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19 October 2001

Understanding Celestial Coordinates

by Alan MacRobert
Adapted from Sky & Telescope magazine

NEWCOMERS TO ASTRONOMY can get thrown for a loop when they first encounter declination and right ascension. Why are the positions of stars that are light-years away in the depths of space stated in a system that's tied to latitude and longitude on Earth?

The celestial coordinate system, which serves modern astronomy so well, is firmly grounded in the faulty world-view of the ancients. They believed the Earth was motionless and at the center of creation. The sky, they thought, was exactly what it looks like: a hollow hemisphere arching over the Earth like a great dome. The stars? "They're fireflies," explains Timón in The Lion King, "stuck to that big, uh, blue-black thing up there."

The celestial dome with its starry decorations had to be a complete celestial sphere, early skywatchers figured out, because we never see a bottom rim as the dome tilts up and rotates around the Earth once a day. Parts of the celestial sphere are always setting behind the western horizon, while other parts are rising in the east. At any time half of the celestial sphere is above the horizon, half below.

Even today this is how the cosmic setup actually looks. Never mind that we're on a moving dust mote orbiting a star in the fringe of a galaxy. In astronomy, appearances and reality are more different than in any other area of human experience. Perhaps for this reason, astronomers are quite comfortable living with both -- as long as the two are kept in their proper relationship. The celestial sphere, with its infinitely large radius, appears to turn daily around our motionless Earth, from which we use telescopes to examine wonders painted on its inside surface.

From Earth to Sky

Whenever you want to specify a point on the surface of a sphere, you'll probably use what geometers call spherical coordinates. In the case of Earth, these are named latitude and longitude.

(Click image to enlarge)

Imagine the lines of latitude and longitude ballooning outward from the Earth and printing themselves on the inside of the sky sphere. They are now called, respectively, declination and right ascension.

Directly out from the Earth's equator, 0° latitude, is the celestial equator, 0° declination. If you stand on the Earth's equator, the celestial equator passes overhead.

Stand on the North Pole, latitude 90° N, and overhead will be the north celestial pole, declination +90°.

At any other latitude -- let's say Kansas City at 39° N -- the corresponding declination line crosses your zenith: in this case declination +39°. (By custom, declinations north and south of the equator are called + and - rather than N and S.) This is the declination of the bright star Vega. So once a day, Vega passes overhead as seen from the latitude of Kansas City.

Hours and Degrees

Of course Vega doesn't move; it's the Earth that's turning. But we're talking appearances here. The celestial sphere seems to rotate around our motionless world once in about 24 hours.

This daily motion is the basis of the numbering system used in right ascension. Instead of counting in degrees, as with longitude around the Earth, right ascension is usually counted in hours, from 0 to 24 around the sky. This is just a different way of putting dividing marks on a circle. One hour in this scheme is 1/24 of a circle, or 15°.

The benefit of this numbering system is that as the Earth rotates, you see the sky turn by about 1 hour of right ascension for each hour of time. This makes it easy to figure out when celestial objects will come in and out of view. The stars become a giant 24-hour clock.

Since ancient Babylonia, people have divided both degrees and hours into finer units by means of base-60 arithmetic. In 1° there are 60 arcminutes, written 60'. One arcminute contains 60 arcseconds, written 60". A good telescope in good sky conditions can resolve details about as fine as 1" on the surface of the celestial sphere. By comparison, 1" of latitude on Earth is about 101 feet. So if you had a telescope at the center of a transparent Earth, you could resolve details about the size of a house lot up on the surface.

Because declination is given in degrees, fine gradations of it are usually expressed in the Babylonian system of arcminutes and arcseconds. For instance, Vega's exact declination (2000.0 coordinates) is +38° 47' 01".

Hours of right ascension are divided into minutes and seconds of time, not of arc. In one hour (1h) are, naturally enough, 60 minutes, written 60m. In one minute of right ascension are 60 seconds, written 60s. Vega's right ascension is 18h 36m 56.3s.

Notice the different notation for the different kinds of minutes and seconds. They're truly different. Just as 1h contains 15°, so does 1m contain 15' and 1s contain 15".

Starting Points

Any spherical coordinate system comes with a natural, built-in zero value for its "latitude" coordinate, whether it is called latitude, declination, or something else. This reference marker is the equator. No other latitude line is like it.

But there's no such natural zero point for counting longitude -- in the sky's case right ascension. All lines of longitude or right ascension are alike. So a zero point has to be picked arbitrarily. On Earth, 0° longitude has long been defined as a line engraved on a brass plate set in the floor under a position-measuring telescope at the Old Royal Observatory in Greenwich, England. In the sky, 0h right ascension is defined as where the plane of the Earth's orbit around the Sun (the ecliptic) crosses the celestial equator in Pisces. This point is called, for historical reasons, the First Point of Aries.

Precession

The First Point of Aries really was in Aries when it was named roughly 2,000 years ago. It has crept into the stars of Pisces because of precession, a slow shift in the orientation of the Earth's axis with respect to the rest of the universe.

Put a spinning top at an angle on a table and it too will precess. Its spin axis will slowly circle around the upward direction of the force that the table applies to the point of the top. In exactly the same manner, the spinning Earth slowly precesses because of the force that the tidal gravitational tugs of the Moon and Sun apply to the Earth's slight equatorial bulge.

Hence we see the north celestial pole, which is currently located close to Polaris, swing across the stars in a wide loop around the north ecliptic pole every 26,000 years. The moving celestial pole drags the whole celestial-coordinate system -- the whole grid of declination and right ascension -- along with it.

Contrary to popular belief, precession does not shift the Earth's axis with respect to the Earth's own geography. The terrestrial North Pole doesn't move to a new location (at least not much on the time scale we're talking about). Precession won't give walruses a tropical suntan. The only noticeable changes are those that result from the grid of celestial coordinates moving against the stars. In 12,000 years, for instance, Vega will be the north star, and Orion will be a constellation of summer, not winter.

Because the coordinate grid insists on sliding around this way, a star's right ascension and declination are continually changing. To fix a star's position you need to specify the date for which a right ascension and declination apply. The current standard is "equinox 2000.0," shorthand for "right ascension and declination at the moment the year 2000 begins." The previous standard, still encountered on some star charts, was 1950.0.

For moving objects such as the Sun, Moon, and planets, right ascension and declination are often given for the "equinox of date": that is, correct for the actual date listed. In Sky & Telescope's monthly table of Sun and planet positions near the center of each issue, positions are given in the coordinate system for each date listed.

Rarely, however, do backyard astronomers need to worry about precession. From 1950 to 2000 the coordinate grid creeps along the ecliptic by only 0.7°, less than the width of the lowest-power view in many telescopes. And that amount applies only at the ecliptic itself. The total shift is less elsewhere, declining to essentially zero at the ecliptic poles.

Which way does precession go? It makes a star's right ascension increase each year. That is, an old right-ascension value precedes the newer value in amount as well as date.

As for right ascension itself, just remember that it increases to the east. If you get confused about which way is east on a star map that shows right ascension, this little mnemonic will get you squared away.

Alan MacRobert is an associate editor of Sky & Telescope magazine and an avid backyard astronomer.