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Why the edge of a half Moon is straight Three Moons in a row, each drawn as a full circle with its lit part pale and its dark part shaded. Above each Moon is the same hoop seen from a different angle: first a wide oval, then a narrow oval, then edge on, where the hoop is just a straight line. The dividing edge on each Moon has the same shape as the hoop above it, so by the third one that edge is ruler straight.

Why a Half Moon Has a Straight Edge

About 14 minutes

You already know the Moon never really changes shape, and that what changes is how much of its sunlit half is turned toward us. That leaves a harder question, and it is the one this article is about.

The Moon is a ball. A ball has no straight edges anywhere on it. So why does a half Moon have one — a clean, ruler-straight line down the middle?

The line you are actually looking at

The Moon has a day side and a night side, and there is a boundary between them. Astronomers call that boundary the terminator. It is the line where the Sun is just coming up, or just going down, on the Moon's surface.

Here is the important part. That boundary is a circle. It runs right the way around the ball, like the seam on a tennis ball, and it is always the same size — a circle as wide as the Moon itself. It never gets bigger, never gets smaller, and never becomes a straight line.

So the straight edge you see is not really straight. It is a circle you are looking at from an unusual angle.

A circle can look like a straight line

Find a coin, a jar lid, or anything else round and flat. Hold it up at arm's length and try this.

  1. Hold it face-on, so you are looking straight at the flat side. It looks like a circle, which is what it is.
  2. Tilt it slowly away from you. The circle squashes. It becomes an oval — the shape mathematicians call an ellipse. It is still a circle. You are just no longer square-on to it.
  3. Keep tilting until it is exactly edge-on. Now it is a straight line. A perfectly flat, straight line, from an object with no straight edges on it anywhere.
  4. Tilt a little further and it opens back out into an ellipse, leaning the other way this time.

That is the whole trick, and the Moon does nothing more clever than your jar lid.

Why the same circle looks like an ellipse, then a straight line, then an ellipse again Three drawings of the Moon side by side, lit from the right each time. The line between the lit part and the dark part is one circle drawn right around the ball. In the first drawing we see that circle at a slant and it looks like a narrow ellipse, leaving a thin crescent. In the second we see the circle edge-on and it looks like a perfectly straight line, so the Moon looks like a half disc. In the third we see the circle slanted the other way and it bulges past the middle, leaving a fat gibbous shape. A dotted curve in each shows where the rest of the same circle runs around the far side of the ball. crescent circle at a slant = a narrow ellipse half circle edge-on = a straight line gibbous slanted the other way = a wide ellipse One circle, three viewing angles. The lit side is on the right in all three. The dotted curve is the same circle carrying on around the back of the ball.
The same circle three times over. Seen at a slant it is an ellipse and you get a crescent or a gibbous Moon; seen exactly edge-on it is a straight line and you get a half Moon.

Now the shape names from the phases stop being eight things to remember and become one thing:

What is really moving

If the lit half never changes and the terminator circle never changes, then something else must be doing the work. It is our viewing angle, and that changes because the Moon is going around us.

Drag the slider to walk the Moon through one month. You are looking down on the whole system from above, with the Sun far away to the left. Watch what the pale half of the Moon does.

The Moon's orbit seen from above, with the lit half always facing the Sun Looking down on the Earth and Moon from above the North Pole. The Sun is off to the left and its light arrives as parallel rays. Earth sits in the middle of a circular orbit and the Moon travels round it counterclockwise. The half of the Moon facing the Sun is always the lit one, and it stays pointing left however far round the orbit the Moon has gone. A dashed line from Earth to the Moon shows the direction we are looking from. Sun far off to the left Earth new first quarter full third quarter Looking down from above the North Pole. The Moon travels counterclockwise.

Move the handle through the month and watch the lit half of the Moon.

The lit half never turns. It cannot: it is simply whichever half happens to be facing the Sun, and the Sun stays where it is. The Moon moves, the dashed sight-line from Earth swings around, and our angle on that fixed lit half changes every night. That is the entire mechanism.

One trip around takes about 29.5 days, and that is why the phases take about a month.

Reading it backwards

Because the shape depends only on the angle, you can run the logic in reverse. The Moon tells you where it is standing.

The terminator — the day-night line on the Moon — is a circle right around the ball. Why does it look perfectly straight at half Moon?

Next time you see a half Moon, look at that straight edge and remember what it is not. It is not a straight thing. It is a circle as wide as the Moon, running all the way around the back where you cannot see it, caught for one night exactly side-on.