Phases of the Moon.

Step 1 of 5

Always half lit

The Moon does not shine by itself: it reflects sunlight, like the Earth. In the Scene the Sun is far off to the right, and the Moon goes round the Earth once every $29.5$⁠ days, from new moon to new moon. Day of the month sets where it is on its orbit.

Turn the view round the Moon and look at it from several sides, and change Day of the month.

Step 2 of 5

First quarter

From the Earth we see only the side of the Moon facing us. How much of it is lit depends on the angle $\theta$⁠ between the Sun and the Moon as seen from the Earth, the phase angle. The lit share of the disc is

$\frac{1 - \cos\theta}{2}$⁠

At new moon $\theta = 0^\circ$⁠ and the share is $0$⁠; at full moon $\theta = 180^\circ$⁠ and it is $1$⁠. It is day $7.4$⁠ now: a quarter of the month.

Step 3 of 5

Full moon

At first quarter the Moon stands at a right angle to the line from the Earth to the Sun. At sunset it is already high in the south, and its lit half faces west, towards the setting Sun.

Step 4 of 5

Three quarters

After first quarter the Moon waxes (waxing gibbous) to full, and after that it wanes, through last quarter, back to new. The same lit share appears twice a month, once on the way up and once on the way down, and on opposite sides of the disc. It is new moon now.

Step 5 of 5

Rising later

The phase also sets when you see the Moon. At new moon it is in the Sun’s direction, rising and setting with it, lost in the daylight. At full moon it is opposite the Sun: it rises at sunset and is up all night. Each day it moves along its orbit, so the Earth has to turn a little further to “catch up” with it.