Why the Moon has phases

From one new Moon to the next takes 29.53 days, about two days longer than one trip round Earth.

Half lit, always

The Sun is the only star in the solar system and its main source of visible light. The Moon is a dark rock that reflects sunlight, and at any moment the Sun lights exactly one half of it, the half that faces the Sun. What changes during the month is how much of that lit half is turned towards us. When the Moon sits roughly between Earth and the Sun, its lit side faces away and we see the dark side: that is the new Moon. When the Moon is on the far side of Earth from the Sun, we look straight at the lit half: that is the full Moon.

In between, we see part of the lit half. A useful number is the angle between the Sun and the Moon as seen from Earth, called the elongation. The fraction of the Moon's disk that looks lit is (1 − cos E) ÷ 2, where E is that angle. At 0° the formula gives 0, a new Moon. At 90° it gives exactly one half: the first quarter. At 180° it gives 1, a full Moon. The model's readout uses this formula, so you can check it at any day you choose.

The names of the eight phases follow this order: new Moon, waxing crescent, first quarter, waxing gibbous, full Moon, waning gibbous, last quarter (also called third quarter), and waning crescent. "Waxing" means growing and "waning" means shrinking. NASA points out a small trap in the word quarter. A first-quarter Moon looks like a half circle, but we are seeing half of the lit half, which is a quarter of the whole Moon. The phase is named after the point in the cycle, a quarter of the way through.

Why 29.53 days and not 27.32

The Moon goes once round Earth, measured against the stars, in 27.32 days. But a phase depends on where the Moon is compared with the Sun, and the Sun is not standing still in our sky. While the Moon makes its circuit, Earth moves about 27° along its own orbit, so the Moon needs a little over two more days to get back to the same angle from the Sun. The two periods are linked by a simple rule: 1 ÷ 27.3217 − 1 ÷ 365.256 = 1 ÷ 29.53. NASA lists the synodic month, from new Moon to new Moon, as 29.53 days.

The same lag makes the Moon rise later each day. It moves about 12° east against the Sun every day, so on average it rises about 50 minutes later than the day before (24 hours ÷ 29.53 ≈ 49 minutes). That gives each phase its own hours. A full Moon rises around sunset and sets around sunrise, which is why it is up all night. A first-quarter Moon rises around midday and sets around midnight. A new Moon rises and sets with the Sun, which is why we cannot see it.

Where you stand on Earth flips the picture. From the Northern Hemisphere a waxing Moon is lit on the right and a waning Moon on the left. From Australia or South Africa the same Moon appears upside down, lit on the left as it grows. Try the Southern view button. One more detail is worth looking for on a clear evening: the dark part of a crescent Moon often glows faintly. That is earthshine, sunlight bounced off Earth onto the Moon and back to your eyes.