In a television show called Kids in the Hall, there was a character who would look at people far away through one eye and pretend to crush their heads between his thumb and forefinger. If you try this trick yourself, you’ll notice that people have to be at least five or so feet away for their heads to be small enough to crush. Their heads don’t actually get smaller, of course, just the angular size of the head does. In fact, you can use this same trick (if sufficiently distant) to crush cars, or planes flying overhead. All because of the fact that as things get more distant, they appear smaller— their angular size is reduced.

The surface of the earth is real and solid. You can easily use absolute units such as feet and miles to measure the distance between objects. The celestial sphere, however, is an imaginary construct, and we do not know the distances between us and the objects. In fact, simply to locate objects in the sky, we don’t need to know their distances from us.

Now, from our perspective on Earth, two stars may appear to be separated by the width of a finger held at arm’s length when they are actually many trillions of miles distant from each other. You could try to fix the measurement between two stars with a ruler, but where would you hold the measuring stick? Put the ruler close to your eye, and two stars may be a quarter-inch apart.

Put it at arm’s length, and the distance between those same two stars may have grown to several inches. Astronomers use angular size and angular separation to discuss the apparent size on the sky or apparent distance between two objects in the sky. For example, if two objects were on opposite horizons, they would be 180 degrees apart. If one were on the horizon and the other directly overhead, they would be 90 degrees apart. You get the picture.

Well, a degree is made up of even smaller increments. One degree is made up of 60 minutes (or arcminutes), and a minute is divided into 60 seconds (arcseconds). Let’s establish a quick and dirty scale. The full moon has an angular size of half a degree, or 30 arcminutes, or 1,800 arcseconds (these are all equivalent). The “smallest” celestial object the human eye can resolve is about 1 arcminute across. The largest lunar craters are about 2 arcminutes across, and separating objects that are 1–2 arcseconds apart is impossible (at least at optical wavelengths) from all but the best sites on Earth.

This difficulty is due to atmospheric turbulence and is a limitation of current ground-based optical observing. Now that you know the full moon is about half a degree across, you can use its diameter to gauge other angular sizes. To estimate angles greater than a half-degree, you can make use of your hand.

Look at the sky. Hold your hand upright at arm’s length, arm fully extended outward, the back of the hand facing you, your thumb and index finger fully and stiffly extended, your middle finger and ring finger folded in, and your pinky also fully extended. The distance from the tip of your thumb to the tip of your index finger is about 20 degrees (depending on the length of your fingers!). From the tip of your index finger to the tip of your pinky is 15 degrees; and the gap between the base of your index finger and the base of your pinky is about 10 degrees.

Celestial Portraits

Well, now that you’re standing there with your arm outstretched and your head full of angles, what can you do with this wealth of information? We now have some rough tools for measuring separations and sizes in the sky, but we still need a way to anchor our altazimuth measurements, which, remember, are relative to where we happen to be standing on Earth. We need the celestial equivalent of landmarks.

Fortunately for us, our ancestors had vivid imaginations. Human brains are natural pattern makers. We have all seen elephants and lions masquerading as clouds in the sky. Present the mind with the spectacle of 3,000 randomly placed points of light against a sable sky, and, before you know it, it will start “seeing” some pretty incredible pictures. The constellations—arbitrary formations of stars that are perceived as figures or designs—are such pictures, many of them inspired by mythological heroes, whose images (in the western world) the Greeks created by connecting the dots.

Centuries later, during the late Renaissance, more constellations were added, and a total of 88 are recognized today. We cannot say that the constellations were really discovered, because they do not exist except in the minds of those who see them.

 Grouping stars into constellations is an arbitrary act of the imagination and to present-day astronomers are a convenience. In much the same way that states are divided into counties, the night sky is divided into constellations.

 The stars thus grouped have no physical relationship to one another and, in fact, are many, many trillions of miles apart. Nor do they necessarily lie in the same plane with respect to the earth; some are much farther from us than others.

 But, remember, we simply imagine that they are embedded in the celestial sphere as a convenience. If the constellations are outmoded figments of the imagination, why bother with them?

The answer is that they are convenient (not to mention poetic) celestial landmarks. We all use landmarks to navigate on land. “Take a right at the gas station,” you might tell a friend. What’s so special about that particular gas station? Nothing—until you invest it with significance as a landmark. Nor was there anything special about a group of physically unrelated stars—until they were invested with significance. Now these constellations can help us find our way in the sky and, unless you are using a telescope equipped with an equatorial mount, are more useful than either the celestial or altazimuth coordinate system.