Celestial Coordinates

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:

• Altitude is the angular distance of an object above the local horizon. It ranges from 0 degrees at the horizon to 90 degrees at the zenith, the spot directly overhead.
• Azimuth is the angular distance of an object from the local North, measured along the horizon. An object which is due North has azimuth = 0 degrees; due East is azimuth = 90 degrees; due South is azimuth = 180 degrees; due West is azimuth = 270 degrees.

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.

Exercises

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 location of the observer on Earth
• the time of the observation

• Textbook on Spherical Astronomy by W. M. Smart
• Computational Spherical Astronomy by L. G. Taff
• Spherical Astronomy by R. M. Green
• Practical Astronomy with your Calculator by P. J. Duffet-Smith
• Astronomical Formulae for Calculators by J. Meeus

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 Latitude is measured north from the plane of the solar system; the North Ecliptic Pole is in Coma Bernices, near RA = 18:00 and Dec = +66:34.
• Ecliptic Longitude is measured east from the Sun, and increases as one moves eastwards away from the vernal equinox.

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

• Galactic Latitude is measured north from the plane of the Milky Way; the North Galactic Pole is in Coma Bernices, near RA = 12:52 and Dec = +26:19.
• Galactic Longitude is measured east from the direction towards the center of the Milky Way, which is in Sagittarius, near RA = 17:45 and Dec = -29:22. It increases as one moves northwards in Dec away from the galactic center (i.e. higher in the sky as seen from Rochester).

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.

  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: