Lunar phase

Phenomenon

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.

Phases of the Moon

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. 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.

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 hours to about 15 days 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).

Waxing and waning

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. 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), 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.

Principal and intermediate phases of the Moon

Timekeeping

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.

Calculating phase

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".

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). 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

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 (1-\cos \theta)/2=\sin^2(\theta/2), where \theta is the elongation (i.e., the angle between Moon, the observer on Earth, and the Sun).

Orientation by latitude

Other observational phenomena

Lunar libration

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

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

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.

Misconceptions

Orbital period

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

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

The phases are not caused by the Earth's shadow falling on the Moon, as some people believe. 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.

Notes

References

Citations

Sources

References

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8. Carter, Jamie. (April 8, 2021). "How, When And Where You Can Gaze At A ‘New Moon In The Old Moon’s Arms’ This Week From Home".
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10. Plait, Phil. (December 28, 2012). "Today's Full Moon is the 13th and Last of 2012". [[Slate (magazine).