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The lunar phases and librations in 2025 as viewed from the Northern Hemisphere at hourly intervals, with titles and supplemental graphics
The lunar phases and librations in 2025 as viewed from the Southern Hemisphere at hourly intervals, with titles and supplemental graphics
A full moon sets behind San Gorgonio Mountain in California on a midsummer's morning.

A lunar phase or Moon phase is the apparent shape of the Moon's day and night phases of the lunar day as viewed from afar. Because the Moon is tidally locked to Earth, the cycle of phases takes one lunar month and moves across the same side of the Moon, which always faces Earth. In common usage, the four major phases are the new moon, the first quarter, the full moon and the last quarter; the four minor phases are waxing crescent, waxing gibbous, waning gibbous, and waning crescent. A lunar month is the time between successive recurrences of the same phase: due to the eccentricity of the Moon's orbit, this duration is not perfectly constant but averages about 29.5 days.

The appearance of the Moon (its phase) gradually changes over a lunar month as the relative orbital positions of the Moon around Earth, and Earth around the Sun, shift. The visible side of the Moon is sunlit to varying extents, depending on the position of the Moon in its orbit, with the sunlit portion varying from 0% (at new moon) to nearly 100% (at full moon).[1]

Phenomenon

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The Moon rotates as it orbits Earth, changing orientation toward the Sun experiencing a lunar day. A lunar day is equal to one lunar month (one synodic orbit around Earth) due to it being tidally locked to Earth. Since the Moon is not tidally locked to the Sun, lunar daylight and night times both occur around the Moon. The changing position of the illumination of the Moon by the Sun during a lunar day is observable from Earth as the changing lunar phases, waxing crescent being the sunrise and the waning crescent the sunset phase of a day observed from afar.[2]

Phases of the Moon

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"Waxing gibbous" redirects here. For the album, see Waxing Gibbous.
"Last quarter" redirects here. For the manga series, see Last Quarter.
The phases of the Moon as viewed looking southward from the Northern Hemisphere. Each phase would be rotated 180° if seen looking northward from the Southern Hemisphere. The upper part of the diagram is not to scale, as the Moon, the Earth, and the Moon's orbit are all much smaller relative to the Earth's orbit than shown here.

There are four principal (primary, or major) lunar phases: the new moon, first quarter, full moon, and last quarter (also known as third or final quarter), when the Moon's ecliptic longitude is at an angle to the Sun (as viewed from the center of the Earth) of 0°, 90°, 180°, and 270° respectively.[3][a] Each of these phases appears at slightly different times at different locations on Earth, and tabulated times are therefore always geocentric (calculated for the Earth's center).

Between the principal phases are intermediate phases, during which the apparent shape of the illuminated Moon is either crescent or gibbous. On average, the intermediate phases last one-quarter of a synodic month, or 7.38 days.[b]

The term waxing is used for an intermediate phase when the Moon's apparent shape is thickening, from new to a full moon; and waning when the shape is thinning. The duration from full moon to new moon (or new moon to full moon) varies from approximately 13 days 22+1⁄2 hours to about 15 days 14+1⁄2 hours.

Due to lunar motion relative to the meridian and the ecliptic, in Earth's Northern Hemisphere:

  • A new moon appears highest at the summer solstice and lowest at the winter solstice.
  • A first-quarter moon appears highest at the spring equinox and lowest at the autumn equinox.
  • A full moon appears highest at the winter solstice and lowest at the summer solstice.
  • A last-quarter moon appears highest at the autumn equinox and lowest at the spring equinox.

Non-Western cultures may use a different number of lunar phases; for example, traditional Hawaiian culture has a total of 30 phases (one per day).[4]

Waxing and waning

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This video provides an illustration of how the Moon passes through its phases – a product of its orbit, which allows different parts of its surface to be illuminated by the Sun over the course of a month. The camera is locked to the Moon as Earth rapidly rotates in the foreground.
Diagram of the Moon's phases: The Earth is at the center of the diagram and the Moon is shown orbiting.

When the Sun and Moon are aligned on the same side of the Earth (conjunct), the Moon is "new", and the side of the Moon facing Earth is not illuminated by the Sun. As the Moon waxes (the amount of illuminated surface as seen from Earth increases), the lunar phases progress through the new moon, crescent moon, first-quarter moon, gibbous moon, and full moon phases. The Moon then wanes as it passes through the gibbous moon, third-quarter moon, and crescent moon phases, before returning back to new moon.

The terms old moon and new moon are not interchangeable. The "old moon" is a waning sliver (which eventually becomes undetectable to the naked eye) until the moment it aligns with the Sun and begins to wax, at which point it becomes new again.[5] Half moon is often used to mean the first- and third-quarter moons, while the term quarter refers to the extent of the Moon's cycle around the Earth, not its shape.

When an illuminated hemisphere is viewed from a certain angle, the portion of the illuminated area that is visible will have a two-dimensional shape as defined by the intersection of an ellipse and circle (in which the ellipse's major axis coincides with the circle's diameter). If the half-ellipse is convex with respect to the half-circle, then the shape will be gibbous (bulging outwards),[6] whereas if the half-ellipse is concave with respect to the half-circle, then the shape will be a crescent. When a crescent moon occurs, the phenomenon of earthshine may be apparent, where the night side of the Moon dimly reflects indirect sunlight reflected from Earth.[7]

Principal and intermediate phases of the Moon

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Moon phases Illuminated portion Visibility Average
moonrise
time[c] 		Culmination
time
(highest point) 		Average
moonset
time[c] 		Illustrations from Photograph
(view from the
Northern Hemisphere)
Northern
Hemisphere 		Southern
Hemisphere 		North
Pole 		South
Pole
New Moon Disc completely in shade
(lit by earthshine only) 		Invisible (too close to Sun),
except during a total or annular solar eclipse
(when the Moon obscures the Sun disc) 		06:00 12:00 18:00
Waxing
moon 		Waxing
crescent 		Right side:
(1%–49%) lit disc		 Left side:
(1%–49%) lit disc 		Late morning to post-dusk 09:00 15:00 21:00
First
quarter 		Right side:
50% lit disc		 Left side:
50% lit disc 		Afternoon and early night 12:00 18:00 00:00
Waxing
gibbous 		Right side:
(51%–99%) lit disc		 Left side:
(51%–99%) lit disc 		Late afternoon and most of night 15:00 21:00 03:00
Full Moon 100% illuminated disc,
except during a total or partial lunar eclipse
(when the Moon crosses the Earth's shadow) 		Sunset to sunrise (all night) 18:00 00:00 06:00
Waning
moon 		Waning
gibbous 		Left side:
(99%–51%) lit disc		 Right side:
(99%–51%) lit disc 		Most of night and early morning 21:00 03:00 09:00
Last
quarter 		Left side:
50% lit disc		 Right side:
50% lit disc 		Late night and morning 00:00 06:00 12:00
Waning
crescent 		Left side:
(49%–1%) lit disc		 Right side:
(49%–1%) lit disc 		Pre-dawn to early afternoon 03:00 09:00 15:00

Timekeeping

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Main articles: Lunar calendar, Lunisolar calendar, Metonic cycle, Intercalation, and History of calendars

Archaeologists have reconstructed methods of timekeeping that go back to prehistoric times, at least as old as the Neolithic. The natural units for timekeeping used by most historical societies are the day, the solar year and the lunation. The first crescent of the new moon provides a clear and regular marker in time and pure lunar calendars (such as the Islamic Hijri calendar) rely completely on this metric. The fact, however, that a year of twelve lunar months is ten or eleven days shorter than the solar year means that a lunar calendar drifts out of step with the seasons. Lunisolar calendars resolve this issue with a year of thirteen lunar months every few years, or by restarting the count at the first new (or full) moon after the winter solstice. The Sumerian calendar is the first recorded to have used the former method; Chinese calendar uses the latter, despite delaying its start until the second or even third new moon after the solstice. The Hindu calendar, also a lunisolar calendar, further divides the month into two fourteen day periods that mark the waxing moon and the waning moon.

The ancient Roman calendar was broadly a lunisolar one; on the decree of Julius Caesar in the first century BCE, Rome changed to a solar calendar of twelve months, each of a fixed number of days except in a leap year. This, the Julian calendar (slightly revised in 1582 to correct the leap year rule), is the basis for the Gregorian calendar that is almost exclusively the civil calendar in use worldwide today.

The time of day at a location on Earth (except at the poles) can be inferred from the culmination of the Moon in the sky and its phase: each lunar phase culminates closest to the zenith (being exactly south or north of it, crossing the meridian) in the sky at a specific daytime, as marked in the diagram, rising (east) and setting (west) during the time of the day preceding and succeeding the culmination.[8]

Calculating phase

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A crescent Moon over Kingman, Arizona

Each of the four intermediate phases lasts approximately seven days (7.38 days on average), but varies ±11.25% due to lunar apogee and perigee.

The number of days counted from the time of the new moon is the Moon's "age". Each complete cycle of phases is called a "lunation".[9]

The approximate age of the Moon, and hence the approximate phase, can be calculated for any date by calculating the number of days since a known new moon (such as 1 January 1900 or 11 August 1999) and reducing this modulo 29.53059 days (the mean length of a synodic month).[10][d] The difference between two dates can be calculated by subtracting the Julian day number of one from that of the other, or there are simpler formulae giving (for instance) the number of days since 31 December 1899. However, this calculation assumes a perfectly circular orbit and makes no allowance for the time of day at which the new moon occurred and therefore may be incorrect by several hours. (It also becomes less accurate the larger the difference between the required date and the reference date.) It is accurate enough to use in a novelty clock application showing lunar phase, but specialist usage taking account of lunar apogee and perigee requires a more elaborate calculation. Also, due to lunar libration it is not uncommon to see up to 101% of the full moon or even up to 5% of the lunar backside.

Calculating phase size

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The phase is equal to the area of the visible lunar sphere that is illuminated by the Sun. This area or degree of illumination is given by , where is the elongation (i.e., the angle between Moon, the observer on Earth, and the Sun).

Orientation by latitude

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The observed orientation of the Moon at different phases from different latitudes on Earth (the different orientation displayed between the phases at each latitude show merely the extremes of orientation due to libration)

In the Northern Hemisphere, if the left side of the Moon is dark, then the bright part is thickening, and the Moon is described as waxing (shifting toward full moon). If the right side of the Moon is dark, then the bright part is thinning, and the Moon is described as waning (past full and shifting toward new moon). Assuming that the viewer is in the Northern Hemisphere, the right side of the Moon is the part that is always waxing. (That is, if the right side is dark, the Moon is becoming darker; if the right side is lit, the Moon is getting brighter.)

In the Southern Hemisphere, the Moon is observed from a perspective inverted, or rotated 180°, to that of the Northern and to all of the images in this article, so that the opposite sides appear to wax or wane.

Closer to the Equator, the lunar terminator will appear horizontal during the morning and evening. Since the above descriptions of the lunar phases only apply at middle or high latitudes, observers moving towards the tropics from northern or southern latitudes will see the Moon rotated anti-clockwise or clockwise with respect to the images in this article.

The lunar crescent can open upward or downward, with the "horns" of the crescent pointing up or down, respectively. When the Sun appears above the Moon in the sky, the crescent opens downward; when the Moon is above the Sun, the crescent opens upward. The crescent Moon is most clearly and brightly visible when the Sun is below the horizon, which implies that the Moon must be above the Sun, and the crescent must open upward. This is therefore the orientation in which the crescent Moon is most often seen from the tropics. The waxing and waning crescents look very similar. The waxing crescent appears in the western sky in the evening, and the waning crescent in the eastern sky in the morning.

Other observational phenomena

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Lunar libration

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Animation showing progression of the Moon's phases.

The eccentricity of Moon's orbit leads to slight variation in its apparent size as viewed from Earth, and also causes it to be seen from slightly different angles at different times.

The effect is subtle to the naked eye, from night to night, but it can be seen in time-lapse photography.

Lunar libration causes part of the back side of the Moon to be visible to a terrestrial observer some of the time. Because of this, around 59% of the Moon's surface has been imaged from the ground.

Effect of parallax

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Main article: Lunar parallax

The Earth subtends an angle of about two degrees when seen from the Moon. This means that an observer on Earth who sees the Moon when it is close to the eastern horizon sees it from an angle that is about 2 degrees different from the line of sight of an observer who sees the Moon on the western horizon. The Moon moves about 12 degrees around its orbit per day, so, if these observers were stationary, they would see the phases of the Moon at times that differ by about one-sixth of a day, or 4 hours. But in reality, the observers are on the surface of the rotating Earth, so someone who sees the Moon on the eastern horizon at one moment sees it on the western horizon about 12 hours later. This adds an oscillation to the apparent progression of the lunar phases. They appear to occur more slowly when the Moon is high in the sky than when it is below the horizon. The Moon appears to move jerkily, and the phases do the same. The amplitude of this oscillation is never more than about four hours, which is a small fraction of a month. It does not have any obvious effect on the appearance of the Moon. It does however affect accurate calculations of the times of lunar phases.

Earthlight

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An overexposed photograph of a crescent Moon reveals earthshine and stars.

When the Moon seen from Earth is a thin crescent, Earth viewed from the Moon is almost fully lit by the Sun. The dark side of the Moon is dimly illuminated by sunlight reflected from Earth, called earthshine, which is bright enough to be easily visible from Earth. This is sometimes referred to as "the old moon in the new moon's arms" during a waning crescent or "the new moon in the old moon's arms" during a waxing crescent.[12]

Misconceptions

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Orbital period

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It can be confusing that the Moon's orbital sidereal period is 27.3 days while the phases complete a cycle once every 29.5 days (synodic period). This is due to the Earth's orbit around the Sun. The Moon orbits the Earth 13.4 times a year, but only passes between the Earth and Sun 12.4 times.

Eclipses

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As the Earth revolves around the Sun, approximate axial parallelism of the Moon's orbital plane (tilted five degrees to the Earth's orbital plane) results in the revolution of the lunar nodes relative to the Earth. This causes an eclipse season approximately every six months, in which a solar eclipse can occur at the new moon phase and a lunar eclipse can occur at the full moon phase.
The lunar phase depends on the Moon's position in orbit around the Earth and the Earth's position in orbit around the Sun. This animation (not to scale) looks down on Earth from the north pole of the ecliptic.

It might be expected that once every month, when the Moon passes between Earth and the Sun during a new moon, its shadow would fall on Earth causing a solar eclipse, but this does not happen every month. Nor is it true that during every full moon, the Earth's shadow falls on the Moon, causing a lunar eclipse. Solar and lunar eclipses are not observed every month because the plane of the Moon's orbit around the Earth is tilted by about 5° with respect to the plane of Earth's orbit around the Sun (the plane of the ecliptic). Thus, when new and full moons occur, the Moon usually lies to the north or south of a direct line through the Earth and Sun. Although an eclipse can only occur when the Moon is either new (solar) or full (lunar), it must also be positioned very near the intersection of Earth's orbital plane about the Sun and the Moon's orbital plane about the Earth (that is, at one of its nodes). This happens about twice per year, and so there are between four and seven eclipses in a calendar year. Most of these eclipses are partial; total eclipses of the Moon or Sun are less frequent.

Mechanism

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The phases are not caused by the Earth's shadow falling on the Moon, as some people believe.[13][14] They are caused by the Moon's shadow on itself, just as the Earth's shadow makes it night on one side of the Earth. The angle of the Sun in relation to the Moon determines how much of the Moon is illuminated.

See also

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  • Blue moon – Name for three (unconnected) events
  • Earth phase – Phases of Earth as seen from the Moon
  • Lunar effect – Unproven proposal of influence of lunar cycle on terrestrial creatures
  • Lunar month – Time between successive new moons. (Also known as a "lunation".)
  • Lunar observation – Methods and instruments used to observe the Moon
  • Planetary phase – Part of planet seen to reflect sunlight
  • Planetshine – Illumination by reflected sunlight from a planet
  • Tide – Rise and fall of the sea level under astronomical gravitational influences
  • Week – Time unit equal to seven days
  • Month – Unit of time about as long the orbital period of the Moon
  • Parmenides – 5th-century BC Greek philosopher, who tried to explain lunar phases

Footnotes

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Lunar phase

View on Grokipedia
from Grokipedia
Lunar phases are the cyclical changes in the visible shape of the Moon as observed from Earth, resulting from the Moon's orbit around Earth and the relative positions of the Earth, Moon, and Sun. These phases occur because the Sun illuminates only one half of the Moon at a time, and the portion visible from Earth varies as the Moon completes its approximately 29.5-day synodic cycle. The cycle begins with the new moon, when the Moon is positioned between the Earth and Sun, making its illuminated side face away from Earth and rendering it invisible to observers. As the Moon orbits Earth, the phases progress through eight primary stages: following the new moon comes the waxing crescent, a thin sliver of light visible on the right side (from the perspective); then the first quarter, where half the Moon is illuminated and it rises around noon; the waxing gibbous, with more than half but less than fully illuminated; the , when the entire Earth-facing side is lit and it rises at sunset; the waning gibbous, shrinking from full; the third quarter, half-illuminated on the left and rising around midnight; and finally the waning crescent, a thin sliver of light visible on the left side (from the perspective), often resembling a "C" shape, the final stage sometimes referred to as the "end of moon shape" before returning to new. This sequence is influenced by the Moon's to , meaning the same side always faces our planet, and the of about 27.3 days for one relative to the stars, extended to 29.5 days due to Earth's own motion around the Sun. Lunar phases have been observed and documented across cultures for , influencing calendars, , and rituals, while modern astronomy uses them to study the 's surface and orbital dynamics. They are distinct from eclipses, which occur only when the Sun, , and align precisely during new or full phases. The average - distance of 238,855 miles (384,399 km) ensures these phases are visible worldwide, though the exact appearance varies slightly by .

Fundamentals

Definition and Phenomenon

Lunar phases refer to the cyclical variations in the portion of the Moon's illuminated disk that is visible from Earth, arising from the changing angle between the Sun, Earth, and Moon. These phases manifest as the apparent shape of the Moon shifting over time, creating a sequence of distinct appearances observable in the night sky. The Moon produces no light of its own but reflects sunlight from its surface, with only the half facing the Sun illuminated at any time. From Earth's perspective, the visible illuminated fraction changes because the Moon orbits Earth, altering the alignment of the three bodies; this cycle repeats approximately every 29.5 days, known as the synodic month. During this period, the Moon's position relative to the Sun determines how much of its lit side observers see, from none to fully illuminated. Records of lunar phases date back to Stone Age peoples, who tracked the cycle to measure days and predict seasonal changes. Ancient civilizations, including the Babylonians and Egyptians, observed these phases for practical purposes such as agriculture, navigation, and developing calendars. The visual progression begins with the new moon, when the Moon is nearly invisible as it aligns between Earth and the Sun. It then transitions to the waxing crescent, a thin illuminated sliver growing toward the first quarter, where half the disk is lit. This continues through the waxing gibbous phase to the full moon, when the entire visible disk glows brightly opposite the Sun. The cycle then reverses with the waning gibbous, last quarter, waning crescent, returning to new moon.

Cause of Lunar Phases

The lunar phases result from the geometry of the Sun-- system, where the reflects sunlight but appears to change shape due to the varying portion of its illuminated hemisphere visible from . The is always half-illuminated by the Sun, similar to how half of is lit during , but the observer on Earth sees different fractions depending on the relative positions. This visibility is determined by the phase angle, defined as the elongation between the and the Sun as viewed from . When the phase angle is 0°, the Moon and Sun share the same ecliptic longitude from Earth's perspective, positioning the Moon's illuminated side toward the Sun and away from Earth, resulting in a new moon that is invisible or nearly so. Conversely, at a phase angle of 180°, the Moon is directly opposite the Sun, with its fully illuminated hemisphere facing Earth, producing a full moon. Intermediate angles yield partial illuminations, such as crescent or gibbous appearances. The Moon's orbit around Earth is prograde—counterclockwise when viewed from the north side of the plane—and nearly coplanar with the , inclined by a mean of 5.145° relative to Earth's around the Sun. This configuration, combined with Earth's simultaneous revolution , defines the synodic month of 29.53059 days as the period for the Moon to return to the same phase, longer than the sidereal of 27.32166 days because the reference point (the Sun) advances during that time. Tidal interactions have caused the Moon to become tidally locked, with its rotational period synchronized to its , always showing the same face to ; however, the phases themselves arise independently from the illumination geometry and would occur even without this locking. —the boundary separating the Moon's sunlit and shadowed hemispheres—shifts across the visible disk based on the observer's , appearing as a straight line at quarter phases (90° angle) and curving at other elongations. In diagrams of the system, is depicted as the edge where incoming grazes the lunar surface tangent to 's viewpoint, highlighting how the changing alignment alters the shadowed fraction.

Types of Phases

Principal Phases

The principal lunar phases consist of four key stages in the Moon's cycle as observed from : the New Moon, First Quarter, , and Last Quarter. These phases mark the moments when the Moon's elongation—the angular separation between the Sun and Moon as seen from —is at 0°, 90°, 180°, and 270°, respectively. They represent the primary divisions of the synodic month, which averages 29.53 days, with each principal phase separated by roughly one-quarter of this period. The begins the cycle, occurring when the Moon lies directly between the and the Sun in conjunction, with its illuminated side facing away from . At this phase, the Moon appears invisible from due to 0% illumination on the side facing our planet, though it may be visible as a dark during a total . It rises and sets with the Sun, making it unobservable against the daytime sky. Approximately 7.4 days after the New Moon, the First Quarter phase arrives, with the Moon at a 90° elongation east of the Sun. From the , the right half of the Moon's disk appears illuminated at 50%, as sunlight illuminates the side facing while the Moon is positioned to the east in its . This half-lit Moon rises around noon and sets around midnight, becoming prominent in the evening sky. The occurs about 14.8 days after the , when the reaches 180° elongation in opposition to the Sun. The entire visible disk is illuminated at 100%, with the fully lit side facing as the is on the opposite side of our planet from the Sun. It rises at sunset and sets at sunrise, providing bright nighttime illumination. Roughly 22.1 days into the cycle, the Last Quarter (also known as Third Quarter) phase takes place at 270° elongation, with the 90° west of the Sun. In the , the left half of the disk is illuminated at 50%, reflecting the waning portion of the cycle. This phase rises around midnight and sets around noon, visible primarily in the morning sky. The terms "First Quarter" and "Last Quarter" derive from the Moon's position in its orbit, dividing it into quadrants relative to the Sun-Earth line, rather than indicating a 25% illumination fraction—these phases actually show 50% of the disk lit due to the geometry of illumination.

Intermediate Phases

The intermediate phases of the Moon occur between the principal phases and are characterized by gradual changes in the visible illuminated portion of the lunar disk, transitioning from less than 50% to more than 50% illumination and vice versa. These phases are divided into crescent and gibbous categories based on the fraction of the Moon's Earth-facing hemisphere that is illuminated by the Sun: crescent phases feature less than 50% illumination, while gibbous phases exceed 50% but fall short of 100%. The principal quarter phases mark exact boundaries at 50% illumination. Following , the phase emerges as a thin, illuminated sliver on the 's right side (as viewed from the ), with illumination progressively increasing but remaining below 50%. This phase becomes visible shortly after sunset in the western sky, as the angle between the Sun, , and Moon allows a small portion of the sunlit lunar surface to face . After the first quarter phase, the Moon enters the waxing gibbous stage, where more than 50% but less than 100% of the disk is illuminated, appearing as a bulging, humpbacked shape that continues to grow brighter each night. The term "gibbous" derives from the Latin word for "hunchbacked," reflecting the convex form of the illuminated region. This phase is prominent in the evening , rising in the southeast and remaining visible for most of the night. Symmetrically, after the full moon, the waning gibbous phase mirrors the waxing gibbous, with illumination decreasing from over 50% toward 50% as the 's position shifts. The illuminated portion appears on the left side ( view), gradually shrinking while still dominating more than half the disk, and the Moon rises later each night after sunset. Finally, the waning crescent phase, sometimes referred to as the "end of moon shape," precedes the new moon as the final stage in the lunar cycle. It presents a thin, fading sliver of light on the left side (as viewed from the Northern Hemisphere), often resembling a "C" shape, with less than 50% illumination. This phase is often barely discernible except near dawn and becomes visible low in the eastern sky before sunrise, as the Moon approaches alignment with the Sun from Earth's perspective.

Waxing and Waning Cycles

The lunar phase cycle, known as a lunation or synodic month, begins at , when the Moon is in conjunction with the Sun as viewed from , and progresses through a sequence of increasing and decreasing illumination over an average duration of 29.53 days. During the first half, the illuminated portion of the Moon's visible disk "," or grows, from a thin to the at opposition, approximately 14.77 days later on average. In the second half, the illumination "wanes," or diminishes, symmetrically in reverse through gibbous and stages back to , completing the cycle at the next conjunction. The term "" derives from the verb weaxan, meaning "to grow" or "increase," reflecting the apparent expansion of the lit area, while "waning" comes from wanian, meaning "to decrease" or "become smaller," describing the subsequent shrinkage. Although the waxing and waning phases mirror each other in the progression of illumination—from 0% to 100% and back to 0%—the cycle lacks perfect symmetry due to the 's elliptical around , which causes variations in its . The moves faster near perigee (its closest point to ) and slower near apogee (farthest point), altering the time required to traverse equal angular separations relative to the Sun; as a result, the interval from new moon to can differ from the return interval by up to about 1.5 days, typically ranging from 13.9 to 15.2 days for each half. This , with an average value of 0.0549, shifts the timing slightly each month, ensuring the waning phase often lags or leads the waxing by 1 to 2 days depending on the 's position at conjunction. The overall length of the synodic month also varies seasonally due to this eccentricity and the combined motion of and around the Sun, fluctuating between approximately 29.27 and 29.83 days. At perigee, the Moon's increased speed hastens phase changes, shortening the cycle, while at apogee, slower motion extends it, with extremes occurring when conjunction aligns near these orbital points. These variations, though small, influence the precise timing of phases and have been accounted for in astronomical calculations since ancient times.

Calculation Methods

Determining Phase Angle

The lunar phase angle is defined as the angle between the ecliptic longitudes of the and the Sun as observed from , representing the geocentric elongation that determines the Moon's apparent illumination cycle. This angle, denoted E, ranges from 0° at new moon, when the Moon and Sun share nearly the same ecliptic longitude, to 180° at , when they are separated by half a circle along the ; it then increases from 180° to 360° over the subsequent half-cycle, completing the synodic month. The full elongation (0° to 360°) distinguishes from waning phases, while the principal value (0° to 180°) serves as a fundamental parameter for identifying the Moon's position in its orbital cycle relative to the Sun. To calculate the phase angle, astronomers first convert the desired date and time to Julian date, a continuous count of days since a fixed , which standardizes temporal computations in . Using this, the mean anomaly of the (its angular position relative to its last perigee) and the mean anomaly of the Sun are derived through low-precision approximations or higher-order ephemerides; these anomalies, combined with like eccentricity and inclination, yield the ecliptic longitudes λ_moon and λ_sun. The phase angle E is then computed as the difference E = λ_moon - λ_sun, adjusted by adding or subtracting 360° if necessary to obtain a value between 0° and 360°. A widely adopted for these calculations is the Meeus method, outlined in Astronomical Algorithms, which provides step-by-step approximations for solar and lunar positions accurate to about 0.1° over centuries without requiring full tables. The process begins with the Julian date to compute the number of centuries past J2000.0, then applies series expansions: for the Sun, longitude is approximated using terms involving the and Earth's ; for the Moon, it incorporates the , the , and perturbations from the Sun and planets, truncated for practicality to a few dozen terms. The resulting longitudes are differenced to yield the elongation E; this method underpins many computational tools and achieves sufficient precision for phase determination except near eclipses. Historically, ancient civilizations determined lunar phases primarily through direct observation rather than mathematical calculation, tracking the Moon's nightly position relative to the Sun and to predict cycles for calendars and . peoples etched phase sequences on bones and cave walls as early as 30,000 years ago, while Mesopotamians and Egyptians around 2000 BCE maintained observational records to align festivals with new moons, relying on visibility thresholds without quantitative angular measures. In modern practice, phase angles are computed using astronomical software that integrates Meeus-style algorithms or precise ephemerides from sources like the Jet Propulsion Laboratory's DE430 series, enabling real-time predictions for any date. Tools such as the U.S. Naval Observatory's data services or open-source libraries implement these routines, outputting phase angles to arcminute accuracy for applications in astronomy and navigation.

Calculating Illuminated Fraction

The illuminated fraction of the Moon's disk, denoted as kk, represents the proportion of the visible lunar surface directly lit by the Sun, ranging from 0 (completely dark at new moon) to 1 (fully illuminated at ). This value is derived from the geocentric elongation EE (as calculated above), with the selenocentric phase angle ϕ\phi approximately equal to 180∘−E180^\circ - E under the assumption of parallel solar rays (valid since the Sun-Earth distance greatly exceeds the Earth-Moon distance). The standard simple formula for kk is k=1−cos⁡E2k = \frac{1 - \cos E}{2} for 0∘≤E≤180∘0^\circ \leq E \leq 180^\circ, or equivalently using the selenocentric ϕ\phi, k=1+cos⁡ϕ2k = \frac{1 + \cos \phi}{2} for 0∘≤ϕ≤180∘0^\circ \leq \phi \leq 180^\circ. This expression arises from the projected geometry of the illuminated hemisphere onto the observer's line of sight, where the terminator (boundary between light and shadow) divides the disk such that the lit portion's area fraction equals the average over the spherical surface projection. At the extremes, E=0∘E = 0^\circ yields cos⁡0∘=1\cos 0^\circ = 1, so k=0k = 0 (0% illuminated); E=180∘E = 180^\circ gives cos⁡180∘=−1\cos 180^\circ = -1, resulting in k=1k = 1 (100% illuminated). For intermediate values, such as the first or last quarter phase where E=90∘E = 90^\circ, cos⁡90∘=0\cos 90^\circ = 0, yielding k=0.5k = 0.5 (50% illuminated). The visible disk area illuminated is exactly proportional to kk in this spherical model. The full moon appears about 6–9 times brighter than at quarter phase due to both this fraction and the opposition effect (enhanced backscattering near full phase). While the terminator traces an ellipse in projection (with eccentricity depending on EE), the integrated illuminated area fraction simplifies exactly to kk without requiring elliptic integrals, as the projection symmetry preserves the linear relation for a uniform sphere. To compute kk for a specific date, first obtain the geocentric elongation EE (as detailed in the phase angle determination), then substitute into the ; for more precision near the limb or accounting for finite distances, use the full selenocentric calculation with data. For example, on a date with E≈120∘E \approx 120^\circ (waxing gibbous), cos⁡120∘=−0.5\cos 120^\circ = -0.5, so k=(1−(−0.5))/2=0.75k = (1 - (-0.5))/2 = 0.75 (75% illuminated). A simple step-by-step calculation or implementation might proceed as follows:
  1. Input the geocentric elongation EE in degrees (e.g., from astronomical software or ephemeris).
  2. Convert to radians if needed: Erad=E×π/180E_{\text{rad}} = E \times \pi / 180.
  3. Compute k=(1−cos⁡Erad)/2k = (1 - \cos E_{\text{rad}}) / 2.
  4. Multiply by 100 for percentage.
In pseudocode:

E_deg = 90 # example geocentric elongation E_rad = E_deg * pi / 180 k = (1 - cos(E_rad)) / 2 print(f"Illuminated fraction: {k * 100:.1f}%")

E_deg = 90 # example geocentric elongation E_rad = E_deg * pi / 180 k = (1 - cos(E_rad)) / 2 print(f"Illuminated fraction: {k * 100:.1f}%")

This yields 50.0% for E=90∘E = 90^\circ. This geocentric approximation assumes a perfect and neglects , which causes apparent rocking of the and can alter the visible illuminated portion by up to a few percent; for higher precision, especially near the limb, use selenocentric coordinates that incorporate the Moon's instantaneous orientation relative to .

Observational Effects

Visibility by

The visibility and appearance of lunar phases vary significantly with the observer's latitude on , primarily due to the orientation of the Moon's terminator—the boundary between the illuminated and dark portions—and the Moon's path relative to the horizon. At equatorial latitudes, near 0°, the Moon's path is nearly vertical, rising due east and setting due west, passing close to the . This results in symmetric phase appearances, where quarter moons (first and third) display exact halves of the disk illuminated, with aligned vertically along the north-south meridian, creating a precise semicircular division without tilt. Crescent phases here resemble a "boat" lying on its side, with the illuminated portion curving horizontally. In contrast, the orientation of illuminated portions differs between hemispheres. From the , the first quarter phase shows the right half of the Moon lit, while the third quarter shows the left half lit; these are mirrored in the , where the left half is lit during the first quarter and the right half during the third quarter. This reversal arises from the observer's perspective relative to the plane, though the overall illuminated fraction remains identical worldwide. At high latitudes above approximately 66° (beyond the and ), the Moon's visibility is profoundly affected by its , which ranges from about +28.7° to -28.7°. During certain phases, particularly when the Moon's aligns with the observer's latitude, it may remain entirely above or below the horizon without rising or setting. For instance, in the , the near the is continuously visible (circumpolar) north of the , while in the , it occurs near south of the . In these cases, it circles the sky low on the horizon without dipping below it. Near the poles themselves, the can remain above the horizon for up to about 15 days during its synodic month, allowing continuous observation of phase changes over extended periods. This prolonged visibility has historically influenced indigenous timekeeping, such as among communities in the , who incorporated the 's position alongside circumpolar stars to mark seasonal and daily time passages.

Libration and Parallax

Libration refers to the apparent oscillatory motion of the as observed from , which allows viewers to see slightly more than half of the lunar surface over time. This phenomenon arises because the Moon's rotation is tidally locked to its , but several factors cause subtle shifts in the orientation of its visible disk. The three primary types of libration are longitudinal, latitudinal, and daily, each contributing to variations in the apparent position of lunar features relative to —the boundary between the illuminated and dark portions of the Moon's disk. Longitudinal libration, also known as libration in , results from the Moon's elliptical around . According to Kepler's second law, the Moon moves faster near perigee (its closest point to ) and slower near apogee, while its rotational speed remains constant. This mismatch causes an east-west swinging motion, with an of approximately 7.9°, revealing additional terrain along the eastern or western limb depending on the orbital phase. Latitudinal libration stems from the 5.1° inclination of the 's relative to the and its axial obliquity of 6.7° relative to the Earth-Moon . As the , this geometry produces a north-south nodding effect, with an of about ±6.8°, allowing glimpses of regions near the lunar poles that would otherwise be hidden. Daily libration, sometimes termed diurnal libration, occurs due to the observer's changing position on Earth's rotating surface over the course of a night. This parallax-like effect shifts the apparent lunar orientation by up to 1° at the 's typical distance, subtly altering the view of the limb and contributing to the overall visible area. Parallax, distinct from but related to daily libration, is the apparent displacement of the Moon's position against the background stars when viewed from different points on Earth's surface. The Moon's horizontal averages about 1° (precisely 57 arcminutes), arising because observers are not at Earth's but offset by up to half the planet's . For observers separated by significant east-west baselines, such as across continents, this causes a minor shift in the apparent position of relative to the Sun, resulting in slight differences in the observed phase edge—though the overall phase remains nearly identical globally. Together, and enable approximately 59% of the Moon's total surface to become visible from over a full cycle, compared to the 50% expected from perfect . This combined effect manifests as libration zones along the lunar limb, where features periodically appear and disappear, aiding historical efforts in selenographic mapping by astronomers like in the .

Earthshine and Other Effects

During the crescent phases of the Moon, the otherwise dark portion of the Earth-facing lunar disk is faintly illuminated by earthshine, which consists of sunlight reflected from 's surface onto the . This subtle glow, often visible to the under clear skies, arises because the receives reflected light from the dayside of , which appears gibbous or nearly full from the lunar perspective during these times. The intensity of earthshine peaks when the Earth- phase angle allows for maximum reflection, making the "old in the new 's arms" particularly evident shortly after sunset or . Earth's average of approximately 0.30—driven largely by reflective clouds and oceans—contrasts with the Moon's lower of about 0.12, resulting in earthshine that is roughly 2.5 times brighter per unit area than the illuminating Earth during a . This enhanced reflectivity ensures that earthshine provides a discernible illumination on the lunar night side, though it remains far fainter than direct sunlight on the crescent portion. Historically, provided the first known scientific explanation of this phenomenon in his around 1510, attributing the glow to sunlight bouncing off 's watery surfaces, an insight later refined to account for atmospheric and cloud contributions. Other notable observational effects tied to lunar phases include the opposition surge, which causes the full Moon to appear disproportionately bright due to retroreflection in the lunar regolith; this effect boosts brightness by more than 40% as the observer, Moon, and Sun align closely, minimizing shadows among regolith particles through mechanisms like shadow hiding and coherent backscattering. Seasonal variations in the Moon's apparent color also occur from Earth's atmospheric scattering, with full moons in autumn (such as the harvest moon) often appearing orange or reddish when low on the horizon in northern latitudes, as longer light paths through denser air scatter shorter blue wavelengths more effectively. Modern photometry of earthshine, pioneered in projects like those at Big Bear Solar Observatory since the late 1990s, employs precise imaging to measure these effects and track global changes in Earth's albedo, revealing fluctuations of up to 0.01 in reflectance over decades linked to cloud cover and climate patterns.

Practical Applications

Timekeeping and Calendars

Lunisolar calendars integrate the lunar cycle with the solar year, defining months based on the phases of the while adding intercalary months to prevent drift from the seasons. These systems typically begin each month at the new moon or the first visible , with month lengths alternating between 29 and 30 days to approximate the synodic month of about 29.53 days. The Jewish calendar, a lunisolar system in use since the CE, employs a 19-year in which seven years include an extra month ( II) to align 235 lunar months with 19 solar years, ensuring festivals like remain in spring. The Chinese calendar similarly adds an intercalary month every two to three years, based on the absence of a principal in a , to keep the in the eleventh month and support agricultural timing. In the Hindu tradition, as reflected in calendars like the , intercalary months are inserted approximately every three years to reconcile the 354-day lunar year with the , maintaining seasonal alignment for religious observances. Purely lunar calendars, such as the Islamic Hijri calendar, consist of 12 months totaling 354 or 355 days, with each month starting upon sighting the new crescent moon. This results in an annual drift of about 11 days relative to the solar year, causing months to cycle through all seasons over approximately 33 years. Historically, lunar phases informed timekeeping through devices like astrolabes, which medieval scholars used to compute the Moon's position and phase for determining and nocturnal hours. Geared astrolabes from the Islamic world and Europe often featured dials displaying lunar phases alongside , aiding in precise astronomical observations. Water clocks, or clepsydrae, were adapted in ancient and medieval contexts to track influenced by lunar phases, with sailors correlating the Moon's age to predict high and low for and coastal activities. In modern applications, astronomical almanacs from institutions like the U.S. Naval Observatory provide tabulated predictions of lunar phases, enabling accurate dating of events such as the start of , which depends on the new moon's . These computations, based on ephemerides, support global coordination for religious and scientific purposes. Lunar phases have played a crucial role in traditional , particularly among Polynesian voyagers who integrated the moon's and position into their systems. In Polynesian , the moon's phases helped determine direction by observing its rising and setting points relative to stars and the horizon, forming part of a mental "star " that included the sun, planets, and swells. For instance, the voyages revived ancient techniques where navigators like used the moon's phase to orient during long ocean crossings . Additionally, the full moon's brightness facilitated nighttime travel and hunting on land and sea, providing essential illumination in pre-modern societies without artificial lights. In historical European maritime navigation, the "" method relied on measuring the angular separation between the moon and fixed stars or the sun during specific phases to calculate at sea, a technique pioneered by astronomers like in the . This approach, detailed in the from 1767, allowed sailors to determine time and position without relying solely on chronometers, revolutionizing global exploration until the widespread adoption of accurate clocks. The method's precision depended on the moon's predictable motion through its phases, making and waning periods critical for observations. Across cultures, lunar phases hold profound mythological and symbolic significance, often embodying cycles of life, death, and renewal. In , , the goddess of the moon, was depicted riding a chariot across the sky, her phases representing her eternal journey and influence over and human emotions, as described in ancient texts like Hesiod's . Similarly, in Chinese lore, ascended to the moon during its full phase after consuming an immortality elixir, symbolizing longing and sacrifice; this narrative underpins festivals celebrating the moon's completeness. These myths highlight the moon's phases as metaphors for transformation, with the waxing crescent signifying growth and the waning gibbous evoking decline. Festivals worldwide synchronize with lunar phases to mark seasonal and communal events. The Mid-Autumn Festival in and occurs on the of the eighth , honoring family reunion and harvest abundance through mooncakes and lanterns, a dating back over 3,000 years to agrarian rituals. In , , the festival of colors, aligns with the of Phalguna (February-March), celebrating spring's arrival with bonfires and revelry that symbolize the triumph of good over evil, as rooted in like the Puranas. These observances underscore the phases' role in fostering social bonds and agricultural timing. Indigenous knowledge systems further illustrate the cultural depth of lunar phases, tying them to environmental and spiritual cycles. Among Native American tribes, such as the Algonquin, the full moon in September is known as the Harvest Moon, named for its extended evening light aiding crop gathering, a nomenclature shared across groups like the Lakota and reflecting seasonal adaptations. In African traditions, the San people of southern Africa invoked the new moon's darkness for stealthy hunts, while Yoruba communities in West Africa honor deities like Oshun during waxing phases, linking lunar cycles to fertility and riverine seasons in oral histories. These practices demonstrate how phases guided practical survival and worldview. In modern culture, lunar phases continue to inspire , , and exploration milestones. The full moon's association with transformations stems from medieval European beliefs in lycanthropy tied to lunar cycles, popularized in 19th-century like The Were-Wolf by Clemence Housman and later films, symbolizing inner conflict and the uncanny. Poets such as evoked the moon's phases in works like "Walking Around," using the waxing gibbous to represent elusive beauty and melancholy. Notably, NASA's Apollo missions timed landings, including on July 20, 1969, during the waxing crescent phase to optimize solar illumination for safe descent and surface visibility, a strategic choice that influenced all six successful lunar touchdowns.

Misconceptions and Clarifications

Orbital Period Confusions

One common confusion in understanding lunar phases arises from distinguishing between the sidereal month and the synodic month, which govern different aspects of the 's motion. The sidereal month, the time for the to complete one orbit relative to the , measures 27.32166 days. In contrast, the synodic month, which determines the cycle of lunar phases from one new moon to the next, lasts 29.53059 days on average. This difference occurs because the orbits the Sun, requiring the to travel an additional —about 360 degrees relative to the stars plus roughly 29 degrees due to 's motion—to realign with the Sun for the same phase. Observers often puzzle over why the 's position among the stars shifts backward relative to its phase progression, as the sidereal period is shorter and does not account for solar alignment. Further complicating perceptions is the anomalistic month, the interval between successive perigees (the Moon's closest approaches to ), which averages 27.554550 days. Due to the Moon's elliptical orbit, this period influences the variable speeds at which the travels, leading to fluctuations in the duration of individual synodic months. For instance, synodic months range from approximately 29.27 days (when new moon occurs near perigee) to 29.82 days (near apogee), a variation of about 13 hours driven primarily by the Moon's and secondarily by 's . A widespread error is the assumption of a fixed 28-day lunar cycle, often conflated with human menstrual periods or simplified calendars, whereas the actual synodic period averages 29.53 days with the noted variations. This misconception overlooks the dynamic geometry of the solar system. Ultimately, lunar phases depend on the relative positions in the Sun-Earth-Moon system, not solely the Earth-Moon , ensuring that phase cycles align with solar references rather than stellar ones.

Eclipses and Phases

Lunar eclipses occur when the full moon passes through 's shadow, while solar eclipses happen during the new moon when the moon passes between and the sun, blocking . However, these alignments alone are insufficient; the moon's orbit must position it near one of the two ascending or descending nodes where its intersects the , the plane of around the sun. These conditions define seasons, which arise approximately twice per year, each lasting about 35 days, when the sun is near the nodes. A common misconception is that every new or results in an , but the 's orbital plane is inclined by about 5.1° relative to the , causing the to typically pass above or below or the line of sight to the sun. This tilt reduces the probability to roughly 20%, with an occurring only if the (for lunar) or new (for solar) falls within approximately 17° of a node. Lunar eclipses are classified as penumbral (moon passes through the faint outer penumbra, causing subtle dimming), partial (part of the enters the dark umbra), or total (entire enters the umbra, often appearing reddish due to atmospheric scattering). Solar eclipses include total (sun fully obscured, revealing the corona), partial (sun partially covered), or annular ( appears as a when farther from ). Importantly, lunar phases proceed uninterrupted during penumbral phases or when the remains outside the umbra, maintaining the appearance despite reduced brightness. The recurrence of eclipses follows the Saros cycle, a period of 223 synodic months or approximately 18 years and 11 days, after which similar repeat with the same type and visibility path, shifted by about 120° in longitude due to . This cycle, recognized since ancient times, enables long-term predictions and occurs in over 40 separate series for lunar eclipses alone.

Common Mechanistic Errors

One prevalent misconception about lunar phases is that the waning phases occur because falls on the Moon, gradually darkening it as it orbits. In reality, only affects the during a , which is a rare event happening at most a few times per year when the Sun, , and align precisely. Lunar phases result from the changing angle of sunlight illuminating the 's surface as viewed from , with line separating the lit and dark portions shifting due to the 's orbital position around . Another common error is the belief that the Moon's rotation on its axis causes the phases by turning different parts of its surface toward Earth. The Moon is tidally locked to Earth, meaning it rotates once on its axis for every orbit around Earth, always presenting the same face to our planet. Phases arise solely from the relative positions in the Earth-Moon-Sun system: as the Moon orbits, observers on Earth see varying portions of the always-half-illuminated lunar surface, from new moon (unlit side facing Earth) to full moon (lit side facing Earth). Many people assume lunar phases appear identical worldwide, but in fact, the orientation of and waning crescents is mirrored between hemispheres. In the , the lit portion of a is on the right side, while in the , it appears on the left; further influences the 's path across the sky, affecting rise and set times and the angle of visibility. This hemispheric difference stems from observers' positions relative to the ecliptic plane, the apparent path of the Sun and . The term "blue moon" is often misunderstood as a rare event where the appears blue, but it actually refers to the second in a single month, occurring on average every 2.7 years due to the lunar synodic month of about 29.5 days being slightly shorter than most calendar months. An older definition denotes the third in a with four, but the monthly version is more commonly used today; the does not change color, appearing as a standard . Similarly, the "harvest moon" is sometimes thought to be exceptionally large or bright due to some unique lunar property, but it is simply the full moon closest to the September equinox in the Northern Hemisphere. Its distinctive shallow rise—where it climbs the horizon at a low angle, appearing larger and redder due to atmospheric refraction—results from the ecliptic's shallow tilt relative to the horizon at that time of year, causing the moon to rise nearly at the same time for several evenings and providing extended twilight illumination for pre-industrial farmers.

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