Reading the Moon: one angle explains everything

In Discover you met the idea: half the Moon is always lit, and the phase is how much of that lit half faces us.

That is the right picture, but it is not yet a tool. With it alone you cannot say what the Moon will look like on the 19th, or what time it will rise, or which craters will show up best in binoculars.

This layer turns the picture into a tool. It comes down to a single number — the angle between the Sun and the Moon as seen from Earth — and once you can read that angle, everything else follows: the shape, the name, the fraction lit, the rise time, the set time, and even which way up it looks.

Stand on Earth. Point one arm at the Sun. Point the other arm at the Moon. The angle between your arms is called the elongation of the Moon.

That single angle decides the phase completely.

• Elongation 0 degrees: Sun and Moon in the same direction. Its lit half points away from you. New moon.
• Elongation 90 degrees: a right angle. You are looking at the lit half exactly side-on, so you see half of it. Quarter moon.
• Elongation 180 degrees: Sun and Moon in opposite directions, Earth in the middle. The lit half is aimed straight at you. Full moon.

Between those, the phase changes smoothly. Elongation does not jump; it grows steadily, day after day, from 0 all the way round to 360 — and 360 is the same as 0, so the cycle begins again.

Here is the whole month in one table. Every number in it was calculated from the elongation, not looked up.

Read it across: the phase, where the Moon is in its orbit as an angle, how many days into the month that is, and how much of the disc is bright.

Elongation tells you the shape. It also tells you where the Moon is in the sky, because elongation is literally the angle between the Sun and the Moon.

The sky turns 360° in 24 hours, which is 15° every hour. So if the Moon is 15° east of the Sun, it crosses the sky exactly one hour behind the Sun. If it is 90° east, it is four hours behind. If it is 180° away, it is twelve hours behind — which is why a full moon rises as the Sun sets.

That gives a rule you can do in your head:

Hours behind the Sun = elongation ÷ 15.

A waxing crescent at 45° elongation is 3 hours behind the Sun: it rises about 3 hours after sunrise, is highest about 3 hours after noon, and sets about 3 hours after sunset. That is exactly why a young crescent is an early-evening object that disappears before your bedtime.

In Discover you learned that from India a waxing Moon is bright on the right. Here is why — and why it is not true everywhere.

The Moon is always lit from the side the Sun is on. In the northern hemisphere, when you face the Moon in the evening, the Sun has just set to your right-hand side (to the west), so the bright edge faces right. Later in the month, when the Moon trails the Sun by more than half a day, you see it in the morning with the Sun rising on your left, and the bright edge faces left.

Three consequences, all worth knowing:

1. In the southern hemisphere it is the other way round. In Australia, a waxing crescent is bright on the left, and the D-O-C trick becomes C-O-D. Same Moon, same phase, upside-down view.
2. Near the equator the crescent lies on its back. From Kerala or Tamil Nadu, a young crescent often looks like a smile or a boat rather than a letter D, because the Sun sets almost straight down and the lit edge ends up along the bottom.
3. The bright edge always points at the Sun. This is the single reliable rule for every place on Earth. Draw a line from the middle of the dark side through the middle of the bright side, keep going, and you are pointing at the Sun — even when the Sun is below the horizon.

The curved line dividing the bright part of the Moon from the dark part has a name: the terminator. It is the Moon's sunrise-and-sunset line.

Along the terminator, the Sun is just on the horizon as seen from the lunar ground. That means shadows there are enormously long — the same way your own shadow stretches down the whole street at sunset. Every crater rim, every mountain, every ridge throws a black streak across the surface.

Move away from the terminator towards the middle of the bright part and the Sun climbs higher in the lunar sky. Shadows shorten. At full moon the Sun is almost directly overhead across the whole visible face, and there are hardly any shadows at all.

Which leads to an unexpected rule for anyone with binoculars:

The full moon is the worst night of the month to look at the Moon.

It is dazzlingly bright and almost completely flat, like a photograph taken with the flash on. The best views are around first quarter and last quarter, when the terminator runs straight down the middle of the disc and the craters along it stand out in three dimensions.

Find a crescent Moon three or four days after new moon, on a clear evening, once the sky has properly darkened. Look at the part that should be black.

It is not black. There is a faint, ghostly grey glow filling the whole unlit disc, so that you can see the Moon's complete round outline with a bright crescent stuck on one edge. Sailors and poets called it the old Moon in the new Moon's arms.

The explanation is lovely, and it is the same idea as the whole lesson, run one step further.

You are looking at the Moon's night side. There is no sunlight there. But there is light: light from Earth. At that moment, an astronaut standing on that dark lunar ground would look up and see a huge, brilliant, nearly full Earth in the sky — four times wider than the Moon looks to us and dozens of times brighter, because Earth's clouds and oceans reflect far more sunlight than grey Moon rock.

That Earthlight falls on the lunar night side, bounces off, and comes back to your eye. It has made a round trip: Sun → Earth → Moon → you.

Look at the full moon and you will see dark patches that people all over the world have turned into pictures: a rabbit, a man's face, a woman carrying a bundle of sticks, a buffalo.

Now here is the strange part. Your grandparents saw exactly the same patches. So did everyone who has ever lived. The Moon keeps one face permanently turned towards Earth. The other half has never been visible from the ground, from anywhere, at any time in human history.

The usual guess is that the Moon does not spin. That guess is wrong, and the truth is more interesting: the Moon spins exactly once for every orbit it makes. One rotation takes 27.32 days; one orbit takes 27.32 days. The two are locked together, which is why the same side always points our way.

This is called synchronous rotation, or tidal locking, and it is not a coincidence. Earth's gravity pulls slightly harder on the near side of the Moon than on the far side, which stretches it very slightly into a non-spherical shape. Over billions of years, the friction of that stretching acted like a brake on the Moon's spin, slowing it until it settled into the one rate where the stretch stops fighting the rotation: exactly once per orbit.