Measuring The Sky

Today, an article for beginners that’s well past due. Many new readers of One-Minute Astronomer have trouble understanding our reference to “degrees”, “arc minutes”, and “arc seconds” when talking about the separation of celestial objects. So here’s a primer on measuring angular distances. You’re one minute away from knowing an essential skill to finding your way around the sky.

The Basics

• Astronomers measure angular separation of objects in degrees. There are 360 degrees in a circle. And the angular separation of any point on the horizon and the point directly overhead (the zenith) is 90 degrees. Halfway from the zenith to the horizon is 45 degrees. So far, so good.

• Smaller angles are a little trickier. But your hands and fingers are a remarkably accurate (and convenient) measuring tool. When you hold your hand at arm’s length, you can estimate angles like this:

- Stretch your thumb and little finger as far from each other as you can. The span from tip to tip is about 25 degrees
- Do the same with your index finger and little finger. The span is 15 degrees
- Clench your fist at arms length, and hold it with the back of your hand facing you. The width is 10 degrees
- Hold your three middle fingers together; they span about 5 degrees
- The width of your little finger at arms length is 1 degree.

A Deeper Look

• Now let’s go smaller. When you look through a telescope, you see a field of view of 1 degree or less… a very small slice of sky.

• Astronomers measure angles smaller than 1 degree in arcminutes, or “minutes of arc”. There are 60 arcminutes in one degree, so 1 arcminute is 1/60 degree. The symbol for arcminutes is ‘. So the full Moon, for example, is about 30′ (thirty arcminutes) across. Coincidentally, so is the Sun.

• Each arcminute is divided into 60 arcseconds, or “seconds of arc”. So 1 arcsecond is 1/60 arcminute and 1/3600 degree. The symbol for arcseconds is “. The face of Jupiter, which you can see this summer, is about 50″ across. The two components of the double star alpha Herculi are 4.6″ apart. A good optical telescope in steady skies can resolve down to about 1″ (one arcsecond).

Good To Know

As most sailors know, the angular distance from the horizon to the the north celestial pole, marked almost exactly by the star Polaris, is your latitude. Same for southerners, relative to the south celestial pole. Although there is no bright star at the south celestial pole.