Degrees, Arc-Minutes and Arc-Seconds

How do we measure things in the sky?

Throughout the descriptions of astro-happenings here on Darker View, I use the terms degrees, arc-minutes, and arc-seconds. This is how astronomers measure size and separation of objects in the sky.

The degrees used by astronomers are the same as those you learned in high school geometry, the same as marked on that old school protractor forgotten in the back of the desk drawer. 360 degrees mark a circle, 360 degrees reach once around the sky.

Degrees measure rotation, and just about everything in astronomy rotates… As the Earth rotates on is axis, the sky goes wheeling overhead. When we move a telescope from one point in the sky to another we rotate the telescope about its axis. How far does it rotate? That is measured in degrees.

Standing under a dark sky it is easy to begin using this sort of angular measurement. Straight overhead is a point called zenith, this is 90° from the horizon. Something half-way from the horizon to zenith is 45° from the horizon. Look due east, then turn to the right to look due south, you have just swung through 90°.

Angular Size by HandMeasuring angular size by hand

In astronomy we need to measure small differences in angle, thus it is useful to use smaller units than degrees to get better precision. One can simply add a few decimal places to indicate better precision, and this is often done. However the older, traditional way is to use arc-minutes and arc-seconds, an idea which parallels time-keeping.

There are 60 arc-minutes in one degree. Thus the Moon, which is about half a degree across, can also be said to be about 30 arc-minutes across. Arc-seconds are the smallest of the angular units we use in astronomy. There are 60 arc-seconds in one arc-minute, 3600 arc-seconds in one degree. Arc-seconds are on the scale of the smallest features visible in the telescope, the planets of our solar system range in size from a few arc-seconds to a few tens of arc-seconds.

In addition to degrees you will also find hours used to indicate a position. Hours are used to measure right ascension, the distance east or west in the sky. Declination (north and south) is indicated in degrees. As there are 24 hours and 360 degrees it is fifteen degrees per hour.

Why is it this way? 360 and 60 seem like odd numbers to measure something. What you have to remember is that in navigation and astronomy angles and time are intimately related. As the Earth rotates, as the stars wheel overhead, you can measure time by measuring the motion. To find something in the sky you must add the time to the celestial coordinates (the right ascension) of the object. Having both of these numbers expressed with hours, minutes, and seconds makes the math easy, particularly when all calculations were a pen and paper exercise. The sky simply becomes a large clock, no surprise, it is the original clock.

Arc-minutes are often abbreviated with a single quote, arc-seconds with a double quote. Thus an angle could be written as 25°10’45” denoting 25 degrees, 10 arc-minutes, and 45 arc-seconds. Stellar coordinates are often written in this notation. Simply using decimal places, 4.5° is the same as 4°30′.

When measuring things in angular size, we ignore the distance to the objects. While it might appear that Jupiter is only two degrees from the Moon in the sky, this is just what we see from our point of view. In reality the Moon is a mere quarter-million miles away, while Jupiter is hundreds of millions of miles distant, vastly further. It is correct to append the word “apparent” to an angular size. While the object appears to be 10 arc-minutes across, when it may actually be light-years across.

For an amateur skywatcher looking up at the night sky, the skill of estimating distances in degrees is quite useful and worth learning. You will know where to look for any particular object, how high in the sky, or how far from something you can easily find.

A few pointers might help you get started…

The Sun and Moon are quite close to half a degree across, 30 arc-minutes. When estimating a few degrees simply imagine a few widths of the Moon in place of the angle you need. Thus two degrees would be the same as four full Moons, side-by-side.

One degree is about the same as the width of your little fingertip held at arm’s length. The back of your fist, across the top of the four finger knuckles is about ten degrees when held at arm’s length. This is a quick and approximate way that can be improved by actually checking with some known stars. I find my little finger is a bit fat, about 1.5°, and my fist about 9° across the knuckles.

The sky rotates about 15° each hour, adding up to 360° each 24 hours. Objects near the eastern and western horizons will move (very roughly depending on your latitude) this far. Thus a star rising in the east will be 15° above the horizon in an hour, 30° in two hours.

Author: Andrew

An electrical engineer, amateur astronomer, and diver, living and working on Mauna Kea, Hawai'i.

3 thoughts on “Degrees, Arc-Minutes and Arc-Seconds”

  1. Hi Andrew, thanks again as always. Assuming zenith is 90 degrees, what is 0 and what is 180? Is East always 0 degrees? Also, does the same thing translate to North-South? You seem to be using the terms to describe apparent size more than as an indication of position, is that mostly how it is used?

    Aloha!

    1. Angular measurement can be used several ways… To describe position in the sky, to describe apparent size, and to describe separation. It is the apparent size and separation that appear so often in the event descriptions here on Darker View, thus I concentrated on those uses for this article. I do try to keep it simple on the blog, for a general audience. That simplification sometimes skips over important details.

      You need two numbers for azimuth and elevation, the system you are trying to figure out. Elevation is the distance above the horizon, assuming a perfectly flat horizon in all directions. So elevation uses 0=horizon and 90=zenith. Azimuth is always measured from north, to east, to south, to west and back to north. Thus 0=north, 90=east, 180=south, and 270=west. Use the two numbers together, azimuth and elevation, and you can plot anything in the local sky. And then there is Right Ascension and Declination. I expect there will be another article sometime on astrometric coordinates.

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