Lunation

Cycle of the phases of the moon during a lunation. The fact that both lunar poles (north above) are visible is a result of the libration .

The lunation (from Latin luna 'moon') is the variable period of time for one orbit of the moon around the earth , based on its position to the sun , and thus the synodic period of the moon.

The respective lunation duration is measured for an entire cycle of the moon phases from a certain new moon to the following new moon, i.e. when the moon is again in conjunction with the sun. Lunations last different lengths of time and can differ from one synodic lunar revolution to the next by more than 3 hours. Over the course of some years of a decade, there are differences of over 13 hours. The calculated average is currently around 29.53 days; this mean lunation period is also called the synodic month .

The term lunar month stands astronomically in general for periods of a lunar revolution in relation to a certain reference point ; In addition to the synodic month, this also includes the anomalous , sidereal , tropical and draconian months. For a lunar month in the calendar calculations , even lunar month called different lunar related periods can form the base.

Occasionally, in the obstetrics , the period of 28 days lunar month or lunar month called and pregnancy divided into ten such sections.

The astronomical lunar months

Synodic Month (Middle Lunation)

Observed from earth, the moon reaches the same position to the sun again after a synodic month. This term of the month corresponds to the common understanding of a month as a "period of the phases of the moon". On average, the period from new moon to new moon is about 29.53 days.

Lunations are a characteristic feature of the sun - earth - moon system. To a good approximation, the orbit of the moon around the earth and the orbit of the earth around the sun can each be represented by Kepler ellipses , and for this idealization the synodic period of rotation of the moon can be calculated. For various reasons, the actual duration of a single lunation varies (see also the figure below ). The synodic month is the mean synodic period of the moon averaged over decades and is currently the average value:

29.530589  d (29 days, 12 hours, 44 minutes, 2.9 seconds)

Variations in the duration of the lunation

Since the orbital speeds of the earth and the moon change during the orbit (see 2. Kepler's law ), the duration of the time span from one new moon to the next or one full moon to the next also changes. The calculation of these dates and the current lunation duration is one of the most complex tasks of the lunar theory or the ephemeris calculation of the moon.

Annual fluctuations

As a first approximation, the moon moves around the earth on an elliptical orbit. As a result of orbital disturbances by the sun and the planets, however, the point closest to the earth, the perigee , shifts and the apses rotate in the direction of rotation . Therefore, an orbit related to the recurring perigee, an anomalistic month , lasts longer than the sidereal month , which is related to the position in front of the fixed star background. In general, the moon moves faster when it is close to perigee and more slowly in apogee, the point furthest from the earth. The dates for the new moon and full moon, however, are not determined according to perigee or fixed star reference, but rather according to the position of the moon orbiting the earth to the sun: At new moon the moon is close to the sun in conjunction between earth and sun, at the full moon, conversely, it is in opposition away from the sun . Towards the new moon date it moves towards the sun. If the perigee then also lies in the direction of the sun, the moon moves faster and, due to the stronger gravitational effect from the sun, now even faster than would be expected for the undisturbed two-body system earth-moon based on Kepler's laws alone . In addition, these two form a double system and thus circle around the earth-moon center of gravity (EMS); However, since "(ecliptical) conjunction" is a term defined for the centers of the earth, moon and sun, those periods of time that it takes until EMS-moon-sun are added or subtracted in addition to those for the orbit of the moon are added or subtracted , but the center of the earth – moon – sun are in one line. If the new moon is close to the earth, the earth covers this distance in a shorter time than if the moon is far from the earth. The lunations therefore reach a minimum when the new moon and the perigee passage coincide, or they last ever shorter until the point in time at which the apsidal line (the connecting line perigee-apogee) coincides with the earth-sun line. Thereafter, the lunation durations increase again in the course of the year and reach a maximum when the full moon date falls on the passage of the perigee. The moon runs progradly around the earth, in the same direction as the earth around the sun; at the new moon it therefore apparently moves against the direction of the earth.

Variations in the cycle of the apses

The perigee of the lunar orbit ellipse moves around the earth in an interval of about 8.85 years ( apse rotation of the moon; difference between the slightly longer anomalous month and the sidereal lunar month). Therefore, viewed over a longer period of time, there are relatively small differences in some years, but relatively strong in others, within the annual fluctuations of the lunation periods. Because if the perigee is traversed to a date which is near the perihelion of the earth (the point of the earth's orbit near the sun, around January 3rd, to which the earth moves fastest), the difference between the short lunations becomes of the new moons near the perigee and the longer ones of the new moons near the apogee attenuated. Conversely, when the moon passes through its perigee near the aphelion of the earth (around July 5th), the differences between the short and long lunations are roughly twice as great.

Further fluctuations

As a result of different degrees of orbital disturbances by the other bodies of the solar system, the shape of the lunar orbit differs not insignificantly from that of an exact (Kepler) ellipse; This means that the duration of the lunation is also subject to further short-term and long-term periodic fluctuations which - with a fluctuation range well below an hour - are superimposed on one another.

Overall, the duration of current lunations varies between about 29.272 d and 29.833 d, with −0.259 d (6 h 12 min shorter) to +0.302 d (7 h 15 min longer) around the middle lunation. This variation of the lunations applies to the interval 1900 to 2100.

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Lunation duration - annual and apsidal-cyclical fluctuations 2000–2018

Full moon and new moon dates

In relation to a lunation span, the duration of which is determined by the new moon dates, the date of the full moon is only roughly in the middle, but not exactly. The fluctuations in the time interval from the full moon to the new moon do not only depend on the different constellation earth to sun (perihelion / aphelion) over the course of the year. The position of the lunar perigee in relation to the sun also has a significant influence (in the course of the lunation duration shown above, recognizable as cyclical changes over about nine years). The indication of the fluctuation ranges caused by this is somewhat less precise in relation to the full moon than in relation to the new moon date; That is why in modern astronomy - which in this question is no longer primarily based on observations, but on numerical calculation models and approximation methods - the lunations are calculated from conjunction to conjunction. Their exact point in time cannot be easily measured, however, since the new moon takes place in the daytime sky or at night below the horizon.

Astrometric new and full moon dates are calculated ecliptically , true new and full moon ( phase angle maximum / minimum, i.e. minimum / maximum illumination of the moon) then fluctuate again around the tabulated date and also depend on the observation location ( topocentric coordinates ); these fluctuations remain under an hour. New moon or full moon occur as events when the observer, moon and sun are in a line or the distance between the moon and the observer-sun line becomes minimal during a lunation (the center points of are exactly in line with the observer's eye Sun and moon probably never). If the distance is sufficiently small, there can be a lunar eclipse at the full moon and a solar eclipse at the new moon .

The lunar calendar month

→ Main article : Lunar calendar

The lunar month is probably - next to day and night  - the most obvious astronomical time parameter and should therefore also form the basis of the earliest calendar models. Today, astronomical lunar calendars, i.e. those that determine the calendar date according to the actual lunations, are still common in Saudi Arabia (moon sighting of the new light ) and some indigenous cultures . All other cultures that use lunar calendars work with an arithmetic calendar system based on the calculated size of the synodic month .

Since the introduction of the Julian calendar in 46 BC. A calendar month only has a name to do with a synodic month. The lunar phases of lunations no longer correlate with these calendar months, but tend to shift backwards against the monthly dates over the course of a year - because on average one month of the Gregorian calendar lasts around 30.44 d (365.2425 d / 12) longer than the synodic one Orbit period of the moon - except in February.

The lunation number

Lunations are numbered consecutively in astronomy. This number is known as the lunation number , and there are different conventions for the beginning of the series counted. The older lunation number introduced by E. W. Brown in connection with his lunar theory takes the year 1923 as the beginning:

L _Brown (BLN): Lunation “1” begins after January 1, 1923 12:00 ( JD  2423421,0):
The new moon of lunation 1 took place on January 17, 1923 3:41 (2:41 UTC ).

In addition, a count is also used that begins with the year 1900:

L ₁₉₀₀ : The lunation "0" begins after December 31, 1899 19:31 (JD 2415020,313) with the standard epoch B1900.0 :
The new moon of lunation 0 took place on January 1, 1900 14:51 (13:51 UTC ) instead of.

The Brown lunation number can be determined using the formula . ${\displaystyle L_{\mathrm {Brown} }=L_{\mathrm {1900} }-284}$

Alternatively, an updated counting method based on Jean Meeus is increasingly being used today, starting in 2000:

L ₂₀₀₀ : The lunation "0" begins after January 1, 2000 11: 58: 55.816 (JD 2451545.0) with the current standard epoch J2000.0 :
The new moon of lunation 0 took place on January 6, 2000 19:14 (18 : 41 UTC).

The conversion works with: ${\displaystyle L_{\mathrm {Brown} }=L_{\mathrm {2000} }+953}$

The current new moon date can therefore be estimated with:

${\displaystyle \mathrm {JD} 2451545,0+L_{\mathrm {2000} }\cdot 29{,}530589\pm 0{,}25}$

Web links

• The Lunations of 2018. APOD animation, September 12, 2018

Individual evidence

1. ^ ^{A b c} Jean Meeus : Astronomical Formulas for Calculators. 4th edition. Willmann-Bell, Richmond (VA) 1988 - after Eric Weisstein: Lunation. In: scienceworld.wolfram.com. April 26, 2006.
2. ↑ In fact, the relative speed of the moon to the earth is significantly smaller than that of the earth to the sun; Viewed heliocentrically, both move in the same direction.
3. ↑ John Walker's Home Planet (Version 3.2, Windows ) 2002 - ( web link ).
4. ^ Hermann Mucke , Jean Meeus: Canon of Solar Eclipses -2003 to +2526 , 3rd edition, p. XXX. Astronomical Office Vienna, 1992
5. ↑ Fred Espenak , Jean Meeus: Five Millennium Catalog of Solar Eclipses: –1999 to +3000 , p. 2. NASA Goddard Space Flight Center, 2009
6. ↑ Weisstein: Lunation. Converted to L ₂₀₀₀ .