It was a beautiful sunny day in 1966, and I remember it well. There I sat in Mrs. Moyer’s 10th-grade geometry class, daydreaming out the window and pondering everything except acute angles, midpoints and spheres.

“After all,” I reasoned, “What use is knowing that a circle can be broken into 360 equal parts, each 1 degree wide? I’ve got better things to think about!”

The irony is that out that very window existed circles that I would use just about every day of my professional life.

We can’t see them, of course, but the heavens contain many “great circles” that help us define the position and movement of any celestial object.

The easiest to imagine is the one we know as the horizon. Face due north, and keep your eye on the horizon as you turn eastward. When you again face due north, you will have rotated 360 degrees.

360 degrees … Just what does that mean? One degree along this circle equals approximately the width of your little finger held at arm’s length. Your fist from thumb to little finger — also held at arm’s length — spans about 10 degrees.

The position of an object along the horizon is called its azimuth, and it’s always measured eastward from true north. So, for example, something that lies due east is said to have an azimuth of “90 degrees east of north.” And something in the north-northwest might have an azimuth of “315 degrees east of north.”

Seems odd, I know, but that’s the way it’s done.

Try this next time under the nighttime sky, and you’ll find you’ve got an instant ruler on which to measure a celestial object’s “azimuth.” It provides a more precise way to describe directions than using broad terms such as “south” or “northeast.”

Another great circle that we can imagine begins on the horizon, passes directly overhead (the zenith) and continues down to the opposite side of the horizon. Since we see only half a circle in the sky, we can divide it into 180 degrees and use it to measure the altitude of any celestial object. You can use your hand for this as well.

Check it out with Polaris, the North Star, which remains relatively fixed in our sky. Remember, you can always find Polaris by following the two stars at the end of the Big Dipper’s bowl.

If you live in San Diego, for example, you’ll find that the altitude of Polaris is about 32 degrees, while from the New York City area, Polaris appears about 41 degrees above the northern horizon. That’s because the altitude of the North Star conveniently equals your latitude.

Many other “great circles” exist in the heavens as well — the ecliptic, the meridian, the celestial equator — and knowing these helps astronomers grasp the layout and movement of our starry night sky.

I’m sure my poor geometry teacher had a rough time reaching me, but she never gave up, and soon I became fascinated by how we can measure the universe with geometrical figures and angles, and how important it all is to astronomers.

And for that gift, Mrs. Moyer, I thank you … beyond all measure!

Dennis Mammana is an astronomy writer, author, lecturer and photographer working from under the clear dark skies of the Anza-Borrego Desert in the San Diego County backcountry. Contact him at mammana@skyscapes.com and follow him on Twitter: @dennismammana. The opinions expressed are his own.

## Dennis Mammana

Dennis Mammana is an astronomy writer, author, lecturer and photographer working from under the clear dark skies of the Anza-Borrego Desert in the San Diego County backcountry. Contact him at dennis@mammana.com and connect with him on Facebook: @dennismammana. The opinions expressed are his own.