Why does the Moon have phases?

Half lit, always

The Moon makes no light of its own. It shines because sunlight falls on it, and sunlight can only reach the half that faces the Sun. So at every moment, exactly half of the Moon is lit and half is in night. The line between the two, where the Sun is rising or setting on the Moon’s surface, is called the terminator.

The Moon goes round Earth once a month. From Earth we always see the half of the Moon that faces us. The phase is simply how much of the lit half falls inside the half facing us. When the Moon is roughly between us and the Sun, the lit half faces away and we see almost nothing: a new moon. When the Moon is on the far side of Earth from the Sun, the lit half faces us squarely: a full moon. Everything else is in between.

A few names make this precise. The elongation is the angle between the Sun and the Moon as seen from Earth: 0° at new moon, 90° at the quarters, 180° at full. The illuminated fraction is the share of the Moon’s visible disc that is lit. For sunlight arriving in parallel lines (the Sun is about 390 times farther away than the Moon, so that is a good approximation), it is

illuminated fraction = (1 − cos E) / 2

where E is the elongation. At 90° the cosine is zero and half the disc is lit. Astronomers also use the phase angle, the angle Sun–Moon–Earth measured at the Moon; it is close to 180° minus the elongation.

While the lit part is growing (from new to full) the Moon is waxing; while it shrinks it is waning. Less than half lit is a crescent; more than half is gibbous, from the Latin for “humped”. The “quarters” are named for the Moon being a quarter and three quarters of the way round its orbit, not for how much of it is lit: a quarter moon is half lit. One full cycle of phases takes 29.53 days on average: the synodic month.

The shadow test

If Earth’s shadow made the phases, where would that shadow have to be? A shadow always points directly away from the light. Earth’s shadow is a long, slowly narrowing cone stretching about 1.4 million km behind Earth, on the side opposite the Sun. By the Moon’s distance, 384,400 km away, its dark core (the umbra) is still about 9,400 km across (that is 1.4° of sky, counting the 2% the atmosphere adds; the plain geometry gives 9,200 km), a little over two and a half times the Moon’s width of 3,475 km. Around it is a fainter fringe, the penumbra, where only part of the Sun is hidden.

So the shadow can only reach the Moon when the Moon is on the far side of Earth from the Sun, which is exactly when it is full. A crescent moon is on the same side as the Sun, where there is no shadow of Earth at all.

Two things give the shadow away. First, it only ever arrives near full moon. Second, its edge has the wrong shape. The inner edge of a crescent or gibbous moon is the terminator seen at a slant, so it is half an ellipse that always runs from the Moon’s north point to its south point. The edge of Earth’s shadow is part of a circle more than twice the Moon’s size, and it can cut across the disc at any angle. When the shadow does reach the Moon, the result is not a phase but a lunar eclipse: in the umbra, the Moon turns a dim copper colour, lit only by sunlight bent through Earth’s atmosphere.

The Moon moves across the sky relative to the Sun by about 0.5° an hour, its own width, so crossing the shadow takes a few hours. In Figure 2 the shadow swallows the Moon at every full moon. In reality most full moons pass it by.

Why not an eclipse every month?

Because the Moon’s orbit is tilted. It is inclined 5.1° to the ecliptic, the plane of Earth’s orbit round the Sun (and so the path the Sun seems to follow across the sky). Five degrees sounds small, but at the Moon’s distance it lets the Moon pass up to 34,000 km north or south of the line from the Sun through Earth. The umbra is only about 9,400 km wide, so at most full moons the Moon slips above or below it. Solar eclipses have the same problem in reverse: at most new moons the Moon’s shadow passes above or below Earth.

The Moon’s tilted orbit crosses the ecliptic at two points called nodes. An eclipse needs a new or full moon to happen close to a node. The line through the two nodes keeps pointing in almost the same direction in space as Earth carries it round the Sun. Twice a year, about 173 days apart, that line points at the Sun. For a few weeks around each of those times, called an eclipse season, every new moon and full moon falls near a node, and eclipses happen.

For 2026 this simple model finds the same four eclipses that NASA lists: an annular solar eclipse on 17 February (the Moon too far from Earth to cover the Sun completely, leaving a ring), a total lunar eclipse on 3 March, a total solar eclipse on 12 August across Greenland, Iceland and Spain, and a partial lunar eclipse on 28 August. They come in pairs, a fortnight apart, one pair per eclipse season.

The nodes are not quite fixed. The Sun’s pull swings them slowly backwards round the orbit, once every 18.6 years. So the Sun comes back to the same node every 346.6 days, the eclipse year, which is about 19 days shorter than a calendar year. Each year’s eclipse seasons come about 19 days earlier than the last. Change the year in Figure 3 to watch them drift.

The same face

One more thing about the Moon never seems to change: its face. The dark patches that make the “man in the Moon” are always in the same places. That is not because the Moon doesn’t spin. It spins exactly once for every trip round Earth, so the same side keeps facing us. This is called synchronous rotation, or tidal locking. Earth’s gravity stretches the Moon slightly along the Earth–Moon line, and over billions of years the friction of that stretching slowed the Moon’s spin until it matched its orbit.

Figure 4 counts time in the sidereal month, 27.32 days: one orbit measured against the distant stars, which is also one spin of the Moon. The phases repeat every 29.53 days instead. The difference comes from Earth’s own motion. During one sidereal month Earth travels about 27° round the Sun, so the Moon must go a little more than one full orbit to get back to the same angle from the Sun. In numbers: 1/29.53 = 1/27.32 − 1/365.26, per day. The same 29.53 days is the length of a day on the Moon, from one sunrise to the next.

That also settles the “dark side of the Moon”. The far side gets just as much sunlight as the near side. At new moon, when we see nothing, the far side is fully lit.