Astronomical Angle Measurement

As many of you know, I get excited about astronomy. So this post is the first in a series devoted to understanding the math behind the measurements of our solar system.

Next clear night, go take a look at the stars, and try to identify some of the constellations. If you want some help, sky maps for June and July are available that I like. For the sake of this post, try especially to identify the big dipper -- which will be visible in the Northwest, about halfway between the horizon and the "zenith" which is the point straight above you.

If you've never done it before, hold out your hand straight in front of you, about as far as you can reach, and see how much of the big dipper you can cover up. Don't worry about looking silly or foolish -- that just means you're doing something cool. I do it all the time and no one ever mocks me about it.

Every time you do this, you should notice that the dipper looks about the same size. What you have done is effectively measured the size of the constellation, in a repeatable way. Now you can try to find Cassiopeia (the W in the North) or the teapot (part of Sagittarius, low in the southeast) and compare the size of those constellations with something more familiar.

Maybe you'll be fortunate enough to see the moon on this night, it will be about half full. Hold up your pinky and I bet you can make it disappear? Try it when it looks "HUGE" near the horizon and you'll realize how it's just an illusion. Try the same thing with the sun today or the next day and see if you can compare how big they look.

Astronomers have tools a little more sophisticated than their hands by which to measure things, but you can estimate the same sorts of measurements they make.  What you are measuring specifically is an angle. Angles can be measured from lots of places, but usually they are measured up from the horizon, in which case they are called "altitudes."  Below I am demonstrating two altitudes approximately 20 degrees and 10 degrees respectively.

Approximately 20 degrees

Approximately 10 degrees

The outstretched hand represents approximately 20 degrees for most people -- and the closed hand width represents about 10 degrees. You can measure how accurate your hands measure angles by trying to measure how high it is from the horizon to the zenith -- straight above you. It is exactly 90 degrees, and so you should be able to measure 4-5 hand-spreads up, or about 9 hand widths.

Some other measurements I often use are the width of my thumb or pinky:

Approximately 2 degrees

Approximately 1/2 degree

So? How big is the big dipper? How many degrees is it from the big dipper to the North Star?