Why the Moon has phases
The short answer
The Sun always lights exactly half of the Moon. As the Moon circles Earth, we see that lit half from a changing angle, so it looks new, crescent, half, gibbous and full. Earth's shadow points away from the Sun and reaches the Moon only at a full Moon, in an eclipse. One lap round Earth takes 27.3 days, but Earth moves round the Sun meanwhile, so a full cycle from new Moon to new Moon takes 29.5 days.
Chapters and transcript
- 0:00
The Moon seems to change shape. It never does.
Night after night the Moon looks like a different shape, yet the Moon itself never changes.
- 0:12
Seen from above: the Sun lights exactly half of it.
Seen from above Earth, sunlight always lights the half of the Moon that faces the Sun; the other half is in night.
- 0:19
As it circles us, we see that half from a new angle.
As the Moon circles Earth, we see its lit half from a changing angle. The view from Earth on screen is drawn from that angle.
- 0:30
New, crescent, half, full, and back.
The share of the face we see lit is (1 − cos φ) ÷ 2, where φ is the Moon's angle from the Sun as seen from Earth: none at new Moon, half at the quarters, all of it at full Moon.
- 0:40
One cycle: 29.5 days.
From new Moon to new Moon takes 29.53 days (NASA Moon Fact Sheet).
- 0:55
It is not Earth's shadow.
The phases are not Earth's shadow falling on the Moon.
- 1:00
The shadow points away from the Sun, far from any crescent.
Earth's shadow points away from the Sun, but a crescent Moon is on the Sun's side of Earth, nowhere near it.
- 1:06
It reaches the Moon only at full Moon: an eclipse.
Only when the Moon is full, on the far side of Earth from the Sun, can it pass through Earth's shadow. That is a lunar eclipse.
- 1:12
Its orbit is tilted 5°, so it can pass above or below.
The Moon's orbit is tilted 5.145° to Earth's, so at its distance of 384,400 km it can be up to about 34,500 km above or below the line from the Sun. Earth's shadow there is about 9,200 km wide, computed from the radii of Earth and the Sun.
- 1:18
One lap round Earth takes 27.3 days.
Measured against the stars, the Moon goes once round Earth in 27.3217 days.
- 1:25
But Earth has moved round the Sun.
In that time Earth has moved part of the way round the Sun, so the Sun is in a different direction.
- 1:32
Catching up takes 2.2 more days: 29.5 in all.
The Moon needs about 2.2 more days to line up with the Sun again: 1 ÷ (1/27.3217 − 1/365.256) = 29.53 days, using NASA's figures for the Moon's lap and Earth's year.
- 1:40
The Moon is always half lit. Only our view of it changes.
The Moon is always half lit by the Sun. What changes is the angle we see it from.
Sources
Every figure in the film comes from these. The animation is illustrative.