by David L. McNaughton

In "Hamdard Islamicus" (Karachi, Pakistan), vol. XIX no. 1 (Spring 1996): pp. 81-86.

Characteristics of Solar Eclipses

The sight of a total eclipse of the sun is an awe-inspiring experience. Daylight quickly becomes near-darkness, and all birdsong ceases as those creatures are deceived into thinking that night has fallen.

However, only a small area of the globe enjoys the privilege of admiring the total phase of such an eclipse whenever one sweeps across our planet. Even so, astronomers can now predict accurately those places and their times - enabling many of them to go and witness such an event. Total solar eclipses provide by far the best opportunity to study the seething atmosphere in the sun's outer atmosphere, so scientists are always present to take photographs and carry out spectrographic and other measurements.

A solar eclipse can occur only at New Moon, but not every New Moon produces a solar eclipse. That is because the plane containing the lunar orbit is inclined to the plane defined by Earth's much larger orbit round the sun (called the "ecliptic" plane). Thus, at the instant of its birth a New Moon's position in the celestial firmament is usually either above or below the sun: under those circumstances the sun cannot become eclipsed.

About twice every year, however, New Moon happens to take place just as the moon is passing through the ecliptic plane. That produces almost perfect alignment of the three celestial bodies, enabling the moon to hide the sun from some terrestrial observers. The moon's umbra (full shadow) traces out a comparatively narrow path across Earth's surface; people there see a total eclipse. At the same time, a much larger area of our globe falls within the moon's penumbra (its partial shadow); observers there are close enough to the axis of alignment for the sun to appear partially covered.

Sometimes the umbra just misses the Earth, but a portion of our planet still lies within the penumbra - experiencing a partial eclipse. On rare occasions the umbra can just graze the Earth - but without the axis of the moon's shadow-cone ever intersecting the surface of our planet: such eclipses are termed "total but non-central".

If the lunar orbital plane remained pointing in the same direction, then solar eclipses would always occur near the same Gregorian date, year after year. However, the lunar orbital plane gradually swings round, completing a revolution every 18.6 years; inevitably that movement affects the dates of solar eclipses. The result is that the interval between them tends to be either six or (less commonly) five lunar months. That is why solar calendar dates of eclipses are often slightly earlier than ones experienced during the previous year.

Lunar Eclipses

To produce a lunar eclipse, Earth must lie between the sun and moon. Once again, alignment needs to be nearly exact, so (like a solar one) this sort of eclipse is possible only when the moon is on or near the ecliptic plane. This time it is Earth which is casting the shadow - sometimes over the entire lunar disc (total eclipse); on other occasions on just a portion of it (partial eclipse). A lunar eclipse can take place only at Full Moon, and may be observed from absolutely anywhere in Earth's night-hemisphere.

About two weeks before or after a lunar eclipse, there is always some sort of solar one - because alignment on the first occasion means that there will still be sufficient alignment for the second. In fact, in rare instances it is even possible to have a small partial solar eclipse just prior to the beginning of an Islamic month, followed by a lunar one in mid-month, and then by another small partial solar eclipse near the end of the same month. (A "small" partial eclipse affects a very restricted area of Earth's surface, with just a minute fraction of the solar disc appearing to be covered).

Every now and again, there is an eclipse during the Holy Month of Ramadan - either a lunar eclipse near the middle of the month or a solar one near the end. Islamic months cannot begin until a day or two after a sun-moon conjunction (to give time for the crescent to become visible), so it is not possible to experience a solar eclipse at the beginning of an Islamic month.

A detailed analysis of Ramadan eclipses reveals a surprising pattern: they seem to be restricted to certain dates in the Gregorian calendar. Every total lunar eclipse which has ever occurred during Ramadan, for example, has fallen within one of three short intervals: 22nd February to 13th March, 20th June to 11th July, or 16th October to 7th November (1), which together add up to less than 20 per cent. of the entire year. (To maintain continuity, dates recorded in the old Julian calendar prior to AD 1582 (or 1752) were converted to "extrapolated" Gregorian-style dates for this particular illustration). Thus, there has never been a Ramadan total lunar eclipse in December/January, nor April/May, nor in August/ September. (Eventually there will be, but not for many thousands of years) (2).

Dates of central solar eclipses occurring during Ramadan have ranged from 12th November to 25th December, or from 20th March to 26th April, or from 16th July to 22nd August (3): (as above, these are Gregorian dates). Here, it is appropriate to include annular as well as total eclipses provided they are "central" (i.e. lying on the lunar umbral axis). The only difference with annular eclipses is that they display a narrow ring of sunlight around the dark lunar disc - caused by the moon being slightly further away from us, or by the sun being closer to Earth than normal.

So why do Ramadan eclipses prefer certain dates? They appear to be tuned to a near-synchronisation between three and a half revolutions of the moon's orbital plane - and the 65-year period during which the date of mid-Ramadan migrates twice round our solar calendar. The full explanation for the "date-clustering" is complicated, involving periodic readjustments caused by slow accumulation of the difference between the cycle-lengths in that near-synchronisation (4).

Sometimes a Ramadan will contain a solar and a lunar eclipse. That inevitably provokes comment, because of traditions that such a "double-eclipse" is a portent for some unusual event. Ithna'asheri Shi'ites, for example, believe that their Twelfth Imam will reappear after a Ramadan double-eclipse (although those two phenomena will supposedly take place in reverse order, with the solar one occurring in mid-month (5); that will require the moon to suddenly double its speed of movement after the onset of the Holy Month!)

In March/April 1894 (Ramadan 1311), Mirza Ghulam Ahmad (founder of the Ahmadiyya or Qadiani movement in Pakistan) interpreted a double-eclipse as a sign that he was a genuine modern-day prophet (6). The lunar eclipse during that particular month was only partial, although the solar one two weeks later was total in a few places in eastern Asia (7). However, there was nothing at all extraordinary about those two eclipses: every 22 or 23 Islamic years there is at least one Ramadan featuring a pair of eclipses two weeks apart (8) - one of which is usually partial; see Table 1.

Very much rarer is a Ramadan containing two total eclipses. Table 2 lists all such occasions since AH 1, as well as during the next 200 years (9); (its solar eclipses are all central, with annular ones also included).

It will be interesting to see whether the two total eclipses scheduled to occur during Ramadan 1424 (AD November 2003) - are cited to support a claim similar to that made by Mirza Ghulam Ahmad, or as proof of the significance of some extraordinary event.

TYPE AND DATE

. . . . . . . . . .AH . . .AD . . . . . . . . . . . . . . . .LUNAR . . . . . . . . . SOLAR

. . . . . . . . .1402 . .1982 . . . . . . . . . . . . . . .T . .6 Jul . . . . . . . . .P . .20 Jul
. . . . . . . . .1401 . .1981 . . . . . . . . . . . . . . .P . 17 Jul . . . . . . . .CT .31 Jul

. . . . . . . . .1379 . .1960 . . . . . . . . . . . . . . .T . 13 Mar . . . . . . .P . .27 Mar
. . . . . . . . .1378 . .1959 . . . . . . . . . . . . . . .P . 24 Mar . . . . . . .CA . 8 Apr

. . . . . . . . .1357 . .1938 . . . . . . . . . . . . . . .T . .7 Nov . . . . . . . .P . .21 Nov
. . . . . . . . .1356 . .1937 . . . . . . . . . . . . . . .P . 18 Nov . . . . . . .CA . 2 Dec

. . . . . . . . .1335 . .1917 . . . . . . . . . . . . . . .T . .4 Jul . . . . . . . . . P . .19 Jul
. . . . . . . . .1334 . .1916 . . . . . . . . . . . . . . .P . 15 Jul . . . . . . . .CA .30 Jul

. . . . . . . . .1312 . .1895 . . . . . . . . . . . . . . .T . 11 Mar . . . . . . .P . .26 Mar
. . . . . . . . .1311 . .1894 . . . . . . . . . . . . . . .P . 21 Mar . . . . . . .C . . .6 Apr

. . . . . . . . .1290 . .1873 . . . . . . . . . . . . . . .T . .4 Nov . . . . . . . .P . .20 Nov
. . . . . . . . .1289 . .1872 . . . . . . . . . . . . . . .P . 15 Nov . . . . . . . C . 30 Nov

. . . . . . . . .1267 . .1851 . . . . . . . . . . . . . . .P . 13 Jul . . . . . . . . CT . 28 Jul

. . . . . . . . .1245 . .1830 . . . . . . . . . . . . . . .T . . 9 Mar . . . . . . . .P . .24 Mar
. . . . . . . . .1244 . .1829 . . . . . . . . . . . . . . .P . 20 Mar . . . . . . . CT . .3 Apr

. . . . . . . . .1223 . .1808 . . . . . . . . . . . . . . .T . .3 Nov . . . . . . . . P . .18 Nov
. . . . . . . . .1222 . .1807 . . . . . . . . . . . . . . .P . 15 Nov . . . . . . . .C . .29 Nov

. . . . . . . . .1200 . .1786 . . . . . . . . . . . . . . .T . 11 Jul . . . . . . . . CT . .25 Jul

. . . . . . . . .1178 . .1765 . . . . . . . . . . . . . . .T . .7 Mar . . . . . . . . .P . .21 Mar
. . . . . . . . .1177 . .1764 . . . . . . . . . . . . . . .P . 18 Mar . . . . . . . .CA . .1 Apr

. . . . . . . . .1156 . .1743 . . . . . . . . . . . . . . .T . .2 Nov . . . . . . . . .P . . 16 Nov
. . . . . . . . .1155 . .1742 . . . . . . . . . . . . . . .P .12 Nov . . . . . . . . .CA .27 Nov

. . . . . . . . .1133 . . 1721 . . . . . . . . . . . . . . T. . 9 Jul. . . . . . . . . . P . . 24 Jul

. . . . . . . . .1110 . . 1699 . . . . . . . . . . . . . . P . .15 Mar . . . . . . . .C . .31 Mar

. . . . . . . . .1089 . . 1678 . . . . . . . . . . . . . . T . .29 Oct . . . . . . . . P . .14 Nov
. . . . . . . . .1088 . . 1677 . . . . . . . . . . . . . . P . . .9 Nov . . . . . . . CT . 24 Nov

. . . . . . . . .1066 . . 1656 . . . . . . . . . . . . . . T . . .6 Jul . . . . . . . . .(T) . 21 Jul

. . . . . . . . .1044 . .1635 . . . . . . . . . . . . . . .T . . .3 Mar . . . . . . . . P . 18 Mar
. . . . . . . . .1043 . .1634 . . . . . . . . . . . . . . .P . .14 Mar . . . . . . . .CT .29 Mar

. . . . . . . . .1022 . .1613 . . . . . . . . . . . . . . .T . .28 Oct . . . . . . . . .P . 12 Nov
. . . . . . . . .1021 . .1612 . . . . . . . . . . . . . . .P . . .8 Nov . . . . . . . . C . 22 Nov

. . . . . . . . . .999 . . 1591 . . . . . . . . . . . . . . T . . .6 Jul . . . . . . . . . .P . .20 Jul
. . . . . . . . . .998 . . 1590 . . . . . . . . . . . . . . P . .17 Jul . . . . . . . . . CA .31 Jul

Notes for Table 1

Dates apply to the instant of maximum eclipse.

Lunar eclipses: P=Partial; T=Total;
Central lunar eclipses are always total.

Solar eclipses: CA=Central and Annular; CT=Central and Total;
(T)=Total but non-central; P=Partial;
C=Central, alternating between Total and Annular.

Table 2: Ramadans with two central eclipses

. . . . . . . . . . . . . . . . . . . . . . . LUNAR . . . . . . . . . . . . . . . . . . . . . . . . . . SOLAR

AH . . AD . . . . . . . . . . Date . . . Where visible . . . . . . . . . . . . . . . Date . . .Where visible

.283 . .896 . . . . . . . ..29 Oct . . .Pacific & adjacent . . . . . . . . . . 12 Nov . Canada; Alaska;
. . . . . . . . . . . . . . . . .(25 Oct) . . landmasses . . . . . . . . . . . . . . . .(8 Nov) . NE Pacific

.305 . .918 . . . . . . . . .5 Mar . . .Eurasia; . . . . . . . . . . . . . . . . . . .20 Mar . .Antarctic; south
. . . . . . . . . . . . . . . . .(28 Feb) . .NE Africa . . . . . . . . . . . . . . . . .(15 Mar) . .Indian Ocean

.462 . 1070 . . . . . . . . .2 Jul . . . Pacific & adjacent . . . . . . . . . . . 16 Jul . . .Arctic; Siberia
. . . . . . . . . . . . . . . . . (26 Jun). . .landmasses . . . . . . . . . . . . . . . .(10 Jul)

.529 . 1135 . . . . . . . . . 4 Jul . . . America; Pacific; . . . . . . . . . . . .19 Jul . . .Antarctic; far
. . . . . . . . . . . . . . . . . . (27 Jun) . New Zealand . . . . . . . . . . . . . .(12 Jul) . . .south Pacific

.596 . 1200 . . . . . . . . . 5 Jul . . . Pacific & adjacent . . . . . . . . . . *19 Jul . Siberia; Arctic;
. . . . . . . . . . . . . . . . . . (28 Jun) . .landmasses . . . . . . . . . . . . . . . (12 Jul) . . NW Atlantic

1200 . 1786 . . . . . . . . .11 Jul . . .Pacific & adjacent . . . . . . . . . . .25 Jul . . South Africa &
. . . . . . . . . . . . . . . . . . . . . . .. . . . landmasses . . . . . . . . . . . . . . . . . . . . . . adjacent oceans

1424 . 2003 . . . . . . . . . 9 Nov . . .Europe; SW Asia; . . . . . . . . . . 23 Nov . Antarctic; south
. . . . . . . . . . . . . . . . . . . . . . . . . . .Africa; America . . . . . . . . . . . . . . . . . . . . Indian Ocean

1580 . 2155 . . . . . . . . .9 Mar . . Europe; Africa; . . . . . . . . . . . . . *2 Apr . .China; Russia;
. . . . . . . . . . . . . . . . . . . . . . . . . . .America . . . . . . . . . . . . . . . . . . . . . Kashmir; Mongolia;
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .Afghanistan

Notes for Table 2

Central lunar eclipses are always total.
*The central solar eclipses listed above are total unless asterisked - in which case they are annular.
Dates apply to the instant of maximum eclipse.
Extrapolated Gregorian dates are given even on occasions when the old Julian calendar was in operation;
the corresponding Julian date is then shown below in brackets.

NOTES and REFERENCES

1. Bao-Lin Liu and A.D. Fiala, "Canon of Lunar Eclipses, 1500BC- AD3000", 1992; Willmann-Bell Inc., Richmond, Virginia.

Or: J. Meeus and H. Mucke, "Canon of Lunar Eclipses, -2002 to 2526", 1983 (2nd edition); Astronomical Office, Vienna. See also note 2.

2. Eclipses may also be examined with computer software such as EclipseMaster, MoonTracker, SunTracker and AstroCalc; Zephyr Services, Pittsburgh, Pennsylvania. To help with the preparation of Tables 1 and 2, AstroCalc was modified to print out celestial positions of the Sun and Moon near each Ramadan (i.e. every 354.367 days). Occasions when the mid-Ramadan Full Moon or the Eid New Moon were close to the ecliptic plane could then be highlighted - demonstrating that this occurs every 22 or 23 Islamic years.

3. Ibid. See also H. Mucke and J. Meeus, "Canon of Solar Eclipses, -2003 to +2526", 1983; Astronomical Office, Vienna.

4. Letter from D.L. McNaughton to the "Journal of the British Astronomical Association" volume 105 no. 4 (1995); (it has been appended here).

5. Attributed to the Fifth Imam of the Shi'ites - Muhammed al-Baqir ibn Ali ibn Husayn - who was describing events which would precede the eventual appearance of the Mahdi. Narrated by Amar ibn Shamir, quoting Jabir; see "Dar-e-Qatni" volume I, p. 188.

6. See Mirza Ghulam Ahmad, "Ruhani Khaza'in" volume 17, p. 132.

7. See notes 1, 2 and 3 above.

8. Ibid.

9. Ibid.

Letter to the Journal of the British Astronomical Association 105/4, 1995

(From Dr David L. McNaughton)

Recently I was asked to examine occurrences of all lunar eclipses during Ramadan since AD 622 (i.e. since the beginning of the Islamic era), and an unexpected pattern emerged. I am trying to put together a tentative explanation for the pattern, and would appreciate comments.

Every total lunar eclipse taking place during Ramadanhas been restricted to certain dates, comprising the three short intervals 22 February to 13 March, 20 June to 11 July and 16 October to 7 November. (To maintain continuity, dates recorded in the old Julian calendar prior to AD 1582 (or 1752) were converted to 'extrapolated' Gregorian-style dates for this particular illustration).

So why do Ramadan eclipses prefer certain dates? They appear to be tuned to a near-synchronisation between three and a half revolutions of the moon's orbital plane - and the 65-year period during which the date of mid-Ramadan migrates twice round our solar calendar. (Is that close resonance purely accidental?)

Detailed eclipse calculations do actually reveal a very slow drift: e.g. after AD 3000 those Ramadan eclipses will tend to move into late March, late July and mid-November.

Ramadan total lunar eclipses may be grouped into three parallel series. Each such progression comprises events 65 years and 2 days apart (on average). That is of course virtually the same as 67 Islamic years (804 lunations). (Furthermore, this time-span is just two hours short of 872½ draconic months). The three parallel series are separated by phase differences of 21 or 22 years; at present they comprise March, July and (mostly) November eclipses respectively.

Within each progression, the two extra days every 65 years do cause a slow but steady date-shift which continues for a few centuries. However, that gradually moves the eclipses away from the lunar nodal points, so this date-shift cannot be maintained indefinitely. Eventually, the progression is disrupted by a 'backward jump', which occurs after two successive Ramadans witness a total lunar eclipse. The second member of that pair then takes over as the starting point of a new series of eclipses 65 years and 2 apart, but containing dates displaced 11 days earlier than those taking place in the first series. Thus, this readjustment process interferes with and retards the tendency for Ramadan eclipses to drift.

References and Software

See notes 1 and 2 of the main paper above.

David McNaughton - e-mail: DLMcN@yahoo.com