The Moon seems to change shape. It never does.

Seen from above: the Sun lights exactly half of it.

As it circles us, we see that half from a new angle.

New, crescent, half, full, and back.

One cycle: 29.5 days.

It is not Earth's shadow.

The shadow points away from the Sun, far from any crescent.

It reaches the Moon only at full Moon: an eclipse.

Its orbit is tilted 5°, so it can pass above or below.

One lap round Earth takes 27.3 days.

But Earth has moved round the Sun.

Catching up takes 2.2 more days: 29.5 in all.

The Moon is always half lit. Only our view of it changes.