Lesson - Three D Constellations

Many people are familiar with the constellation of Ursa Major, or at least the part of it we call the Big Dipper. It is possibly the most familiar pattern in the night sky. But it would only look the way it does from Earth, another observer on a different planet would get an entirely different view.

1. Suppose you could take the stars that make up the big dipper, and rotate the whole thing by 90 degrees. Draw a picture of what you think the Big Dipper might look like from this perspective.

Early astronomers thought that all of the stars were the same distance away, and mapped them out on the inside of a large sphere which was to them the edge of the universe. Our way of finding objects on the sky still reflects this, where we map stellar objects out by celestial coordinates on the sky, similar to longitude and latitude on Earth.

The Celestial Coordinates, Ra and Dec

The celestial coordinate system is a projection of earth's coordinate system into the celestial sphere. Being just like Earth's system it contains an "equator", lines of "latitude" and "longitude", and even poles. (Though we don't always use the same words for it.) One suggestion one might have would be to just extend the Earth's latitude, longitude, out into the night sky, but the Earth is constantly spinning. For the Celestial coordinates, we have to pick some fixed reference to go by.

The equivalent of Earth's equator in celestial coordinates is the celestial equator. The celestial equator is the projection of the Earth's equator across the night sky. Since the equator is drawn on the Earth in relation to its rotational poles, it doesn't matter that much that the Earth is rotating (though we do have to correct for the precession of the Earth every so often.)

The equivalent of latitude for the night sky is declination (Dec). Dec measures the angle that a given object is above or below the celestial equator. Dec is measured in degrees, and is usually expressed in degrees, arc-minutes, and arc-seconds. Like the minutes and seconds that measure time, there are 60 arc seconds in one arc minute and 60 arc minutes in one degree. Objects below the celestial equator (further south in the sky) are given a negative value and objects above the celestial equator are given a positive value.

If there are coordinates of latitude, there must be coordinates of longitude. Right ascension, or RA, is the celestial equivalent of longitude. RA measures angular distance along the celestial equator, and is measured in units of hours. These are evenly spaced around the sphere, one every 15 degrees. This makes sense because the Earth rotates roughly once every 24 hours. RA is often expressed in hours, minutes and seconds, where in this case one minute is 1/60 of an hour of angle, and one second is 1/60 of a minute of angle.

(Thanks to Dennis Miller, the science teacher not the former SNL fake news reporter, for suggested corrections to the page.)

2. How many arc-minutes as used for Dec are in one minute of angle as used for RA?

Distance

While the ancient astronomers thought that all of the stars were the same distance away, all placed on the inside of a huge sphere, we now know that each of the stars is a different distance away.

Determining the distance to a star can be very difficult, but for nearby stars we can use parallax. Parallax is the apparent motion of a foreground object with respect to a background object due to the motion of an observer. Perfectly clear, right? Consider this. Imagine you are looking at a treetop, and there is a cloud behind it in the distance. Step from side to side, keeping your eye on the cloud. The cloud seems to keep the same position in the sky, but from your perspective, the treetop appears to move back and forth. We can do the same thing with nearby stars. More distant stars appear to remain fixed as the Earth goes around the Sun, but nearby stars seem to move a little side to side. The closer they are, the more they move.

This actually gives us one of our units of distance in space. One parsec is the distance something would need to be from Earth to have a parallax of one arc-second. This means that if we measure the back and forth motion across the sky of a star with respect to its neighbors, we can get the distance to it. The equation for this is

            1
D (pc) = --------
          P (as)

3. As you look at stars that are further and further away, what happens to the parallax of those stars?
4. Why can parallax only be used for nearby stars?

Build your own constellation

When you are trying to visualize something in three dimensions, sometimes it is more helpful to be able to think of it in X, Y, and Z coordinates.

5. Look up the data for the Big Dipper. Convert RA, Dec, and parallax to X, Y, and Z coordinates for each star, and make a 3-D model. You can do this either with materials such as paper mache or styrofoam balls and sticks, or you can use a computer program.