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Celestial Coordinates

Homework for today

Right Ascension (or "RA") and Declination (or "Dec") are global coordinates: any particular star has the same RA and Dec for all observers on Earth, and that position remains the same, night after night. Altitude and Azimuth, on the other hand, are local coordinates: each observer sets up his own reference frame. Moreover, the altitude and azimuth of a given star will change over just a few minutes as the star appears to rise, move across the sky, and set.

Right Ascension and Declination

On Earth, one way to describe a location is with a coordinate system which is fixed to the Earth's surface.

The system is oriented by the spin axis of the Earth, and has special points at the North and South Poles. We use lines of latitude and longitude to demarcate the surface. It's obvious that latitude is measured away from the equator. But where is the starting point for longitude? There is no "obvious" choice. After a lot of dickering, European nations finally decided to use the location of the Greenwich Observatory in England as the starting point for longitude.

There are several ways to specify a location -- for example, that of the RIT Observatory. One can use degrees:

 latitude 43.0758 degrees North, longitude 77.6647 degrees West of Greenwich

Or degrees, minutes and seconds:

 latitude 43:04:33 North, longitude 77:39:53 West 

Or, in the case of longitude, one can measure in time zones. The sun will set at the RIT Observatory about 5 hours and 11 minutes later than it does at Greenwich, so one could say

 latitude 43:04:33 North, longitude 05 hours 11 minutes West

The celestial coordinates

On can make a similar coordinate system which is "fixed to the sky":

Once again, we use the Earth's rotation axis to orient the coordinates. There are two special places, the North and South Celestial Poles. As the Earth rotates (to the East), the celestial sphere appears to rotate (to the West). Stars appear to move in circles: small ones near the celestial poles, and large ones close to the celestial equator:

Image copyright
David Malin.

We again use two orthogonal coordinates to describe a position:

As with latitude, Declination is measured away from the celestial equator. But there is again no obvious choice for the starting point of the other set of coordinates. Where should we start counting Right Ascension? The rather arbitrary choice made by astronomers long ago was to pick the point at which the Sun appears to cross the celestial equator from South to North as it moves through the sky during the course of a year. We call that point the "vernal equinox".

Once again, there are several ways to express a location. The star Sirius, for example, can be described as at

  Right Ascension 101.287 degrees, Declination -16.716 degrees

We can also express the Declination in Degrees:ArcMinutes:ArcSeconds, just as we do for latitude; and, as usual, there are 360 degrees around a full circle. For Right Ascension, astronomers always use the convention of Hours:Minutes:Seconds. There are 24 hours of RA around a circle in the sky, because it takes 24 hours for the Sun to move all the way from sunrise to the next sunrise.

  Right Ascension 06:45:09, Declination -16:42:58

What's the difference between an "arcminute" and a "minute"?


  1. How many degrees are there all the way around the celestial equator? How many hours are there around the celestial equator?
  2. How many degrees make up one hour of Right Ascension?
  3. How many degrees are there in one minute of Right Ascension?
  4. How many arcminutes are there in one minute of Right Ascension?
  5. How many arcseconds are there in one second of Right Ascension?

Altitude and Azimuth

These two coordinates, altitude (or "alt") and azimuth (or "az"), are centered on the observer.

These two angles specify uniquely the direction of any object in the sky. Some telescopes have alt-az mounts which swivel in these two perpendicular axes; camera tripods and tank turrets are other examples of alt-az devices.

The altitude of an object is especially important from an practical point of view: any object which has an altitude less than zero is below the horizon, and hence inaccessible. Moreover, the altitude of an object is related to its airmass, a measure of how much air the light from that object must traverse to reach the observer. The larger the airmass, the more light is scattered or absorbed by the atmosphere, and hence the fainter an object will appear. We'll deal with airmass at greater length a bit later.

However, note that two observers at different locations on Earth will not agree on the (alt, az) position of an object. Moreover, as the Earth rotates, an object in the sky appears to move from East to West, so its (alt, az) position changes from moment to moment.


  1. Polaris, the North Star, is close to Declination = +90 degrees. If you were standing on the Earth's North Pole, where would you see it in the sky?
  2. If you were standing on the Equator, where would you see Polaris in the Sky?
  3. The latitude of Rochester is +43 degrees North. How far above the horizon is Polaris as seen in Rochester?
  4. What is the Declination of the southernmost stars we can see in Rochester?

It is possible to convert from (RA, Dec) to (alt, az), or vice versa. One needs to know two factors:

The calculations involve some spherical trigonometry. One can find the details in any good book on celestial mathematics, such as

In these modern times, it's usually easiest to use one of the many fine planetarium programs on a computer to do this work.

Ecliptic (Solar System) coordinates

For objects within our solar system -- planets, asteroids, comets -- it often helps to use a coordinate system centered on the Sun, with its equator running along the plane of the planetary orbits. We call this the ecliptic coordinate system.

The ecliptic coordinate system is convenient when dealing with objects in the solar system: they are concentrated towards the ecliptic equator:

If you zoom in, you can see that the major planets lie slightly above or below the ecliptic equator, because their orbits around the Sun are inclined slightly with respect to the Earth's.

Ecliptic coordinates can also be important when you want to avoid the solar system. Telescopes in space, such as the Hubble Space Telescope or the Chandra X-ray Telescope, cannot point close to the Sun (or else they might suffer damage to their detectors). For some purposes, astronomers want to make very, very long exposures: days or even weeks long. During such a long exposure, the Earth may move a significant fraction of its entire orbit, which can cause a target originally far from the Sun ....

... to move closer to the Sun, from the telescope's point of view.

Therefore, astronomers sometimes choose their very deep fields

to be near the ecliptic poles; the Sun is ALWAYS ninety degrees away from these locations.

Galactic Coordinates

One more set of coordinates comes into play if one studies the distribution of stars within our Milky Way Galaxy, or the distribution of other galaxies in the far reaches of space.

On a warm July evening in Rochester, the Milky Way stretches overhead, with the galactic center just above the southern horizon.

If you make a map of the sky in galactic coordinates, the Milky Way runs right across the middle. The section we see in the summer sky from Rochest is in mostly the left half of this map.

Map courtesy of the Lund Observatory

An infrared map of the sky in galactic coordinates made by the COBE satellite is dominated by emission from dust in the Milky Way, but also shows a faint band of light due to emission by dust particles in the solar system. Note that the plane of the solar system is tilted by almost ninety degrees relative to the plane of the Milky Way.

Converting between coordinates

Suppose that you know the coordinates of an object in one system, but you need to know its coordinates in a different system. For example, someone tells you that you should consider using HST to study a quasar located at

  RA = 18:14:15   Dec = -29:03:39

Is this a good idea? Perhaps you should see where it lies with respect to the Milky Way, by converting its RA and Dec to galactic coordinates. There are several ways to do this -- I recommend one of these tools:


  1. Is it really a good idea to use HST to study that quasar? Why or why not?


  1. What are the current (RA, Dec) coordinates of Mars?
  2. At midnight tonight, will Mars be visible from Rochester? If so, what will be its azimuth and elevation? Express the azimuth in terms of degrees, and in terms of rough compass directions.
  3. What is the current ecliptic longitude of the Sun? What is the current ecliptic longitude of Mars? So, what is the angular distance between the Sun and Mars?


Last modified by MWR 3/13/2012

Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.