Celestial coordinate systems

Several astronomical coordinate systems are in common use. In each system, the position of an object in the sky, or on the celestial sphere, is specified by two angles, similar to latitude and longitude on Earth.

Overview

An astronomical coordinate system is a way to locate an object in the sky or on the celestial sphere using two angles. (The celestial sphere is an imaginary sphere of large size surrounding the Earth, representing the sky as seen from Earth.) There are several astronomical coordinate systems in common usage, and each system is based on a reference plane and a reference direction in that plane. In each system, the intersection of the reference plane and the celestial sphere is a great circle on the celestial sphere, defining the “equator” of the coordinate system. The two “poles” of the system are the two points on the celestial sphere, each 90§ from the system’s equator. 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. (For comparison, in the system of latitude and longitude in England, the reference plane is the Earth’s equatorial plane, and the reference direction is the intersection of the prime meridian passing through Greenwich, England, with the equator. Latitude is measured as the angle north or south of the equator, and longitude is measured as the angle east or west of the prime meridian).

Four astronomical coordinate systems are commonly used: alt-azimuth (or horizon), equatorial, ecliptic, and galactic.

The alt-azimuth, or horizon, system has the plane of the horizon as its reference plane, which is a great circle on the celestial sphere 90° from the zenith (the point directly over the observer). Its reference direction is the North point (the point on the horizon due north). Its latitude-like coordinate, called Altitude (h), is the angle above or below the horizon (positive above and negative below). Altitude ranges from +90° at the zenith to –90° at the nadir (the point directly underneath the observer). The longitude-like coordinate, called azimuth (A), is the angle measured to the east along the horizon from the north point. Azimuth varies from 0° due north to 90° due east, to 180° due south, to 270° due west, and to 360° (equivalent to 0° ) as the north is approached from the west. This system is convenient for giving approximate directions to objects in the sky at any one moment from any one location on Earth. Still, the altitude and azimuth for any object are different, as seen from various locations on Earth, and they constantly change as objects appear to move across the sky due to the Earth’s rotation.

In the equatorial system, the reference plane is the plane of the Earth’s equator; its intersection with the celestial sphere defines the celestial equator. The extension of the Earth’s rotational axis through the north and south terrestrial (or geographic) poles intersects the celestial sphere at the north and south celestial poles. The reference direction is given by the Sun’s apparent position at the moment of the vernal equinox when the Sun is directly above some point on the Earth’s equator in March. The latitude-like coordinate, called declination, is measured as the angle north or south of the celestial equator (positive to the north and negative to the south). Declination ranges from +90° at the north celestial pole (the point on the celestial sphere directly over the Earth’s north pole) to –90° at the south celestial pole (the point on the celestial sphere directly over the Earth’s south pole). The longitude-like coordinate, right ascension, is measured east along the celestial equator from the vernal equinox point. Instead of specifying this angle in degrees, right ascension is given traditionally in hours, minutes, and seconds. Because the Earth rotates on its axis, the sky appears to turn through 360° in approximately twenty-four hours: exactly twenty-four hours of sidereal time, but twenty-three hours, fifty-six minutes, and four seconds of mean solar time (the difference in these two time systems is due to the Earth’s revolution around the Sun). A full circle of 360° around the celestial equator is defined as twenty-four hours of right ascension. Thus, one hour of right ascension corresponds to 15° of arc, one minute of right ascension corresponds to fifteen arc minutes, and one second of right ascension corresponds to fifteen arc seconds.

This equatorial system rotates with the apparent daily motion of the sky. Hence, most astronomical objects' declination and right ascension remain nearly constant for a reasonably short time, up to a few years. However, over the long run, declination and right ascension change due to two main factors: precession and proper motion. (Note that the Sun, Moon, and planets appear to move through the sky concerning the stars, so their right ascension and declination noticeably change much more rapidly over timescales of hours to months.) Precession is a slow change in the direction of the Earth’s rotational axis, which traces a double-cone figure in space over approximately 25,800 years due to the gravitational pull of the Moon and Sun on the Earth’s equatorial bulge. As a result, the positions of the celestial poles and celestial equator do not remain fixed on the celestial sphere, but they shift predictably. Each of the two celestial poles traces out a circle with an angular diameter of 47° on the celestial sphere over 25,800 years. Because of precession, the equinoxes shift westward relative to the stars, gradually changing the seasonal constellations. The vernal equinox (occurring in March) is now located in Pisces, but 2,000 years ago, it was in Aries, and in about 600 years, it will shift into Aquarius. Polaris is the north pole star, but at the time of building the great Pyramids in Egypt 5,000 years ago, the star Thuban in Draco was the north pole star. In about 12,000 years, the star Vega in Lyra will approximately mark the north celestial pole. Because of precession, catalogs listing the declination and right ascension of stars, nebulae, galaxies, and other objects must specify the epoch (year) for which the coordinates are rigorously correct. Corrections must be calculated using standard precessional formulas to convert the listed coordinates to other years.

The declination and right ascension of individual stars also change due to their proper motion, which is the change in the direction of a star as seen from Earth due to the star’s actual motion through space relative to our solar system. For most stars, the proper motion is small enough so that its practical effect on declination and right ascension can be ignored. Still, some stars have proper motions of several arc seconds per year (the largest proper motion known is that of Barnard's star, 10.4 arc seconds per year), so over timescales of decades, the declination and right ascension of these stars can change by arc minutes. (A very long-term effect of proper motions is that over timescales of thousands of years or more, the familiar shapes of constellations slowly change.)

In the ecliptic system, the reference plane is the plane of the Earth’s orbit around the Sun. The term “ecliptic” is used for Earth’s orbital plane and the great circle that marks its intersection with the celestial sphere. The reference direction is the same as in the equatorial system: the Sun's apparent position at the moment of the vernal equinox. The term “vernal equinox” is used both for the moment in time in March when the Sun is directly above some point on the Earth’s equator and for one of the two intersections of the ecliptic and the celestial equator on the celestial sphere. (The other intersection is called the autumnal equinox and marks the Sun’s apparent position when it is directly above some point on the Earth’s equator in September.) The latitude-like coordinate, called ecliptic latitude, is measured as the angle north (positive) or south (negative) of the ecliptic; it ranges from +90° to –90°. The longitude-like coordinate, called ecliptic longitude, is measured to the east along the ecliptic from the vernal equinox point; it ranges from 0° to 360°. This coordinate system is especially useful in giving the position of solar-system objects. Because many solar-system objects have orbits around the Sun that are not inclined very greatly to the plane of the Earth’s orbit around the Sun, such solar-system objects will be seen near the ecliptic and thus have small ecliptic latitudes.

The galactic coordinate system has a reference plane that is the mean plane of our galaxy, the Milky Way (defined primarily by twenty-one-centimeter, 1,400-megahertz radio observations of neutral hydrogen, which is concentrated in the galactic plane), and a reference direction that points to the galactic center. The latitude-like coordinate, called galactic latitude, is measured as the angle north (positive) or south (negative) of the galactic equator. The longitude-like coordinate, called galactic longitude, is measured along the galactic equator from the direction to the galactic center (as viewed from the position of our solar system) toward the direction of galactic rotation. It varies from 0° in the direction of the galactic center, to 90° in the direction of general galactic rotation, to 180° in the direction opposite to the galactic center (the galactic “anti-center”), to 270° opposite to the direction of general galactic rotation, and up to 360° as the direction to the galactic center is approached again. This system helps indicate the location of objects relative to the Milky Way.

Applications

The primary use of any astronomical coordinate system is to specify the location of celestial objects for observation. Most sources list the equatorial coordinates of right ascension and declination and the epoch (year) for which the right ascension and declination are rigorously correct. In the past, astronomers had to calculate precessional corrections to adjust the right ascensions and declinations to the current date and then calculate the angles to set the telescope based on the observation time. However, the settings of most modern telescopes are computerized, so the right ascension, declination, and listing epoch can be input directly, and the correct settings are automatically calculated.

Another use for old catalogs listing right ascension and declination is determining proper motions. The old coordinates, corrected for precession, are compared to the new coordinates. Any differences are due to the proper motions of the objects.

In the case of an object in our solar system (such as a planet, asteroid, or comet), the elements of its orbit around the Sun (such as semimajor axis, eccentricity, inclination, or perihelion passage time) will often be given. These can be used to calculate the object’s ecliptic latitude and longitude for a specific time and date, and in turn, these can be converted into its right ascension and declination for that same time and date. A list of these coordinates for a series of dates provides an ephemeris of where to observe the object.

In the study of the structure of the Milky Way, coordinates of galactic latitude and longitude often are most useful for visualizing where objects are located. Of course, galactic coordinates can be converted to equatorial coordinates of right ascension and declination for setting telescopes to observe the objects.

Context

The earliest references to locations and motions of stars and planets can be traced back about twenty-five hundred years when Babylonian observer-priests recorded the movement of planets relative to the stars. In the hands of the Greeks, the Babylonian results for periodic and irregular celestial motions became the basis for geometric models trying to explain the structure and motions of the universe. Ptolemy, between 296 and 272 BCE, measured positions for several stars in terms of their angular distances above or below the celestial equator (modern scientists call this declination), as well as differences in their angular positions parallel to the celestial equator (modern scientists call this differences in right ascension). Around 150 BCE, the Greek astronomer Hipparchus compiled one of the first systematic star catalogs, giving the coordinates and apparent magnitudes for about 850 stars.

The development of astronomical coordinate systems was significant for several practical reasons. Most importantly, it allowed an accurate calendar to be constructed, essential for weather prediction and agriculture. The length of the year could be fixed, months and days could be intercalated, and the passing of the solstices and equinoxes could be established. In addition, astronomical coordinate systems led to the development of celestial navigation, enabling commerce to expand to new trade areas and allowing more of the world to be explored.

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