Half a disk. A quarter of a cycle.
Choose first quarter. The Sun and Moon are 90° apart in the sky, and half the disk is sunlit. Look at the overhead view: is Earth blocking any of that sunlight?
FIELD NOTE 12 / MOON PHASES
Same Moon. Changing light.
Follow a crescent back to the geometry that makes it.
NewFirst quarterFullLast quarterNew
THE VIEW RIGHT NOW
Waxing crescent
A growing sliver of the sunlit half faces Earth.
- Disk lit by the Sun
- 14.6 %
- Age since new Moon
- 3.69 days
- Sun–Moon separation
- 45.0°
WHEN WOULD YOU LOOK UP?
A phase has a place in the day.
Ideal equatorial sky · local solar time
- Rises around
- 09:00
- Highest around
- 15:00
- Sets around
- 21:00
Moon altitudeSun altitude
00:00 · midnight24:00 · midnight
Move the time control to compare the Moon and Sun.
This daily view holds the selected phase fixed, with both bodies on the celestial equator. It explains the timing pattern; it is not a local rise/set forecast. Seasons, latitude and the Moon’s actual orbit change the times. Being above the horizon does not guarantee visibility, especially near the Sun.
Compare all eight phase landmarks
| Phase | Model age | Rise | Highest | Set |
|---|---|---|---|---|
| New Moon | 0.00 d | 06:00 | 12:00 | 18:00 |
| Waxing crescent | 3.69 d | 09:00 | 15:00 | 21:00 |
| First quarter | 7.38 d | 12:00 | 18:00 | 00:00 |
| Waxing gibbous | 11.07 d | 15:00 | 21:00 | 03:00 |
| Full Moon | 14.77 d | 18:00 | 00:00 | 06:00 |
| Waning gibbous | 18.46 d | 21:00 | 03:00 | 09:00 |
| Last quarter | 22.15 d | 00:00 | 06:00 | 12:00 |
| Waning crescent | 25.84 d | 03:00 | 09:00 | 15:00 |
The phase cycle is playing. Move the Moon or change a setting as it runs.
Make a prediction. Change one thing. See what happens.
Model notes & references ↗FOLLOW THE SCIENCE
One illuminated world.
Many ways to see it.
Moonlight is reflected sunlight. Away from eclipses, the Sun lights roughly half the lunar globe at a time. As the Moon orbits Earth, our line of sight meets that illuminated half at a changing angle. That is the origin of the phases. NASA: reflected sunlight and the lunar day ↗
In the overhead diagram, the bright half always faces the incoming sunlight. In the Earth view, only the part facing us is visible. The same geometry produces a sliver, a half disk, or an almost complete circle.
A FEW QUESTIONS TO TRY
Move something. Look again.
Find the rest of the Moon.
Choose a thin crescent, then switch Earthshine off and on. The dark portion never disappears; it receives very little light from our direction.
A familiar face needs a turn.
Compare tidal locking with no spin, then move through the month. Does changing the rotation change the phase, the visible terrain, or both?
The names describe a continuous change.
Waxing means the sunlit fraction is growing; waning means it is shrinking. A crescent shows less than half the disk lit; a gibbous Moon shows more than half. First and last quarter refer to progress through the phase cycle—not to a quarter of the visible disk being bright. U.S. Naval Observatory: phases and illuminated fraction ↗
The terminator is the Moon’s day–night boundary. On the sphere it is approximately a great circle. In projection, it appears as part of an ellipse, becoming a straight line at quarter phase. Surface relief near that low-Sun boundary creates long shadows; this simple renderer shows the large-scale geometry rather than individual crater shadows.
f = ½(1 − cos θ) = ½(1 + cos α)
θ measures progress from new Moon around the cycle. α is the Sun–Moon–Earth angle at the Moon. With the Sun treated as very distant, α = 180° − ψ, where ψ is the Sun–Moon angular separation seen from Earth. Try ψ = 0°, 90° and 180°: the sunlit disk fraction becomes 0, ½ and 1. The fraction describes area, not reflected power or how bright the Moon looks.
TWO CLOCKS IN ONE MONTH
An orbit ends before the phases repeat.
The Moon completes a circuit relative to distant stars in about 27.32 days: the sidereal month. Meanwhile, Earth moves along its orbit around the Sun. The Moon must travel a little farther to recover the same Sun–Earth–Moon geometry, taking about 29.53 days: the synodic month. NASA: the Moon’s motion ↗
These buttons move every view to the selected model day and keep your Play/Pause setting.
1 / Psynodic = 1 / Psidereal − 1 / Pyear
- Model time from reference new Moon
- 3.69 d
- Moon’s angle travelled among stars
- 48.6°
- Earth’s angle travelled around Sun
- 3.6°
Compare the two directions as the month unfolds.
The same face is not a permanently dark face.
TIDAL LOCKING
One spin per orbit.
The Moon rotates once relative to the stars during each sidereal orbit. That synchronized rotation keeps nearly the same face toward Earth. Use the blue surface marker to follow it. With the no-spin comparison, the marker keeps a fixed direction among the stars and different terrain turns into our view. The illumination fraction is unchanged.
NEAR SIDE · FAR SIDE
Both have day and night.
“Far side” means the side normally turned away from Earth. It receives sunlight too. Near new Moon, much of the far side is in daylight while the near side is in lunar night. Real libration lets us glimpse beyond the average near-side boundary over time; the model omits that gentle rocking. NASA: tidal locking ↗
Why can you sometimes see the dark part?
Light can take a second route: Sun → Earth → Moon → your eyes. Earth reflects enough sunlight to faintly illuminate the lunar night side. This Earthshine is easiest to notice beside a thin crescent, when Earth appears nearly full from the Moon. Toggle it to separate direct sunlight from this softer contribution. NASA: Earthshine ↗
Turn the Earth view upside down as well. Left and right swap, but the illuminated fraction and waxing/waning state do not. Northern and southern observers often describe opposite apparent orientations; the exact tilt against a local horizon also changes during the night. North up and south up here are reference orientations, not latitude-specific predictions.
The Moon belongs to the daytime sky too.
The daily plot follows directly from the phase geometry. Near new Moon, the Moon is close to the Sun’s direction and shares its daytime schedule, though solar glare hides it. Around first quarter it is highest in the evening; around full Moon it is opposite the Sun and highest near midnight. Last quarter is highest in the morning. These are broad patterns, not fixed clock times.
Earth must rotate a little extra to bring the eastward-moving Moon back to the meridian. In this mean-motion model, successive lunar transits are about 24 h 50 min apart. Real day-to-day moonrise shifts vary with the Moon’s path, your latitude and the horizon. The sky plot isolates the basic geometry by holding phase fixed during each displayed solar day.
A phase is not an eclipse.
| Ordinary phase | Lunar eclipse |
|---|---|
| We see different portions of the Moon’s own day side and night side. | Earth blocks sunlight that would otherwise reach the Moon. |
| The phase cycle repeats throughout the year. | An eclipse needs a full Moon near an orbital node. |
The lunar orbit is tilted by about 5.1° relative to Earth’s orbital plane. At most new and full Moons, the three bodies miss the alignment needed for an eclipse. The overhead diagram flattens that third dimension and deliberately leaves out eclipse shadows. NASA: the Moon’s tilted orbit and eclipses ↗
Explore the shadows in Eclipse Lab ↗The mathematics, assumptions & references
One consistent geometric model
The Moon and Earth follow uniform circular, coplanar mean motions. Psidereal = 27.321661 d and Pyear = 365.256363 d give Psynodic = 29.530588 d. Time zero is an arbitrary reference new Moon, not a calendar epoch. The main diagram keeps the Sun on the left: its axes turn with the Earth–Sun direction. The month comparison instead keeps a fixed stellar direction.
θ(t) = 2πt(1/Psidereal − 1/Pyear)
r̂Moon = (−cos θ, −sin θ)
ŝEarth view = (sin θ, 0, −cos θ)
r̂Moon = (−cos θ, −sin θ)
ŝEarth view = (sin θ, 0, −cos θ)
In the disk view, the coordinates are right, north and toward Earth. A visible surface point has outward normal n̂ = (x, y, √(1 − x² − y²)). It receives direct sunlight when n̂·ŝ > 0. This gives the projected fraction f = (1 − cos θ)/2. The Sun is treated as infinitely distant, and the observer is at Earth’s centre. Finite-distance corrections, parallax, orbital eccentricity, inclination, obliquity, precession and libration are omitted.
The lunar map is sampled on a sphere. Tidal locking holds the central longitude fixed; no spin advances the sampled longitude by 2πt/Psidereal. North/south up rotates the entire disk by 180°, rather than reflecting it. Direct illumination uses a simple cosine response with display gamma. Earthshine adds a small, enhanced term proportional to (1 − f) and the Earth-facing surface normal. This is illustrative shading, not calibrated lunar photometry, albedo, terrain relief or an observing exposure. The image separates illumination from sky glare, so even a dim new-Moon disk can be shown.
The ideal daily sky
Transit hour = 12 + 24θ/(2π) (mod 24)
Rise ≈ transit − 6 h · Set ≈ transit + 6 h
h = asin(cos H) · H = 2π(hour − transit)/24
Rise ≈ transit − 6 h · Set ≈ transit + 6 h
h = asin(cos H) · H = 2π(hour − transit)/24
These sky relations assume an observer on the equator, zero Sun and Moon declination, a flat horizon and no refraction. The phase is held fixed across that one-day chart. Local solar noon is 12:00; time zones and daylight saving are not used. A moving Moon’s mean transit-to-transit interval is 1/(1 − 1/Psynodic) solar days, which gives the approximate 50-minute daily delay. Neither the daily chart nor the table predicts rise/set times for a city.
Every view shares the same model state. Moving the phase or choosing a landmark changes the model time deliberately. Orientation, rotation, Earthshine and local-time controls preserve it. Play resumes without resetting; the orbit and phase cycle keep repeating. The 0–29.53-day slider selects a moment in the reference phase cycle, while the month comparison reports total model days. Reduced-motion preferences start playback paused, and hiding the page freezes it. No audio is synthesized in this lab.