astronomy, there is an abundance of observed facts and Greek independence of thought, combined with theoretical power of abstraction. An acquaintance with Babylonian methods and instruments stimulated Greek scholars to become observers of stars. In the hands of the Greeks, the Babylonian results for the periods and irregularities became the basis of geometrical constructions and led to conceptions of spatial world structure.

The center of world commerce and science around 300 to 30 B.C. was Alexandria, the capital of Egypt. The Macedonian kings, the Ptolemies, founded a kind of academy of science.

Although the extent and regularity of the observations did not compare with the work of the Babylonian priests, the Greeks did use unknown instruments to locate stars. Euclid mentioned a diopter in his astronomical work. This instrument did not have a graduated circle but merely fixed two opposite points of the horizon. Ptolemy, between 296 and 272 B.C. gives distances to the equator--that is, declinations of a number of stars--as well as differences of longitude measured in degrees and subdivisions, indicating that instruments existed with a graduated circle.

The development of the astronomical coordinate system was important for several reasons; however, the most important was that it allowed for the accurate development of a calendar, which was essential for agriculture and navigation. As a result, the length of the year could be fixed, months and days could be intercalated, and the change of the solstices and equinoxes could be established. The establishment of the coordinate system was important to humankind for practical and theoretical purposes, since a precise calendar led to more accuracy in weather prediction and planting schedules. Many of the uncertainties of navigation could be predicted, and with a better understanding, commerce was able to expand to newer trade areas.

Many of the contemporary writers had a great understanding of astronomy and used this understanding to enlighten readers in prose and poetry. In addition, the fixing of the stars by coordinate systems led to the astrologic predictions, almanacs with the positions of planets computed ahead.

The role of coordinate systems in the future is for detailed mapping of galaxies and charting manned and unmanned space exploration.

Principal terms

AZIMUTH: an arc of the horizon measured between a fixed point (as true north) and the vertical circle passing through the center of an object clockwise from the north point through 360 degrees

CELESTIAL EQUATOR: a great circle on the celestial sphere 90 degrees from the celestial poles, separating the northern and southern halves of the sky

CELESTIAL POLES: imaginary points around which the celestial sphere appears to rotate

CELESTIAL SPHERE: the imaginary hollow spherical shell with the earth at the center

DECLINATION: the angular distance north or south from the celestial equator measured along a circle passing through the celestial poles

ECLIPTIC: the apparent annual path of the sun on the celestial sphere

HOUR CIRCLE: a great circle on the celestial sphere passing through the celestial poles

NORTH POINT: that intersection of the celestial meridian and astronomical horizon lying nearest the north celestial sphere

RIGHT ASCENSION: a coordinate for measuring the east-west positions of celestial bodies; the angle measured eastward along the celestial equator from the vernal equinox to the hour circle passing through a body

VERNAL EQUINOX: the point on the celestial sphere where the sun crosses the celestial equator passing from south to north

Bibliography

Abel, George O. EXPLORATION OF THE UNIVERSE. 3d ed. New York: Holt, Rinehart and Winston, 1975. An excellent introductory reference book. Mathematics has been kept to a minimum. Contains an extensive bibliography for each chapter and a useful glossary. Geared for the undergraduate college student.

Bergamini, David. THE UNIVERSE. New York: Time-Life Books, 1969. A popular series written in an informative and easy-to-read and -understand style. Well illustrated, with photographs, drawings, graphs, and tables. There is a limited bibliography. Of particular interest are the first few chapters covering myths and conceptions. An ideal reference for the high school student.

Menzel, Donald H., and Jay M. Pasachoff. FIELD GUIDE TO THE STARS AND PLANETS. 2d ed. Boston: Houghton Mifflin, 1983. An excellent handy reference. Suitable for all high school upper-level students, college students, and the hobbyist. Useful tables give star names and coordinates. In addition, one chapter has an easy-to-read discussion on coordinates, time, and calendars. Highly recommended.

Moche, Dinah L. ASTRONOMY: A SELF-TEACHING GUIDE. 3d ed. New York: John Wiley & Sons, 1987. A self-instructional text designed so that students with no formal astronomy background can easily learn basic principles and concepts. The material in each chapter is presented in short, numbered sections. The chapter on understanding the starry night is especially recommended for its coverage of the coordinate systems. An excellent book for the upper-level high school and lower-level college student.

Pannekoek, A. A HISTORY OF ASTRONOMY. London: Barnes & Noble Books, 1969. As the title denotes, it is a history and as such is written in a nonscientific format. Should appeal to the college-level student and interested general reader. Of special interest are the early chapters covering the Babylonians, Assyrians, and Chaldean contributions. A good general history; recommended.

Roth, G. D. ASTRONOMY: A HANDBOOK. Translated by Arthur Beer. New York: Springer-Verlag, 1975. A college-level text. Presents a wide range of applied astronomy. Divided into theory and practice. The appendix includes the Greek alphabet, astronomical abbreviations and symbols, signs of the zodiac and symbols for the planets, classification of variable stars, double stars, star clusters and nebulas, and the Messier catalog of 1784. Also contains an excellent bibliography of several hundred references.

Stoy, R. H. EVERYMAN'S ASTRONOMY. New York: St. Martin's Press, 1974. Designed to provide the well-informed reader with a compact and reliable guide to astronomy. Of special interest are the star charts given at the end of chapter 1. Compact and well written.

Typical stars identified by right ascension range

Messier Catalog description for the Crab nebula

Messier Catalog description for the star Sirius

Types of Galaxies and Galactic Clusters

Interstellar Clouds and the Interstellar Medium

Protostars and Brown Dwarfs

X-Ray and Gamma-Ray Astronomy