Session 3A: Celestial Coordinates

Coordinates are still a bit new to 4th graders at this point---I know 4th graders have started using maps and map coordinates but only a little. Even though they are a bit new in school, you probably hear about them all the time, especially if your parents have a GPS.

On Earth, we use a set of coordinates called longitude and lattitude. Every place on Earth can be designated with two numbers, one for lattitude and one for longitude. If we look at a globe, you will find it has lines drawn on it forming a grid of coordinates. Because the Earth is a sphere, the coordinate system uses angles instead of fixed-distance separations between grid points. For lattitude, 1° is about 70 miles no matter where on Earth you are. But for measuring longitude, 1° is about 70 miles at the equator, but at the north and south poles, all longitudes converge!

The Celestial Sphere

The stars are not really little dots on a sphere; they are all at different distances. Earth is also not really a sphere (although it is very close); it has mountains and valleys, caves, oceans, an atmosphere, and buildings.

The celestial sphere is also marked off using angle, much like the Earth. For north-south angles, instead of lattitude, astronomers call the measurement declination. For practical purposes, you can imagine the lines of lattitude extending up into the sky and just being called something different. One small difference is that instead of referring to north and south lattitude, astronomers label north declination as positive and south declination as negative. A star that passes directly overhead here in NYC at lattitude 42° North has a declination of +42°. A star that passes overhead at lattitude 42° South has a declination of -42°.

Longitude is different. For Earth, the lines of longitude are fixed on the surface of the Earth. It's hard to imagine anything different: you don't want your longitude to change just because the Earth is spinning! But for coordinates in the sky, we don't want the way we measure tied to the Earth because then the coordinates would change as the Earth spins. We need a grid attached to the sky. The measurements are called right ascension and it is very similar to longitude with two differences. First, it is fixed on the sky; the "zero point" for right ascension is a line drawn from Earth through the Sun on the vernal (spring) equinox. It doesn't really matter where you start for your zero point, just like there is nothing really special about Greenwich, England, the zero point for longitude. But the convention (that is, the agreed upon standard way of doing this) is to measure from that line. Second, right ascension is measured in hours instead of degrees and the numbers from from 0 hours to 24 hours; there are no negative right ascensions.

Most stars do not have names. Only a few hundred have names and even fewer are what would be considered "well-known." Most stars are referenced just by the coordinates. So while we won't be using coordinates (much) in the club, it's important to at least know what they are and how they work.

Stars in 3D

The stars we see in in the night sky form 2-D patterns which we label as different constellations. The stars themselves are, of course, all at different distances just like the people in a family photograph. However, unlike people, the stars all appear as little dots on the sky and it is hard to tell which ones are further away. Astronomers have devised various ways to measure their distances which we won't discuss here. We're going to take the distances which have been determined and turn them into a way to make a 3-D model of a constellation. Since we've been learning about Orion, we'll model that constellation.

There are two angles we have to use; the two coordinates we learned about before: right ascension and declination. Right ascension will turn out to be easy, so we'll come back to that in a minute. Declination is the only one we have to worry about.

Orion is very close to being centered on the celestial equator: his legs hang below the celestial equator, his arms above, and his belt is more-or-less on the celestial equator.

Distances and Angles

In the image above, imaging the blue-green dot as Earth and the yellow dot as the star. The red line goes straight to the star and represents the distance to the star. The white line is the celestial equator extended into space. In fact, think of it as something you could walk on, walking out from Earth until you are standing directly underneath the star. How far is this distance? It's shorter than the distance to the star, but how much?

There is a way to calculate this, but we can do a good enough job just by measuring with a ruler. But why do we care?

Well, if we are making a model of the stars, we can't just hang them out in space. They have to be supported on something. So we'll be mounting (via hot-glue) beads on bamboo skewers. We need to know the length to cut the skewer (that's how high up the star is above our celestial equator) and how far away from earth to put it (that's the distance we "walked" to get directly underneath the star).

Actually, for the length of the skewers, we'll add a bit. Some of the stars in Orion are below the celestial equator and its rather inconvenient to have skewers coming out of the bottom of the model. So we'll offset the bottom of the model to keep all the stars above.