Moon phases

Why phases happen

Goal: build the geometry physically, with objects you already own, before touching any equations.

Time: 20 minutes, in a dark-ish room.

Observe

You need:

• A lamp with the shade off, or a torch: this is the Sun
• A ball, an orange, a tennis ball, anything round: this is the Moon
• Your head: this is Earth

Put the lamp on one side of the room. Stand a few metres away, holding the ball at arm's length.

Predict

Before you move anything, answer:

1. How much of the ball is lit by the lamp at any moment?
2. When the ball is between you and the lamp, what do you see?
3. When the ball is on the far side of you from the lamp, what do you see?

Write them down.

Run

Hold the ball at arm's length and slowly turn on the spot, keeping the ball out at the same distance, so it circles you.

Ball between you and the lamp. The lit side faces away. You see a dark disc. New Moon.

Turn 90°. The lamp is now off to one side. You see exactly half the ball lit, split down the middle. First quarter.

Turn until the ball is opposite the lamp, over your shoulder, out of your own shadow. Fully lit. Full Moon.

Turn another 90°. Half again, lit on the other side. Last quarter.

Keep going and you are back to new.

Learn

The one thing to hold on to

Half the ball is lit the entire time. You never changed that. The lamp never moved, and it always illuminated exactly one hemisphere.

What changed is how much of the lit half you could see.

This is the whole of lunar phases. There is nothing else in it. The phase is not a property of the Moon; it is a property of the angle between you, the Moon, and the Sun.

That angle has a name, elongation, and it is the quantity every phase calculation actually computes.

The eight phases

Waxing = growing, waning = shrinking. Gibbous is from the Latin for humped.

"Quarter" means a quarter of the way through the cycle, not a quarter lit. A first quarter Moon looks half lit. This confuses everyone once.

Why phase controls when you see it

The elongation also fixes when the Moon is up, and this falls straight out of the geometry:

A full Moon is opposite the Sun, so it must rise as the Sun sets. It cannot do anything else. If someone shows you a photo of a full Moon high in a blue midday sky, it is a composite.

This table is worth internalising. It turns "what phase is it?" into "when should I go outside?"

Why not an eclipse every month?

The obvious objection: if the Moon passes between Earth and Sun every new Moon, why is there not a solar eclipse every month?

Because the Moon's orbit is tilted about 5.1° to Earth's orbital plane. Most new Moons, the Moon passes above or below the Sun rather than across it. Only when new Moon happens near one of the two nodes (the points where the orbits cross) do you get an eclipse.

That tilt is why moon.position() returns an ecliptic latitude as well as a longitude. Check it: it swings between about ±5.1°.

Change one variable

Back to the lamp. Now tilt the ball's circular path slightly, so it passes above the lamp on one side and below on the other.

Notice that the "new Moon" position no longer blocks the lamp; the ball goes above it. That is why most new Moons are not eclipses. Adjust the tilt until it does line up, and you have found a node.

Validate

moonfield phase
moonfield now

Check the phase against the rise/set table above. If it says waxing gibbous, the Moon should rise in the afternoon and set after midnight. Does moonfield now agree?

Then check your own log from Go and look.

Explain

Here is a question worth sitting with: why is a half Moon exactly half, and not more or less?

Because at first quarter the Sun-Earth-Moon angle is 90°. You are looking at the terminator edge-on, straight down the boundary between lit and unlit. Any other angle and you see some of the lit side curving toward or away from you.

And that is why the terminator on a crescent is curved while on a half Moon it is straight. It is the same circle (the edge of the lit hemisphere) seen at different angles. A circle seen at an angle is an ellipse; seen edge-on, a straight line.

phase.ascii_moon() draws exactly this, and the code says so.

Checkpoint

• I can demonstrate the phases with a ball and a lamp
• I can explain that half the Moon is always lit
• I know what elongation is
• I can name all eight phases and say roughly how lit each is
• I can say when a full Moon rises, without looking it up
• I can explain why there is not an eclipse every month
• I can explain why a half Moon has a straight terminator

Try it yourself

1. Do the lamp experiment. Actually do it; it is much better than reading it.
2. Predict tonight's moonrise time from the phase alone, then check
3. From a photo of a crescent, work out which way the Sun is
4. Explain the phases to someone else using only your hands
5. Track moon.position().ecliptic_latitude over a month and find the nodes

Questions to think about

• What would phases look like from a planet with two moons?
• What phase is Earth in, seen from the Moon, when we see a full Moon here?
• If the Moon's orbit were not tilted, how often would eclipses happen?
• Why do we always see the same face of the Moon? (Different question,

different cause: tidal locking, module 03.)

Common questions

Is the dark part Earth's shadow? No, and this is the most common misconception in all of lunar astronomy. Earth's shadow only touches the Moon during a lunar eclipse, which is rare. The dark part of a normal Moon is simply the half not facing the Sun.

Why can I sometimes faintly see the dark part? Earthshine, sunlight reflected off Earth onto the Moon. Best on a thin crescent.

Go deeper

• Calculating a phase
• Module 03, The Earth-Moon system

Next: Calculating a phase.