Half of the Moon is always lit by the Sun. But from Earth we see a different part of that bright half — and that is what phases are. Everything below is calculated for the chosen date, by default for right now.
Sunlight comes from the left. The half of the Moon facing the Sun is always lit, and the purple arc marks the half facing Earth. The dot on Earth is an observer in Poland. Distances are not to scale.
The disk as seen by an observer facing south when the Moon is high in the sky. Maria and craters are drawn in approximate positions; we ignore libration.
Keys: ← → day · Shift + ← → hour · Space play · T today (in the Phases and Eclipses tabs) · 1–6 modes
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Icons show the phase at noon. Below them are the exact times of new moon, quarters and full moon. Click a day to select it.
After 27.32 days the Moon returns to the same place relative to the stars (purple arrow). But in that time Earth has moved about 27° around the Sun, so the next new moon is still about 2.2 days away: from new moon to new moon takes 29.53 days.
Tides: two bulges of water
The Moon’s gravity weakens with distance. The ocean on the Moon’s side is pulled harder than Earth’s center, and the ocean on the far side is pulled less. This difference stretches the water into two bulges. Earth rotates beneath them, so in many places high tide comes twice a day, about every 12 h 25 min. At new and full moon, the Sun’s tides (about 46% of the Moon’s) add to the lunar ones — these are spring tides. At the quarters they partly cancel — neap tides.
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An equilibrium model, greatly simplified: real tides in harbors lag behind and depend on the shape of the seas (in the Baltic Sea they are only a few centimeters). More about gravity and orbits: Orbit.
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Why aren’t there eclipses every month?
The Moon’s orbit is tilted 5.1° to the plane of Earth’s orbit (the ecliptic) and crosses it at two points — the nodes. At most new moons the Moon passes above or below the Sun’s disk, and at full moon above or below Earth’s shadow. An eclipse is only possible when a new or full moon falls close to a node. The line of nodes points at the Sun roughly every 173.3 days — these are the eclipse seasons. The full cycle is the eclipse year: 346.62 days, shorter than an ordinary year because the nodes drift backward and circle the ecliptic in 18.6 years.
The tilt of the Moon’s orbit is drawn about 2.5 times larger than in reality, and the Moon’s orbit many times larger. The gray circles show Earth every quarter year: the line of nodes barely changes direction in space.
Upcoming eclipses
Jean Meeus’s method: for each new and full moon we check the Moon’s argument of latitude F, and then the distance of the shadow axis from Earth’s center (γ). We checked the results against a list of known eclipses from 1999–2035. We give the type and the time of greatest eclipse (local time) — not where the eclipse can be seen from. Very faint penumbral eclipses at the limit may be missed.
Solar eclipse: total, annular or hybrid?
The Sun is about 400 times larger than the Moon, but also about 390 times farther away, so in the sky they look almost the same size: the Sun about 0.53°, and the Moon from 0.49° (at apogee) to 0.56° (at perigee). The Moon’s shadow (umbra) is about 374,000 km long — almost exactly the distance to Earth. When the Moon is closer, the tip of the shadow reaches Earth and we see a total eclipse. When it is farther, a bright ring remains around its disk — an annular eclipse. When the tip of the shadow falls right at the surface, the eclipse is total in the middle of the path and annular at its ends — a hybrid.
Lunar eclipse: why does the Moon turn red?
At full moon the Moon can enter Earth’s shadow. First it dips into the penumbra — there Earth blocks only part of the Sun and the disk barely darkens (a penumbral eclipse). When it partly enters the umbra, we call it a partial eclipse, and when it is fully inside — a total one.
But the Moon doesn’t vanish completely — it turns coppery red. Earth’s atmosphere acts like a weak lens: it refracts sunlight and bends it into the shadow. On its way through the thick layer of air, blue light is scattered sideways (Rayleigh scattering — the same effect that makes the sky blue), so mostly red light reaches the Moon. At that moment the Moon is lit by all of Earth’s sunrises and sunsets at once.
Danjon scale
The brightness of a total eclipse depends on the state of Earth’s atmosphere, e.g. on dust after volcanic eruptions. André Danjon described it on a scale from 0 to 4:
Where can a lunar eclipse be seen?
A lunar eclipse can be seen at the same time from everywhere the Moon is above the horizon — roughly half of Earth, the night side. The boundary is a circle 90° from the sublunar point (the place where the Moon is at the zenith). We compute this point for each contact of the eclipse: P1 and P4 are entering and leaving the penumbra, U1 and U4 the umbra, U2 and U3 the start and end of totality.
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The white dot is the sublunar point, the yellow one the subsolar point, and the dashed line the Moon’s horizon at the chosen moment. We use the geocentric altitude with a threshold of h₀ = 0° (refraction of about 0.6° and the Moon’s parallax of about 0.95° partly cancel out), so the zone boundaries are accurate to about 1°. For penumbral eclipses the zones cover the whole eclipse (P1–P4). Land outlines are heavily simplified. The slider also moves the Moon in the simulator above.
Saros: the rhythm in which eclipses repeat
After 6,585.32 days (18 years, 10 or 11 days and about 8 hours) the Sun, Earth, Moon and the orbital nodes line up almost exactly as before. Why? Because this span contains an almost exact whole number of three different lunar “months”:
The synodic month — from new moon to new moon (the phase). The draconic month — from node to node (whether there will be an eclipse). The anomalistic month — from perigee to perigee (the distance, and so whether the eclipse will be total or annular). After one saros all three match up, so the next eclipse in the series is very similar to the previous one.
Pick an eclipse and jump by a saros
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Why is the next eclipse somewhere else?
A saros is not a whole number of days — about 8 hours are left over. In that time Earth turns about 1/3 of a rotation, or about 120°. That is why the eclipse of the next generation is seen roughly 120° farther west. After three saroses (the exeligmos: 54 years and about 33 days) the leftover hours add up to almost a whole day and the eclipse returns near the same meridian.
The saros fits almost, but not perfectly. With each repetition the shadow shifts a little north or south. A series is born as a small partial eclipse near one pole, then over centuries produces central eclipses ever closer to the equator, crosses into the other hemisphere and dies out near the other pole. This usually takes about 1,200–1,500 years and yields about 70–85 eclipses. Dozens of series run at the same time, which is why there are several eclipses a year.
The Metonic cycle
Another cycle: 19 years ≈ 235 synodic months (6,939.60 days vs. 6,939.69 days). After 19 years the Moon’s phases fall on almost the same calendar dates. It doesn’t repeat eclipses well, because it doesn’t match the draconic month.
The Babylonians and the Antikythera mechanism
Babylonian astronomers recorded eclipses on clay tablets for centuries. By the 4th century BCE at the latest (and probably earlier) they used a period of 223 months to predict possible eclipses. The name “saros” was given to this cycle only by Edmond Halley in 1691 — by mistake, since the Babylonian word šar meant something else (the number 3,600).
The Antikythera mechanism — a Greek bronze gear device from the 2nd–1st century BCE, recovered from a shipwreck in 1901 — had a saros dial on its back: a spiral divided into 223 months, with symbols for predicted eclipses. A small dial next to it showed the exeligmos, and a second spiral the Metonic cycle.
The series diagram is schematic: instead of the eclipse path we show how far from Earth’s center the shadow axis passes (γ, in Earth radii) — computed by the same algorithm as the eclipse list. Longitude is just a 120° rotation per saros.
Where did the Moon come from?
The most widely accepted explanation is the giant-impact hypothesis: about 4.5 billion years ago a body roughly the size of Mars, called Theia, struck the young Earth. The ejected material formed a disk around Earth, and the Moon formed from that disk. It is a hypothesis, not a certainty: the details are still being studied.
A schematic animation (about 2,500 particles, simple gravity and clumping), not a real SPH hydrodynamic simulation. Time is greatly sped up: the impact lasted hours, and the Moon’s accretion from the disk probably months to years.
What supports the impact idea?
- The same oxygen isotopes. Rocks from the Moon and from Earth have almost identical ratios of oxygen isotopes, while meteorites from Mars and asteroids are clearly different.
- A small iron core. The Moon has a low average density (3.34 g/cm³) and a core only about 1/5 of its radius — it formed mainly from mantle material, not from iron.
- Apollo samples. The 382 kg of rock brought back in 1969–1972 showed, among other things, that the Moon has very few volatile elements — as if it had once been strongly heated.
- A magma ocean. The bright highlands are made of anorthosite — a light rock that floated to the surface of a huge ocean of molten rock. Such an ocean fits a hot, fast formation.
Other ideas: a synestia (after the impact, Earth and the debris briefly formed a single spinning, hot cloud) or several smaller impacts. These models try to explain why Earth and the Moon are so similar in composition.
Why do we always see the same side?
Earth’s tidal forces long ago slowed the Moon’s spin until one rotation about its axis took as long as one orbit around Earth (27.3 days). This is synchronous rotation (tidal locking). The Moon gently “wobbles” — this is libration — so over time about 59% of its surface can be seen from Earth.
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The tides the Moon raises on Earth act like a brake: Earth’s rotation slows down, and angular momentum passes to the Moon, which moves away by about 3.8 cm per year. We measure this by bouncing laser pulses off retroreflectors left by Apollo 11, 14 and 15 and the Soviet Lunokhod 1 and 2 rovers. Tidal braking lengthens the day by about 2.3 ms per century; the measured lengthening is somewhat smaller (about 1.8 ms), because other effects, such as the slow rebound of land after the ice age, speed up the rotation a little.
Points from the past are rough reconstructions from corals, shells and tidal sediments; the further back, the less certain. Today’s rate is unusually high, so you can’t simply multiply it by Earth’s age.
Our Moon among other worlds
The Moon is 3,475 km across — 27% of Earth’s diameter — and 81.3 times less massive. It is the fifth-largest moon in the Solar System, but compared with its planet it is huge: only Charon, about half the diameter of Pluto, is larger relative to its “host.”
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How much would you weigh on other worlds?
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| Body | g [m/s²] | weight | scale reading |
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Mass (the amount of matter) is the same everywhere — what changes is weight, the force F = m·g. The “scale reading” is the number of kilograms a bathroom scale calibrated on Earth would show. We calculate it from GM and the mean radius, ignoring the planet’s rotation. Nothing is saved.
Perfect eclipses are a lucky coincidence
The Sun is about 400 times larger than the Moon and about 390 times farther away, so their disks in the sky are almost equal and the Moon can exactly cover the Sun, revealing the corona. But the Moon is receding: it once covered the Sun with room to spare, and in a few hundred million years total eclipses will no longer be possible — only annular ones will remain. We live at a good moment.
A few facts about the Moon
- The “dark side” isn’t dark. The other hemisphere gets just as much light — it is only invisible from Earth. Better to call it the far side.
- Chang’e 4 — the Chinese probe that on January 3, 2019, became the first to soft-land on the far side (in the von Kármán crater).
- Apollo: from 1969 to 1972, 6 crews landed (Apollo 11, 12, 14, 15, 16, 17), and 12 astronauts walked on the Moon. Apollo 13 did not land because of a failure.
- Water ice hides in permanently shadowed craters near the poles. It was confirmed by, among others, the LCROSS impact (2009) and the M3 instrument on the Chandrayaan-1 probe.
The hammer and the feather
On August 2, 1971, at the end of the last moonwalk of Apollo 15, commander David Scott dropped an aluminum geology hammer (about 1.3 kg) and a falcon feather at the same time. In the vacuum both hit the dust at the same instant — just as Galileo predicted. The feather came from a falcon because the mission’s lander was named Falcon.
In a vacuum, falling time does not depend on mass: t = √(2h/g). We model air resistance simply, through each object’s terminal velocity; the feather’s flutter is only a drawing effect.
With the same takeoff speed, the jump height h = v²/(2g) is about 6 times greater on the Moon. Yet astronauts didn’t leap 3 meters: the suit with its backpack had a mass of over 80 kg, was stiff and hampered movement — which is why they preferred to hop like kangaroos.
Period T = 2π√(L/g). On the Moon it is √(9.81/1.62) ≈ 2.46 times longer: a pendulum clock brought from Earth would run very slow.
A black sky in daytime
With no atmosphere there is no scattering of light, so even in full sunlight the sky is black and shadows are razor-sharp. There is no twilight either: sunset turns straight into night.
Heat and frost
A day on the Moon lasts about 29.5 Earth days. Near the equator the surface heats up to about +120 °C by day and cools to about −170 °C at night. In permanently shadowed craters near the poles it is below −230 °C.
Footprints for millions of years
There is no wind or rain, so astronauts’ bootprints can last a very long time — only the slow rain of micrometeorites will wear them away.
Challenges 0/8
How does it work?
Phase
The lit fraction of the disk k is set by the phase angle i — the Sun–Moon–Earth angle (almost 180° minus the angle between the Sun and Moon in the sky):
Two months
The synodic month S is longer than the sidereal month P, because during it Earth moves along its orbit around the Sun (year Y):
Length of the Moon’s shadow
where D is the Sun–Moon distance, and RS, RM are the radii of the Sun and Moon. The eclipse is total when L is greater than the distance from the Moon to the observer.
Saros
Falling and gravity
We compute the positions of the Sun and Moon with simplified formulas from Jean Meeus’s book Astronomical Algorithms (the main terms of the series, ch. 25 and 47). Times of new moon, quarters and full moon (ch. 49) are accurate to about a minute, and the eclipse type comes from the method in ch. 54. Drawings are not to scale unless stated otherwise.
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