Angular Measurement

Throughout many of the pages on this web site, I describe the location of objects using angular measurements in degrees ( º ), minutes of arc ( ' ), or seconds of arc ( " ). Such practice is common in astronomy since the sky from horizon to horizon can be thought of as a giant dome or semi-circle, which lends itself well to angular measurements. I realize that these terms can seem confusing to a beginner, but once you get used to them they are actually pretty easy to use.

Often I'll write something like Venus is 15º above the horizon, or Jupiter is 5º below and to the left of Venus. Degree measurement of these sizes are pretty large, and you can actually use your hands to help you judge these distances. The chart below describes the different angular measurements you can make when you extend your hand out to arms length. For example, your clenched fist held at arms length covers about 10º of the sky. This works well for almost everyone, child or adult, thanks to the proportions of the human body. Children have shorter arms, but their fists are smaller. Likewise, adults have longer arms, but their fists are larger.

Degree Measure Body Part Held At Arms Length
Width of thumb
Length of thumb
10º Length of closed fist
15º Length of closed fist with thumb extended
20º Length of closed fist with thumb and little finger extended

Minutes and seconds of arc are a little trickier. Sometimes called simply arc minutes or arc seconds, each are simply smaller divisions of a degree, but they are tough to visualize because they get amazingly small. Just like in an hour of time, there are 60 minutes of arc in one degree. The diameter of the Full Moon is about 1/2º, or 30 minutes of arc . Similarly, there are 60 seconds of arc in one arc minute. The average human eye can resolve naked-eye stars that are as close as about 4 arc minutes apart, or about 240 arc seconds. Arc minutes and arc seconds are used most often to describe the apparent separation of close double stars or the apparent diameter of planet's disk. Using a telescope allows the human eye to view objects like double stars that have separations in the arc second range. Most telescopes have a maximum resolving power of at least 2 arc seconds, depending on aperture (see "Factors Affecting Viewing"). But remember, that doesn't get you around the limitations of your eye! Since the average person's unaided eye can only resolve 240 arc seconds, you must magnify an image at least 120 times before you can get the full use of a telescope that can resolve 2 arc seconds (2 times 120 equals 240). The best way to learn to visualize the distance represented by arc seconds is to observe the various double stars that I point out each month in the Constellation of the Month section. Notice how far apart they are through your telescope and compare that distance to the separation that I mention on the page. You'll quickly become familiar with angular measurement this way.