Lab 1: Introduction to Celestial Coordinates and the Planisphere

Introduction

Observing the night sky is a very personal experience. It has inspired poets, statesmen, scientists, and not a few young loves! In order to make a contribution to the body of scientific knowledge - that is, in order to "do science" - however, we must be able to communicate what we have seen and learned. Science is just as much (if not more) about communication as it is about observation. If you haven't communicated anything, you haven't contributed to the body of scientific knowledge - and you haven't done any science. In order for us to communicate with each other, we have to agree on a common framework, a language if you will. One of the most important things (for our purposes at least) we must agree on is how to find objects in the sky. In other words, we need to agree on a coordinate system.

The Horizon Coordinate System

The simplest way to find a star in the sky is to have someone who sees it to just point it out to you. Suppose, however, that the person is not physically present - perhaps she's talking to you over your cellular phone. How can she tell you where to look to find the star? The most natural way is for her to tell you how many degrees above the horizon and how many degrees "left" or "right" of some reference point the star lies. In defining any coordinate system, we must always first indicate the reference point from which we start measuring, the "zero" of the coordinate system. In this case, the distance "up" (above the horizon) has a fairly obvious zero: we begin counting from the horizon itself. But where do we start counting for the "left/right" direction? In your own back yard, you may start from "that funny-looking bush along the back fence", but unless I visit your backyard, I have no idea what bush you're talking about! Since we aren't communicating, we aren't doing any science. So where do we put our zero? In truth, it doesn't matter. We could put it anywhere we want, but it has to be some place we all agree on. By long-standing tradition, we start counting "left/right" distances from north; thus, north is 0 degrees, east is 90 degrees, south is 180 degrees, and west is 270 degrees. We have, also by tradition, agreed on names for the two coordinates of the horizon system: the distance above the horizon we call "altitude", and the distance from north we call "azimuth". Both are usually measured in degrees, as I've hinted.

Now, there are some problems with the horizon coordinate system. First and foremost, the Earth is rotating on its axis from west to east, making the Sun, planets, and stars appear to move across the sky from east to west. Notice that I said appear to move: except for a very small proper motion (which you won't be able to detect in a single night), the stars aren't moving at all - you are. So don't ever let anyone confuse you: you know that the Sun rises in the east and sets in the west, so the stars and planets must do so too - it's all caused by the same effect, the rotation of the Earth. The result of all this is that a star with altitude 20 degrees and an azimuth of 135 degrees at 8:30 won't be at those coordinates at 9:30.

But wait, it gets worse! As shown in Fig. 1-1, as we walk down towards the equator, a given star in the Northern Hemisphere will seem to be lower on the horizon and so will have a different altitude. Also, the stars visible in Washington, D.C., aren't visible in Moscow at the same time since the Earth is in the way; obviously, the good people of Moscow will just have to wait until the Earth rotates enough to make the stars we saw visible. The result of this is that the stars will have different coordinates depending on what time we observe them and where on the Earth we're standing.

Figure 1-1

The Equitorial Coordinate System

So what do we do? In order to catalog the positions of the stars using the horizon coordinate system, we'd have to write down the coordinates of every star at every position on Earth and at every second of time. This would fill rooms with data! There's just no way to do it. To get around this problem, astronomers have come up with another coordinate system. This system is completely invented and its sole purpose is to help us have one unchanging set of coordinates for each object in the sky. You may think, therefore, that this system isn't very important, but when you consider that as astronomers (and by taking this class, you've become an astronomer -- congratulations!) our main interest is in looking at stars, you'll find that we use this system almost exclusively.

Okay, so how does it work? First of all, the system takes advantage of the fact that stars aren't really moving, but the Earth is. As shown in Fig. 1-2, we imagine that all the stars are plastered onto a giant sphere way out at infinity. (Keep in mind that they are really not, but they're so far away that this is a pretty good approximation.) The Earth turns in the center of this sphere - which call the "celestial sphere" - so you can see that to someone standing on the Earth, the stars appear to move, but from our "heavenly" viewpoint, we can see that this isn't so.

Figure 1-2

Now, let's extend a plane out from the Earth's equator as shown in Fig. 1-3. Where this plane intersects the celestial sphere defines the "celestial equator". We can draw lines parallel to the celestial equator and lines perpendicular (at right angles) to it, as shown in Fig. 1-4. Now our celestial is sphere is divided into a grid, and using this grid we can pinpoint the location of any star on the celestial sphere. Better yet, because the celestial sphere never moves and the stars are fixed onto it, these coordinates never change. Looks like we've achieved our goal! We call the distance "up" (that look like lines of latitude on the Earth) "declination", usually abreviated "dec". The lines "left/right" (that look like lines of longitude on Earth), we call "right ascension" or just "RA". If we specify the declination and right ascension of any object on the celestial sphere, that will be its coordinates for all time (basically, but more on that later).

Figure 1-3

Figure 1-4

We mentioned in the section on the horizon coordinate system that we always have to define a "zero" for each coordinate (in that system, the zeros were the horizon and north). What are our zeros here? Well, the obvious place to put the zero of declination is on the celestial equator, so that's what we'll do. We'll make the celestial north pole be at 90 degrees north declination and the celestial south pole be at 90 degrees south declination, similar to what we do for latitude on the Earth. But where do we put the zero of right ascension? You might answer, "Why, right in the middle of the picture, of course!" But if you rotate the celestial sphere 90 degrees, the picture looks exactly as it does in Fig. 1-4. So where do we put it? Once again, the answer is it really doesn't matter. We can put it wherever we like, so long as we all agree on it. We have this same problem wih longitude on Earth. Everyone got together and just decided that the zero of longitutde would be this observatory in Greenwich, England. They could have put it anywhere. They could have put it at my house (they should have put it at my house!), but they had to put it somewhere, so that's what they chose. On Mars, there is a tiny little crater called Ares which we just decided would be the zero of longitude on Mars. Any Little Green Men on the surface may have different ideas, but they didn't exactly make their wishes known, did they? By a very old, very strange tradition, astronomers have made the position of the Sun on the vernal equinox (around March 21 or so) to be the zero of right ascension. Wherever the Sun is on that date, bam! That's our zero. We call this position the "First Point in Ares" because it used to occur in the constellation Ares. Note that I said "used to" The only problem with this tradition is that when it was established, we didn't realize that the Earth was wobbling and precessing on its axis. There are some complicated motions involved that we won't go into, but the result is that the First Point in Ares moves slightly over time. It is because of this fact, astronomers have to update their star catalogs every fifty years or so. It's also because of this fact that even though I'm a Gemini, the Sun was not in Gemini when I was born in spite of what is claimed by astrologers. But don't get me started on astrology; I personally believe astrology is a bunch of bunk, but then again, Geminis are naturally skeptical... The point is that these changes are so slow that unless you plan to stay in this course for the next fifty years, we'll never have to worry about it. For our purposes then, the zero of right ascension is a fixed point. Don't ask me why they chose to do it this way, I think it's all rather odd. We usually measure declination in degrees and right ascension in "hours" since it takes the Earth 24 hours to rotate 360 degrees. The conversion from degrees to hours or hours to degrees is simple if you just remember that one hour is 15 degrees. Incidentally, this is how time zones are defined: 15 degrees of longitude is a change of one hour of time. Works out well!

The Planisphere

To sum up then, the equitorial coordinate system is only good for storing the location of stars in reference books; it tells us nothing about how to actually find something in the sky when we go outside. The horizon coordinate system fulfills the opposite role: it tells us how to find something in the sky, but won't let us save a single position for each star in the reference books. If somehow we could convert between these systems though, we could look up the equitorial coordinates of the star in a reference book and, knowing the time and place of the observation, we could convert these coordinates to horizon coordinates, go outside and find the star. In fact, this is exactly what we do. The conversions, however, involve some rather ugly equations and techniques that really require more time to learn well than we have available in this class. If this were all we had, I'd have no choice, but fortunately for both of us, there is a wonderful device, called a planisphere, that will make these conversions for us.

Figure 1-5

The planisphere consists of two parts, the inner, rotatable wheel and the outer "frame" (see Fig. 1-5). The wheel has the brightest stars marked on it and uses the equitorial coordinate system. The frame has been pre-cut to represent the horizon for your latitude on the Earth. By lining up the month and day on the wheel with the time printed on the frame, we are effectively converting between the equitorial and horizon coordinate systems. Remember, to make the conversion, we needed the time and place of the observation - the frame itself takes care of the place and we just dialed in the time. In the center of the cutout area of the frame - not the metal pivot around which everything rotates - is the point directly overhead, called the zenith (no, it's not an old color television set!). One horizon is marked "north", one is marked "south", and so on. Why, you might ask, are the eastern and western horizons closer to the northern horizon than the southern horizon? Shouldn't it be the same distance? Well, the problem here is that we've taken a spherical globe and smashed it onto a flat disk. We have the same problem with maps of the Earth's surface, and that's why Greenland often looks bigger than California. There's not much we can do about it, unfortunately, unless we build spherical planisphere (which is an interesting idea). Basically, though, the planisphere is just a guide for you to find things in the sky. Because of the distortion, constellations in the sky will not appear as they do on the planisphere, but the planisphere can help us identify bright stars and give us a general idea of where to look for other stars. It's also very useful in figuring out when a certain star will rise or set, as you'll see in the exercises to follow. The best way to get comfortable with the planisphere is simply to take it outside and use it. Like most things, your ability with it will improve with practice. Once you've spent many (probably cold) nights outside stargazing, you'll eventually find that you don't need the plansiphere at all - you just "know" where everything is. After all, the view hasn't changed in thousands of years!

Conclusion

Your goals for this lab are threefold:
  1. Understand the difference between the horizon and equitorial coordinate systems and be able to identify the components of each system.
  2. Use the planisphere to find the approximate coordinates of a star in both the horizon and equitorial coordinate systems.
  3. Use the planisphere to predict the rising and setting times for any given star.

A final note: Not all objects in the sky are on the celestial sphere. Remeber that we assumed all the stars were way out at infinity. That's fine for stars, but it doesn't work at all for anything in the solar system - they are just too close. For this reason, solar system objects seem to move against the background of the stars on the celestial sphere. This is how the planets got their name: "planet" comes from the Greek word which means "wanderer". The declination and right ascension of the planets at any given time can be calculated and put into tables. You may think this is a lot of data, and you'd be right, but it's only for 8 planets and whatever asteroids we're interested in, so it's not all that bad. Just keep this fact in mind: while planets aren't shown on your planisphere, they all can be found within a narrow band tilted slightly from the celestial equator. The band is called the "ecliptic" and is marked on your planisphere. Why should all the planets be found in this narrow region of the sky? Ah, I won't make it that easy for you; you can answer that in the lab, but I'll give you a hint: think of how the Solar System appears if I'm out in space. Are the planets scattered all over the sky, or are they confined to some region? See if you can figure it out. Good luck!