Lunar standstill

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A lunar standstill is the gradually varying range between the northern and the southern limits of the Moon's declination, or the lunistices, over the course of one-half a sidereal month (about two weeks), or 13.66 days. (Declination is a celestial coordinate measured as the angle from the celestial equator, analogous to latitude.) One major, or one minor, lunar standstill occurs every 18.6 years due to the precessional cycle of the lunar nodes at that rate.

At a major lunar standstill, the Moon's range of declination, and consequently its range of azimuth at moonrise and moonset, reaches a maximum. As a result, viewed from the middle latitudes, the Moon's altitude at upper culmination (the daily moment when the object appears to contact the observer's meridian) changes in just two weeks – from highest to lowest above the horizon due north or south, depending on the observer's hemisphere. Similarly, its azimuth at moonrise changes from northeast to southeast and at moonset from northwest to southwest.

This time appears to have had special significance for the Bronze Age societies, who built the megalithic monuments in Britain and Ireland. It also has significance for some neopagan religions. Evidence also exists that alignments to the moonrise or moonset on the days of lunar standstills can be found in ancient sites of other ancient cultures, such as at Chimney Rock in Colorado and Hopewell Sites in Ohio.

Origin of name[edit]

The term lunar standstill was apparently first used by archeologist Alexander Thom in his 1971 book Megalithic Lunar Observatories.[1] The term solstice, which derives from the Latin solstitium: sol- (sun) + -stitium (a stoppage), describes the similar extremes in the Sun's varying declination. Neither the Sun nor the Moon stands still, obviously; what stops, momentarily, is the change in declination. The word tropic, as in Tropic of Capricorn, comes from ancient Greek meaning "to turn", referring to how ascending (or descending) motion turns to descending (or ascending) motion at the solstice.[2]

Informal explanation[edit]

Lunar standstill.GIF

As Earth rotates on its axis, the stars in the night sky appear to follow circular paths around the celestial poles. (This daily cycle of apparent movement is called diurnal motion.) All the stars seem fixed on a celestial sphere surrounding the observer. In the same way that positions on Earth are measured using latitude and longitude, the apparent places of stars on this sphere are measured in right ascension (equivalent to longitude) and declination (equivalent to latitude). If viewed from a latitude of 50° N on Earth, any star with a declination of +50° would pass directly overhead (reaching the zenith at upper culmination) once every sidereal day (23 hours, 56 minutes, 4 seconds), whether visible at night or obscured in daylight.

Unlike the stars, the Sun and Moon do not have a fixed declination. Since Earth's rotational axis is tilted about 23.5° with respect to a line perpendicular to its orbital plane (the ecliptic), the Sun's declination ranges from +23.5° on the June solstice to −23.5° on the December solstice, as Earth orbits the Sun once every tropical year. Therefore in June, in the Northern Hemisphere, the midday Sun is higher in the sky, and daytime then is longer than in December. In the Southern Hemisphere, the situation is reversed. This obliquity causes Earth's seasons.

The Moon's declination also changes, completing a cycle once every lunar nodal period: 27.212 days. Thus, lunar declination ranges from a positive value to a negative one in just under two weeks, and back. Consequently in under a month, the Moon's altitude at upper culmination (when it contacts the observer's meridian) can shift from higher in the sky to lower above the horizon, and back.

The Moon differs from most natural satellites around other planets in that it remains near the ecliptic (the plane of Earth's orbit around the Sun) instead of Earth's equatorial plane. The Moon's maximum and minimum declination vary because the plane of the Moon's orbit around Earth is inclined about 5.14° with respect to the ecliptic plane, and the spatial direction of the Moon's orbital inclination gradually changes over an 18.6-year cycle, alternately adding to or subtracting from the 23.5° tilt of Earth's axis.

Therefore, the maximum declination of the Moon varies roughly from (23.5° − 5° =) 18.5° to (23.5° + 5° =) 28.5°. At the minor lunar standstill, the Moon will change its declination during the nodal period from +18.5° to −18.5°, for a total range of 37°. Then 9.3 years later, during the major lunar standstill, the Moon will change its declination during the nodal period from +28.5° to −28.5°, which totals 57° in range. This range is enough to bring the Moon's altitude at culmination from high in the sky to low above the horizon in just two weeks (half an orbit).

Strictly speaking, the lunar standstill is a moving position in space relative to the direction of Earth's axis and to the rotation of the Moon's orbital nodes (lunar nodal precession) once every 18.6 years. The standstill position does not persist over the two weeks that the Moon takes to move from its maximum (positive) declination to its minimum (negative) declination, and it most likely will not exactly coincide with either extreme.

However, because the 18.6-year cycle of standstills is so much longer than the Moon's orbital period (about 27.3 days) that the change in the declination range over periods as short as half an orbit is very small. The period of the lunar nodes precessing in space is slightly shorter than the lunar standstill interval due to Earth's axial precession, altering Earth's axial tilt over a very long period relative to the direction of lunar nodal precession. Simply, the standstill cycle results from the combination of the two inclinations.

Apparent position of the Moon during standstill[edit]

The azimuth (horizontal direction) of moonrise and moonset varies according to the Moon's nodal period of 27.212 days, while the azimuth variation during each nodal period varies with the lunar standstill period (18.613 years).

For a latitude of 55° north on Earth, the following table shows moonrise and moonset azimuths for the Moon's narrowest and widest arc paths across the sky. The azimuths are given in degrees from true north and apply when the horizon is unobstructed. Figures for a time midway between major and minor standstill are also given.

The arc path of the full Moon generally reaches its widest in midwinter and its narrowest in midsummer. The widest arc path of the new Moon (when it near the Sun in the sky) is in the summer, as for the Sun.[3]

An early-morning moonset in the Mojave Desert, California (February 2016)
Azimuth of full Moon on horizon
(as viewed from 55° north)
narrowest arc widest arc
epoch moonrise moonset moonrise moonset
minor standstill 124° 236° 56° 304°
midway 135° 225° 45° 315°
major standstill 148° 212° 32° 328°

For observers at the middle latitudes (not too near the Equator or either pole), the Moon is highest in the sky in each period of 24 hours when it reaches the observer's meridian. During the month, these culmination altitudes vary so as to produce a greatest value and a least value. The following table shows these altitudes at different times in the lunar nodal period for an observer at 55° north. The greatest and least culminations occur about two weeks apart.

Altitude at culmination
(as viewed from 55° north)
epoch greatest least
minor standstill 53.5° 16.5°
midway 58.5° 11.5°
major standstill 63.5° 6.5°

The following table shows some occasions of a lunar standstill. The times given are for when the Moon's node passed the equinox—the Moon's greatest declination occurs within a few months of these times, depending on its detailed orbit.[4][5] However, the phenomenon is observable for a year or so on either side of these dates.[1]

Times of lunar standstill
major standstill minor standstill
May 1988 February 1997
June 2006 October 2015
April 2025 March 2034[6]
September 2043[6] March 2053[6]

Detailed explanation[edit]

Apparent paths of the Sun and Moon on the celestial sphere (angles exaggerated for clarity)

A more detailed explanation is best considered in terms of the paths of the Sun and Moon on the celestial sphere, as shown in the first diagram. This shows the abstract sphere surrounding the Earth at the center. The Earth is oriented so that its axis is vertical.

The Sun is, by definition, always seen on the ecliptic (the Sun's apparent path across the sky) while Earth is tilted at an angle of e = 23.5° to the plane of that path and completes one orbit around the Sun in 365.25636 days, slightly longer than one year due to precession altering the direction of Earth's inclination.

The Moon's orbit around Earth (shown dotted) is inclined at an angle of i = 5.14° relative to the ecliptic. The Moon completes one orbit around the Earth in 27.32166 days. The two points at which Moon crosses the ecliptic are known as its orbital nodes, shown as "N1" and "N2" (ascending node and descending node, respectively), and the line connecting them is known as the line of nodes. Due to precession of the Moon's orbital inclination, these crossing points, the nodes and the positions of eclipses, gradually shift around the ecliptic in a period of 18.59992 years.

Looking at the diagram, note that when the Moon's line of nodes (N1 & N2) rotates a little more than shown, and aligns with Earth's equator, (from front to back, N1, Earth, and N2, seem to be the same dot), the Moon's orbit will reach its steepest angle with the Earth's equator, and in 9.3 years (from front to back, N2, Earth, N1 seem to be the same dot) it will be the shallowest: the 5.14° declination (tilt) of the Moon's orbit either adds to (major standstill) or subtracts from (minor standstill) the inclination of earth's rotation axis (23.439°).

The declination of the Moon in 2005–06

The effect of this on the declination of the Moon is shown in the second diagram. During the course of the nodal period, as the Moon orbits the Earth, its declination swings from –m° to +m°, where m is a number in the range (e – i) ≤ m ≤ (e + i). At a minor standstill (e.g., in 2015), its declination during the month varies from –(e – i) = –18.5° to +(e – i) = 18.5°. During a major standstill (e.g., in 2005-2006), the declination of the Moon varied during each month from about –(e + i) = –28.5° to +(e + i) = 28.5°.

The maximum declinations of the Moon in 2005–06

However, an additional subtlety further complicates the picture. The Sun's gravitational attraction on the Moon pulls it toward the plane of the ecliptic, causing a slight wobble of about 9 arcmin within a 6-month period. In 2006, the effect of this was that, although the 18.6-year maximum occurred in June, the maximum declination of the Moon was not in June but in September, as shown in the third diagram.

Other complications[edit]

Because the Moon is relatively close to the Earth, lunar parallax alters declination up to 0.95° when observed from Earth's surface versus geocentric declination, the declination of the Moon from the center of the Earth. Geocentric declination may be up to about 0.95° different from the observed declination. The amount of this parallax varies with latitude, hence the observed maximum of each standstill cycle varies according to position of observation.

Atmospheric refraction – the bending of the light from the Moon as it passes through the Earth's atmosphere – alters the observed declination of the Moon, more so at low elevation, where the atmosphere is thicker (deeper).

Not all the maxima are observable from all places in the world – the Moon may be below the horizon at a particular observing site during the maximum, and by the time it rises, it may have a lower declination than an observable maximum at some other date.

2006 standstill[edit]

Events in Sydney, Australia Date/time RA Dec Az. Elev Lunar phase
Closest viewing of "true maximum" on 15 September during civil twilight 14 September 19:53 04:42:57.32 +29:29:22.9 27° 46% waning
Highest visible maximum during civil twilight 4 April 07:49 06:03:11.66 +29:30:34.5 350° 26° 38% waxing
Highest visible maximum during darkness 4 April 09:10 06:05:22.02 +29:27:29.4 332° 21° 39% waxing
Lowest visible minimum during civil twilight 22 March 19:45 18:10:57.40 −28:37:33.2 41° 83° 50% waning
Lowest visible minimum during darkness 22 March 18:36 18:09:01.55 −28:36:29.7 80° 71° 50% waning
Events in London, England Date/time RA Dec Az. Elev Lunar phase
Highest visible maximum during civil twilight 15 September 05:30 06:07:12.72 +28:19:52.6 150° 64° 42% waning
Highest visible maximum during darkness 7 March 19:43 05:52:33.05 +28:18:26.9 207° 64° 60% waxing
Lowest visible minimum during civil twilight 29 September 17:44 17:49:08.71 −29:31:34.4 186° 43% waxing
Lowest visible minimum during darkness 2 September 20:50 18:15:08.74 −29:25:44.0 198° 70% waxing

Note that all dates and times in this section, and in the table, are in UTC, all celestial positions are in topocentric apparent coordinates, including the effects of parallax and refraction, and the lunar phase is shown as the fraction of the Moon's disc which is illuminated.

In 2006, the minimum lunar declination, as seen from the centre of the Earth, was at 16:54 UTC on 22 March, when the Moon reached an apparent declination of −28:43:23.3. The next two best contenders were 20:33 on 29 September, at a declination of −28:42:38.3 and 13:12 on 2 September at declination −28:42:16.0.

The maximum lunar declination, as seen from the centre of the Earth, was at 01:26 on 15 September, when the declination reached +28:43:21.6. The next highest was at 07:36 on 4 April, when it reaches +28:42:53.9

However, these dates and times do not represent the maxima and minima for observers on the Earth's surface.

For example, after taking refraction and parallax into account, the observed maximum on 15 September in Sydney, Australia was several hours earlier, and then occurred in daylight. The table on the right shows the major standstills that were actually visible (i.e. not in full daylight, and with the Moon above the horizon) from both London, UK, or Sydney, Australia.

For other places on the Earth's surface, positions of the Moon can be calculated using the JPL ephemeris calculator.

References[edit]

  1. ^ a b Vincent, Fiona (2005). "A major 'lunar standstill'" (PDF). Journal of the British Astronomical Association. 115 (4): 220. Bibcode:2005JBAA..115..220V. Retrieved 14 January 2012.
  2. ^ Dictionary.com – tropic
  3. ^ Burl, Aubrey (1995). A Guide to the Stone Circles of Britain, Ireland and Brittany. Yale University Press. pp. 19–20. ISBN 9780300063318.
  4. ^ Vincent, Fiona. "Lunar standstills". What's in the sky?. Archived from the original on 14 January 2012.
  5. ^ Vincent, Fiona. "More about lunar standstills". What's in the sky?. Archived from the original on 14 January 2012.
  6. ^ a b c Times of maxima and minima of lunar declination at culmination "Solar System Dynamics". Horizons. NASA Jet Propulsion Laboratory.

External links[edit]