Celestial Coordinates
Published on Mar 4, 2007 at 12:42 pm.
3 Comments.
Filed under astronomy.
Occasionally in posts I have given the location of a star or comet in the sky by a set of coordinates called right ascension and declination. Just the other day, though, someone asked me what that meant. They were clearly coordinates, but just what kind? I realized that I might not have every really defined the terms! They are well known to any astronomer (amateur as well as professional) and to astronomy students. But, of course, unless someone first explains them to you, then you have no idea what they mean.
There are basically two ways to telling where something is located in the sky. The first way is called variously, horizon coordinates, observer coordinates, and alt-azimuth coordinates. It is the way that most people think about directions. It goes something like, “Over that way, and up so far.” This system has two coordinates. One is called azimuth, and the other is altitude. Azimuth is bascially the direction that you face. It is the compass heading. Azimuth is measured in degrees going eastward from North. So, East is 90° and South is 180°. West is 270°, and Southwest is midway between South and West, so that is 225°. If something has an azimuth of 81°, than that means that it is 9° North of due East. Altitude is a measure of how high above the horizon the object is located. An altitude of 10° means that it appears just about a hand’s width above the horizon. An altitude of 30° means that it is 1/3 of the way from the horizon to the zenith (the point directly overhead). And an altitude of 45° is 1/2 of the way between the horizon and the zenith. The zenith, by definition is 90° altitude.The problem with the altitude-azimuth coordinates, though, is that they are entirely dependent upon the observer. Different observers at different locations will see the same object in the sky at different altitudes and azimuths. Even the same observer will see different altitudes and azimuths for the same object at different observing times. So, while this might be a natural way to look at things, it does little to convey positions so that others can go look at a celestial object.
Fortunately, there is another coordinate system that is independent of the observer. We call this system the celestial coordinate system. To assign coordinates in space, you can imagine the entire sky as if it were a giant sphere surrounding Earth. As the Earth turns, you see the sky pass overhead. The most natural coordinate system for a sphere is spherical coordinates. One form of spherical coordinates that everyone is familiar with is latitude and longitude. Latitude measures how far an object is from the equator, and longitude measures how far around the Earth an object is from some reference point, such as the Prime Meridian. A very similar system is used in the sky, only we use the term declination instead of latitude and the term right ascension instead of longitude. But, there are other differences besides the names being different.First, though, let me explain declination, since it is easier. Just like latitude measures degrees north and south of the equator, declination measures degrees north and south of the celestial equator. The only difference is that we customarily use “+” instead of “N” for north declination “-” instead of “S” for south declination. But, how do you define the celestial equator? That is simple. Since it is really Earth that is turning, and not the celestial sphere, you can put the celestial equator right over Earth’s equator. The celestial poles are over Earth’s poles. This has an added advantage for navigators in that the declination of the zenith will equal your latitude (within the margin of error created by the fact that the Earth isn’t really perfectly spherical). So, if you happen to observe a star passing directly overhead, and you know that that star has a declination of +24°, then you know that you are at 24° N latitude.Right ascension is a bit tougher to explain, though. Instead of measuring east and west from a given point like longitude does from the Prime Meridian, right ascension only measures to the east. If you think about it, that makes sense. After all, stars appear to rise in the East because the Earth rotates towards the East. As time passes the point on the celestial sphere where your zenith is found will be farther to the East. So, it makes sense for right ascension to always increase towards the East. Measuring east and west from a meridian is awkward anyway, so the Moon and all other planets measure only in one direction: towards the west.The other aspect of right ascension that is different from latitude is that it is not measured in degrees like latitude, longitude, and declination. Instead, right ascension is measured in units of time. Right ascension goes from 0 to 24 hours instead of 0 to 360 degrees. Now, this takes a bit more explaining. You see, if you look up the coordinates of a star and find its right ascension is 14h25m, this is only a coordinate. It does not tell you the time that it rises, sets, or is highest in the sky.
This might seem a strange way to give a position, but it actually makes sense if you think about it. As the Earth rotates, the sky appears to turn. Things to the east become higher in the sky, and things to the west become lower, and then set. The Earth turns (approximately) 15° in one hour. Thus the Earth would turn about 50° in 3 hours and 20 minutes. So, if you were to see a celestial body 50 degrees east of the meridian (a line running from north to south through the zenith, bisecting the sky into east and west halves) then it would take 3 hours and 20 minutes until it were highest in the sky. An object 34° west of the meridian would have been on the meridian 2 hours and 16 minutes ealier. But, the nice thing about right ascension is that the Earth turns all the way, 360° in 24 hours, so the sky appears to move 1 hour of right ascension each hour. Thus the object 50° east of the meridian would have a right ascension of 3h20m bigger than the right ascension of the meridian, and the object 34° west of the meridian would have a right ascension 2h16m less than that of the meridian. (Note: this is not exactly correct, because the Earth actually rotates 360° in about 23 hours and 56 minutes, not 24 hours. So, the relationship between right ascension differences and the time that an object is on the meridian is off by about 0.3%, but most people wouldn’t notice that.) But, you can see the utility of knowing right ascension differences in units of time. In fact, it is so useful that there is a term for the right ascension that happens to be on the meridian at the moment. That is called the sidereal time. Personally, I don’t like the term, because it isn’t really a measure of time at all, just a coordinate. Calling it time just confuses my students.
The final thing about right ascension is the zero point: the celestial equivalent to the prime meridian. As on Earth, pretty much any place will do. The decision was made to make the zero of right ascension the point in the sky where the Sun’s apparent path through the sky (the ecliptic) crosses the celestial equator going from south to north. This is the Vernal Equinox. The zero of right ascension, the celestial equivalent to the prime meridian, is thus officially called the Vernal Equinoctial Colure. The problem with this is that the Earth wobbles on its axis in two types of motion called precession and nutation. Precession causes the North Pole to point in different directions. This is much like a spinning top that is leaning over. Rather than falling down, it precesses, or changes the direction that it is leaning. Earth’s axis precesses in about 26,000 years. When the axis of rotation shifts, so does the equator. Then the Earth’s equator changes alignment with the sky, the celestial equator shifts. Thus, the point in the sky where the ecliptic crosses the equator also shifts. Thus, the zero of right ascension also shifts. Thus, all of the coordinates of every object in the sky shift. It is a slow shift, to be sure, but it is measurable, and matters to the most precise measurements of the sky. Good star charts will tell for what year they are drawn. Coordinates of celestial bodies should be given with an epoch, which is the year that they would be correct. All this adds complexity to what should have been a simple system.
There are other coordinate systems for the sky, as well. Ecliptic coordinates put the ecliptic equator along the ecliptic. Ecliptic longitude measures from the vernal equinox, and ecliptic latitude measures the angle perpendicular to the ecliptic, north and south. Galactic coordinates do a similar thing, except that the galactic equator runs along the Milky Way, and the zero of galactic longitude is the center of the galaxy. And, there are plenty of other coordinate systems, as well, with specific uses.
-Astroprof
(Images courtesy of the Astronomical League)
A Ler…-- Rastos de Luz on March 5, 2007 at 3:38 pm: 1
[…] “Celestial Coordinates“, no Astroprof’s Page; […]
Astroprof’s Page » Vernal Equinox on March 20, 2007 at 8:22 pm: 2
[…] But, the term Vernal Equinox has more than one meaning to astronomers. As I have indicated above, it is the moment in time that the Sun appears to be over the equator, as the Earth moves around the Sun, passing from when the south pole is tipped more toward the Sun to when the north pole is tipped more toward the Sun. But, there is another meaning. The term Vernal Equinox not only applies to a moment in time, but also to the apparent spot on the celestial sphere that the center of the Sun appears to be at the moment that it is directly over Earth’s equator. This spot on the celestial sphere where the Sun appears to be at that time is called the Vernal Equinox, so when you see the term written down, you need to look at it in context to see if it refers to a moment in time or a spot on the celestial sphere. The postion of the Vernal Equinox on the celestial sphere is the starting point (or prime celestial meridian) for the celestial coordinate of right ascension. Just a few weeks ago I posted a bit about celestial coordinates. So, the celestial prime meridian is called the vernal equinoctial collure. […]
dadster on March 15, 2011 at 9:02 am: 3
why not smeone find a simpler way of indicating the position of a star or deep sky object in the sky esply because astronomy is becoming highy popular with Google-sky maps and iPod ?
Its easier to get the new simpler version published o the net for the information of all concerned
dadster