Half-Lit, Always
The Moon is always half lit by the Sun; a phase is just how much of that lit half happens to face you. · 12 min
Watch the Moon for a month and it seems to change shape — a sliver, a half, a bright full disk, then back to nothing. None of that is happening on the Moon. The Sun always lights one half of it, the half facing the Sun, tonight and every night. What changes is your seat. As the Moon travels around Earth, you see that lit half from a different angle each night.
Guess before you learn
Tonight the Moon is a thin crescent. Right now, how much of the Moon's entire surface is in sunlight?
Half, always. The Sun lights whichever hemisphere faces it, and that never stops. The crescent is not how much is lit — it is how much of the lit half is turned toward you. If you guessed the sliver, you are in good company: most people do, and the whole lesson lives in that correction. Earth's shadow, for the record, only touches the Moon during a lunar eclipse — that story is folio 7's.
9–12
3–5
The Moon circles Earth about once a month, and the Sun lights whichever half of it faces the Sun. Your view of that lit half depends on where the Moon is in its circle. When the Moon sits between Earth and Sun, the lit half faces away from you: no Moon to see. When the Moon is on the far side of Earth from the Sun, the whole lit half faces you: a full Moon. Everywhere in between gives you a slice.
So the phases are not the Moon growing and shrinking. They are a half-lit ball seen from every angle in turn as it circles you — one month per lap.
6–8
A phase is the fraction of the Moon's sunlit hemisphere that faces Earth, and it is set entirely by the Sun–Moon–Earth angle. New Moon: the Moon sits sunward, lit side facing away. First quarter: a quarter-orbit later, you see half of the lit side — a half Moon. Full: the Moon stands opposite the Sun and shows you everything. Third quarter mirrors first. Waxing means the visible slice is growing night by night; waning, shrinking.
The full cycle, new to new, takes 29.5 days — the synodic month. Notice that geometry, not shadow, does all the work here: Earth's shadow touches the Moon only during eclipses, a few nights a year.
9–12
Astronomers measure the geometry with the phase angle: the Sun–Moon–Earth angle measured at the Moon. Near 180 degrees, none of the lit face points our way (new); at 0 degrees, all of it does (full). The Moon's orbit against the stars takes 27.3 days — the sidereal month — but the phase cycle takes 29.5, because Earth has meanwhile moved along its own orbit, and the Moon needs about two extra days to catch up to the Sun's new direction.
The same geometry pins each phase to the clock. A full Moon stands opposite the Sun, so it must rise as the Sun sets. First quarter trails the Sun by 90 degrees — six hours of sky — so it rises near noon and crosses highest at sunset.
K–2
Take a ball into a dark room with one lamp. The lamp lights half the ball. Walk around the ball. From one side you see all of the bright half. From the other side, none. The ball never changed.
The Moon is that ball. The Sun is the lamp. When you see a thin Moon, you are seeing just the edge of its bright half. The rest is still bright — it faces away from you.
Undergrad
The illuminated fraction seen from Earth is k = (1 + cos φ)/2, with φ the phase angle: φ = 90° gives exactly half. The terminator is a great circle on the Moon viewed obliquely, so it projects as half an ellipse — which is why a gibbous Moon's inner edge is a flattened arc, and a straight chord appears only at quarter phase.
Brightness does not follow k. The surface is rough, so reflection is strongly phase-dependent: at large φ, crater walls and boulders shadow the ground; near φ = 0 the shadows vanish from view and the regolith backscatters toward the light source. The disk-integrated light curve is therefore far steeper than the lit fraction — the subject of this folio's ink exercise.
Postgrad
The lunar phase curve is treated photometrically: disk-integrated brightness rises near zero phase far in excess of the Lambertian prediction — the opposition effect, attributed to shadow hiding (mutual obscuration vanishing at zero phase angle) plus coherent backscatter within the regolith. Hapke's bidirectional reflectance formalism parameterizes both terms and is fit to spacecraft and telescopic photometry.
The period bookkeeping generalizes: 1/S = 1/P_sid − 1/P_E relates the synodic and sidereal months through Earth's orbital period. The identical relation, with planetary periods substituted, returns in folio 9 to time oppositions and retrograde loops.
phase
The fraction of the Moon's sunlit half that faces Earth. Set by the Moon's position in its orbit — not by any shadow.
Here is the payoff most people never learn: the phase tells you the Moon's schedule. A full Moon stands opposite the Sun, so it must rise at sunset, ride highest at midnight, and set at sunrise. First quarter trails the Sun by six hours: up at noon, highest at sunset, gone by midnight. A waning crescent leads the dawn. Once you can read the phase, the Moon can never surprise you — and it can serve as a rough clock.
Now for the question this folio is named for. At first quarter you see half of a lit face; at full, all of it. So a full Moon should be about twice as bright as a quarter Moon — that is what nearly everyone expects. Before you read another word, commit a guess in pencil: sketch how the Moon's brightness changes across one whole month.
A full Moon is roughly ten times brighter than a first-quarter Moon — not twice. Two effects conspire. At quarter phase, sunlight strikes the Moon sideways, and the surface is rough: every crater wall and boulder throws a shadow, and shadowed ground sends you nothing. Near full, the Sun stands directly behind you, so each shadow hides behind the very rock that casts it — the shadows still exist, but you cannot see them. The dusty surface also reflects strongly straight back toward the light source. Both effects peak together, and the brightness spikes.
Why is this true?
Why is a full Moon about ten times brighter than a quarter Moon, when only twice the area is lit?
Because brightness depends on shadows as well as area. At quarter phase, sideways light fills your view with dark crater shadows; at full, every shadow hides directly behind whatever casts it, and the dusty surface reflects strongly back toward the Sun — with you standing in that returning beam.
From phase to rise time: a waxing gibbous Moon — the steps fade as you master them
Between first quarter (90 degrees) and full (180 degrees) — call it 135 degrees.
135 ÷ 15 = 9 hours behind the Sun.
6 a.m. + 9 hours = about 3 p.m. — climbing the eastern sky by late afternoon.
You now hold the Moon's whole month in one picture: a half-lit ball on a 29.5-day lap, the phase naming the angle, the angle fixing the schedule, and the shadows on its rough face rationing the light. Next folio we stop asking how much Moon you can see, and start asking what, exactly, you are looking at.
Practice — new ink and old, interleaved
1.Without looking back: what is a phase, and why is a full Moon far more than twice as bright as a quarter Moon?
A phase is the fraction of the Moon's sunlit half facing Earth; near full, the surface shadows vanish from view and the dust backscatters, so brightness spikes to about ten times the quarter Moon's.
How close were you? Grade yourself honestly — it sets your review date.
2.Match each phase to its rise time.
3.About how many months pass before a star that rises at midnight tonight rises at 6 p.m.?
4.In one sentence: why does the phase cycle take 29.5 days when the Moon's orbit takes only 27.3?
5.From latitude 33°N, at about what altitude does Polaris stand?
6.A friend claims the dark part of the crescent Moon is Earth's shadow. What is it really?
7.The first-quarter Moon is highest in the sky at about what clock hour? Answer with an hour from 0 to 24.
8.From a ship on the equator, which stars are circumpolar?
9.A friend reports a bright object at azimuth 270°, altitude 10°. Where is it?