Variations in month-length

On average, a lunar month (or lunation) is 29 days 12.73 hours, but it can sometimes be as short as 29 days 6½ hours, or as long as 29 days 20 hours. Fluctuations in length are cyclic. There is a fast cycle averaging about 412 days (which is just under 14 lunar months); this is associated with changes in the eccentricity, or shape of the lunar orbit. That rapid cycle is modified by a slower one whose mean wavelength is 8.85 years (equal to one complete revolution of the axis of the moon's elliptical orbit). In addition, there are other oscillations, some causing variations extending over many hundreds of years - when it may not even make sense to look for an average wavelength.

Other factors too contribute to the moon's complex behaviour. For instance, longer than normal lunations tend to occur between October and March because of faster movement by the Earth in its orbit round the sun. In February and March, this delays the instant when the moon appears to overtake the sun. Also, the sun lies closer to a newborn crescent than it would if Earth's speed was uniform - thus postponing the onset of New Moon visibility. In October and November, on the other hand, the sun's position on the ecliptic line is "behind schedule" - so the moon overtakes it earlier.

Occasionally, four consecutive lunations will span more than 119 days. Under those circumstances, it is possible to have four successive 30-day months. When that happens, the moon only just becomes visible at the beginning of the first month in the sequence, and just fails to do so on the 29^th of the fourth month.
 
 

The effects of changing geographic (and lunar) longitude or latitude

The Islamic world does not have a uniform policy regarding the acceptance of crescent sightings from other countries when deciding whether or not to declare the onset of a new month. Many authorities will consider only observations made from within their own national boundary. At least once in the past, however, evidence from the Yemen has been cited for the commencement of Ramadan in the United Arab Emirates. Furthermore, many Ihna'asheri Shi'ites are happy to abide by reports made even in another continent - provided they can receive such evidence before their own dawn next morning.

Crescent spotting at dusk tends to become easier as one moves westwards. This is because sunset times become steadily later - when expressed in Universal Time (UT). In fact, in northwest Africa the sun sets approximately eight hours after it does in southeast Asia, and during that interval a New Moon moves an extra four degrees away from the sun - which could make all the difference between a successful sighting and a failure.

Often, a newborn crescent will be much more obvious in the opposite hemisphere, because of seasonal variations in the angle between the ecliptic and the horizon at dusk. In the Northern Hemisphere, this angle is at its steepest during March, thereby maximising the altitude of the New Moon just after sunset. However, in the Southern Hemisphere, that angle is shallowest in March.

Six months later, those relationships are reversed. Thus, it is much easier to spot the crescent from southeast Africa than from Lebanon in September, despite the fact that UT sunset times in those two territories are very similar during this month.

The height of the New Moon above the setting sun is also affected by lunar latitude.If the moon is five degrees below the ecliptic in September, then it will be harder to identify it from the Northern Hemisphere. When south of the equator, the problem becomes much worse when lunar latitude is positive during March (because the southern sky is "upside down" when compared with that seen in the north).
 
 

Predetermined calendars

A predetermined calendar would certainly make it easier to plan events. Unfortunately, it is not always possible to predict that a newborn crescent will definitely be visible or invisible from a given location, because of the wide grey area separating the two categories. This uncertainty is caused by day to day fluctuations in atmospheric water vapour and dust content.

The Bohra community never bothers about moon-sighting, but instead follows a precalculated calendar based on a cycle of 30 Islamic years (eleven of which contain 355 days instead of the more common 354 - thus totalling 10631 days). The accumulated error in that calendar is about one hour per century. This, together with the cyclic variations in the behaviour of the lunar orbit, can bring the Bohra dates two (or on rare occasions even three) days earlier than those governed strictly by crescent visibility. In 1412 H., for example, Bohra Ramadan commenced on the morning of 4^th March 1992, whereas throughout much of India and the Far East, fasting did not start till 7^th March.

There are of course other ways in which a predetermined calendar might be constructed. Mathematical criteria could be laid down - and adopted regardless of whether or not the crescent happens to be observed. Such guidelines might be based, for example, on the age of the New Moon at dusk (suitably defined), or the lag between sunset and moonset, or the number of degrees separating the sun and moon as they descend. It is then essential to specify either the exact time at which the criteria are to be applied (see next section) - or the precise location; (for example, Mecca would probably be universally acceptable).
 
 

A calendar based on sun-moon separation

Let us choose a time when dusk is falling on the extreme western edge of Africa and Europe - say 19.00 Universal Time. (Certainly, it varies with season and with latitude, but in order to construct a precalculated calendar, a sharply defined dividing line needs to be laid down). Calculate the celestial separation between sun and moon: if it exceeds eight degrees, then a new Islamic month should start that evening. (Of course different parameters could be used, as long as some sort of "threshold" is laid down rigorously).

The difference in solar and lunar celestial longitude and latitude determines their total separation (which is simply the hypotenuse of the spherical triangle). Atmospheric refraction and lunar diurnal parallax are not involved at all.

If the separation less than eight degrees, then there is no likelihood of the crescent being spotted from Africa, Europe, or south/west Asia; those territories could then share the same Islamic dates. However, it would be better for America to adopt a later time for their calculations; similarly, the Far East and Australasia could base their decision on the sun-moon separation on an earlier hour - (say) 12.00 Universal Time.
 
 

Two calendars based on lunar birth-time

Another decision-process could be based on the time of birth of New Moon, which is the instant when the centre of the moon crosses the line joining the centres of the Earth and Sun. That moment is therefore the same for every country. Astronomers can predict it well in advance to within a few seconds (but only in "Dynamic Time" - see below); laser measurements can then confirm it afterwards to a fraction of a second.

Saudi Arabia (along with the other countries in its "orbit") utilised such a calendar for a while during the 1990's. If a New Moon was due to be born during a particular night, then they would usually declare the new month at the start of that night. Often, this meant that their dates were as much as two days earlier than elsewhere in the Middle East.

Another possible rule based on lunar birth-time is "Identify the date on which the New Moon is born; the next month should then commence at sunset on the following day". So, if the moon has not yet "caught up" with the sun at midnight, wait another 24 hours and apply the test again. If midnight Universal Time is chosen, then that calendar will correspond reasonably well with the first appearance of the crescent throughout most of Asia and Africa. However, this type of rule should not be regarded as a rigid and infallible guide as to whether or not the crescent will be seen. Nevertheless, a system like this would at least yield the same Islamic dates for every country in the world.

Obviously, midnight in any other time zone could just as easily be adopted - but there should be universal acceptance of whichever zone is chosen.
 
 

Earth's changing rotation-speed

A precalculated Islamic calendar can usually be extended quite far into the future. The main limitation involves uncertainty over future variations in our day-length. This would apply equally to a calendar based on New Moon birth-time, and to one determined (say) by the lag between sunset and moonset at Mecca.

Our planet's rate of spin is not constant, but is gradually slowing down, mainly due to tidal friction. There are also irregular fluctuations in this deceleration, imposed by tectonic and volcanic convulsions, as well as by changes in magnetic coupling effects deep within Earth's interior. Thus, an accurate clock started 3000 years ago would now show the instant of noon to be "wrong" by several hours: this has been confirmed by detailed examinations of the times and positions of ancient eclipses.

It is therefore necessary to have two parallel time-scales - first, the already familiar Universal Time - in which the Greenwich sun really does attain its zenith at noon (on average). The other scale (Dynamic Time) is determined by an atomic clock which is completely "unaware" of variations in Earth's rotation. An arbitrary decision was made to regard those two systems as synchronised in AD 1902. Since then, Dynamic Time has moved ahead of UT, as expected. The discrepancy between the two is known as the DT (Delta-T) value for the year, or even the day being considered.

It is impossible to predict future values of DT accurately. At the beginning of AD 1999, it was 64 seconds. By AD 2100 it will probably be between about 3 and 5 minutes.

Based on the UT birth of New Moon, an Islamic calendar could be calculated and published now for every year up to and including 1510 H. In 1511 H., however, the Ramadan moon will be born very close to a UT midnight - so we do not yet know which date to choose for applying the "rule". If DT on that date is 3.3 minutes or more, then fasting should commence on 24^th March 2088. If DT is 2.9 minutes or less, however (which is quite possible), then the morning of the 25th will become the 1^st of Ramadan.

By the beginning of 1511 H. (in fact probably earlier), we will almost certainly know how DT will affect the date of birth of the subsequent Ramadan moon.
 
 

References & bibliography

HOW LONG IS A LUNAR MONTH? Ala'a H. Jawad. Sky & Telescope, November 1993, pp. 76-77. The lunar cycles are illustrated graphically. Resonance between lunations and anomalistic months is also important.

EXTREME PERIGEES AND APOGEES OF THE MOON. Jean Meeus. Sky & Telescope, August 1981, pp. 110-111. This discusses the 206-day cycle in eccentricity. Low perigee values occur alternately at Full Moon and New Moon, so the complete double-cycle is the one associated with variations in lunation length.

LES DUREES EXTREMES DE LA LUNAISON. Jean Meeus. L'Astronomie (Société de France), July-August 1988 (vol. 102), pp. 288-289. This describes the 8.85-year cycle.

THE ACTUAL SAUDI DATE SYSTEM. See internet address http://www.jas.org.jo/sau.html -
which explains criteria adopted at various times by the Higher Council Majlis al-Ifta' al-A'ala in Saudi Arabia.

A UNIVERSAL ISLAMIC CALENDAR. David McNaughton. Hamdard Islamicus (Karachi), January-March 1997 (vol. XX, no. 1), pp. 77-85. (Diagram misprints were subsequently corrected and reprinted in vol. XX, no. 3, p. 101). Based on New Moon birth in UT, Islamic dates are calculated for 1416 to 1419 H, and past and future instances of four successive 30-day months are tabulated. (When crescent visibility is the criterion, this is more likely to happen in the Southern Hemisphere - where a fifth consecutive long month is even possible!) Diagrams illustrate the ecliptic and the effect of lunar latitude. Table 2 gives other dates with marginal values of DT.

ON THE SMALLEST VISIBLE PHASE OF THE MOON. J.K. Fotheringham. Monthly notices of the Royal Astronomical Society, 1910 (vol. 70), pp. 527-531. The relationship between crescent visibility and vertical height (and azimuth displacement) is also shown on p.323 of Sky & Telescope, September 1989. Similar graphs are used by Mohammad Ilyas in Malaysia; see for example "Limiting altitude separation in the New Moon's first visibility" in Astronomy & Astrophysics, 1988 (vol. 206), pp. 133-135.

LUNAR CRESCENT VISIBILITY. Bradley E. Schaefer. Quarterly Journal of the Royal Astronomical Society, 1996 (vol. 37), pp. 759-768. The grey area between success and failure is amply illustrated. Detailed crescent observations are tabulated in this and in earlier references.

ASTRONOMICAL ALGORITHMS. Jean Meeus. Willmann-Bell Inc., Richmond, Virginia, 1991. Chapters 47 and 48 discuss the lunar orbit. Chapter 9 is devoted to DT, containing formulae constructed by F. Richard Stevenson and Leslie V. Morrison.

EXPLANATORY SUPPLEMENT TO THE ASTRONOMICAL ALMANAC. University Science Books, Mill Valley, California, 1992. See "Terrestrial coordinates and the rotation of the Earth"; figures 4.51.2 to 4.51.4 depict historic values of DT. Section 12.411 discusses calendars.

THE DAY TIME STANDS STILL. Leslie V. Morrison. New Scientist, 27 June 1985, pp. 20-21 (regarding DT). Also see New Scientist, 30 January 1999, pp. 30-33, and Sky & Telescope, February 1999, pp. 53-55.

THE EARTH'S INCONSTANT ROTATION. John Wahr. Sky & Telescope, June 1986, pp. 545-549.
 
 
 
 

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