The sky has no ruler in it, so astronomers measure it in angles — and the measuring stick everybody already owns is their own arm.
You cannot say two stars are "ten centimetres apart", because they are not on a wall — one may be a hundred times further than the other. All you can honestly say is how far apart they look, and that is an angle.
All the way round the horizon is 360°. From the horizon straight up to overhead is 90°. So if something is "30° up", it is a third of the way from the horizon to the top of the sky.
Stretch your arm out as far as it goes and look at your hand. Big people have big hands and long arms; small people have small hands and short arms. The two cancel out, so these measurements work for almost everybody — which is why astronomers have used them for thousands of years.
Always with your arm straight out. Bend your elbow and every number here is wrong.
You do not have to trust the table — the sky will tell you whether your own hand matches it.
The Plough (Big Dipper). The two stars at the end of the "bowl", the ones that point at the Pole Star, sit 5° apart. Hold up three fingers. They should just cover the gap.
The whole Plough, from the tip of the handle to the far edge of the bowl, is about 25° — a little more than one spread hand.
Here is the thing most people get wrong. Hold up your little finger at arm's length and put it over the full Moon. The finger wins. The Moon is only about half a degree across — half the width of your smallest fingernail. It looks enormous, and it is not. Every photograph you have seen of a giant Moon behind a building was taken with a long lens.
| What you hold up | Roughly | Something that size |
|---|---|---|
| Little finger, tip only | 1° | two full Moons side by side |
| Three fingers together | 5° | the Plough's two pointer stars |
| Closed fist | 10° | the bowl of the Plough |
| Hand spread wide | 20° | Orion, belt to shoulder and back again |
| Horizon to overhead | 90° | nine fists stacked up |
This is exactly how the Planetarium gives directions. When Perl says "start at Mirach, sweep about 1 fist toward the east and 8 degrees higher", that means: find the bright star, hold up your fist next to it, and look where the far side of your fist lands. Then look a little above that.
Two fists up from the horizon is 20°. Half a fist is a finger's width times five. Once the numbers are in your hand — literally — the sky stops being a jumble and starts being a place you can give directions in.
You do not need the dark to practise. Pick two things across the street — a chimney and a lamp post — and measure the gap in fists and fingers. Then walk somewhere else and measure again. The angle changes, because angles depend on where you stand. That is the whole idea behind measuring the Earth and measuring the stars.