On the Eclipse of Thales, Cycles and Probabilities

Abstract

According to classical tradition, Thales of Miletus predicted the total solar
eclipse that took place on 28 May 585 BCE. Even if some authors have flatly
denied the possibility of such a prediction, others have struggled to find
cycles which would justify the achievement of the philosopher. Some of the
proposed cycles have already been refuted, but two of them, namely those of
Willy Hartner and Dirk Couprie, remain unchallenged. This paper presents some
important objections to these two possibilities, based on the fact that these
authors do not list all the eclipses potentially visible by their criteria. In
addition, any explanation based on cycles will need to face the complex problem
of visibility (smallest observable eclipse, weather...). The present article
also includes a statistical study on the predictability of solar eclipses for a
variety of periods, similar to that performed by Willy Hartner for lunar
eclipses, resulting in lower probabilities in the solar case (and percentages
depend on the chosen magnitude limit). The conclusion is that none of the
cycles proposed so far provides a satisfactory explanation of the prediction,
and, on statistical grounds, none of the periods studied leads to a significant
probability of success with solar eclipse cycles.

Full text

Miguel Querejeta, ‘On the Eclipse of Thales, Cycles and Probabilities’, Culture
And Cosmos, Vol. 15, no. 1, Spring/Summer 2011, pp. 5–16.
www.CultureAndCosmos.org
On the Eclipse of Thales, Cycles and
Probabilities
Miguel Querejeta
Abstract. According to classical tradition, Thales of Miletus predicted the total
solar eclipse that took place on 28 May 585 BCE. Even if some authors have
flatly denied the possibility of such a prediction, others have struggled to find
cycles which would justify the achievement of the philosopher. Some of the
proposed cycles have already been refuted, but two of them, namely those of
Willy Hartner and Dirk Couprie, remain unchallenged. This paper presents some
important objections to these two possibilities, based on the fact that these
authors do not list all the eclipses potentially visible by their criteria. In addition,
any explanation based on cycles will need to face the complex problem of
visibility (smallest observable eclipse, weather…). The present article also
includes a statistical study on the predictability of solar eclipses for a variety of
periods, similar to that performed by Willy Hartner for lunar eclipses, resulting
in lower probabilities in the solar case (and percentages depend on the chosen
magnitude limit). The conclusion is that none of the cycles proposed so far
provides a satisfactory explanation of the prediction, and, on statistical grounds,
none of the periods studied leads to a significant probability of success with
solar eclipse cycles.
Introduction
From supernovae to comets, from planetary motions to eclipses, the
observation of heavenly changes has had a profound influence on
humans from the earliest civilizations to the present day. Total solar
eclipses stand out among these as some of the most spectacular
astronomical events that can be witnessed, and a number of such events
have had a significant effect on history. According to Herodotus, Thales
of Miletus foretold the loss of daylight which put an end to the battle
between the Lydians and Medes; at that time, the battlefield suddenly
being plunged into night was regarded as a bad omen:

On the Eclipse of Thales, Cycles and Probabilities
Culture and Cosmos
6
They were still warring with equal success, when it
happened, at an encounter which occurred in the sixth
year, that during the battle the day was suddenly turned
to night. Thales of Miletus had foretold this loss of
daylight to the Ionians, fixing it within the year in which
the change did indeed happen. So when the Lydians and
Medes saw the day turned to night, they stopped
fighting, and both were the more eager to make peace.1
There is some controversy about the translation of the Greek text, and
a few editions imply that Thales predicted not only the year, but the date
of the eclipse; the latter would make much more sense from the
astronomical point of view, as, ‘if one can predict an eclipse at all, one
can predict it to the day’.2 Therefore, we will refer to the prediction of the
date of the eclipse throughout this paper, and not only to the
announcement of the year when it happened. Cicero, Pliny, and Diogenes
Laërtius, among others, have also referred to the prediction of Thales,
and, in particular, Pliny points out that the event took place in ‘the fourth
year of the 48 Olympiad’,3 which is widely accepted to correspond to
585/4 BCE. In this context, modern calculations show that a solar eclipse
was visible from Asia Minor on 28 May 585 BCE, and the totality path
crossed, in all likeliness, the region where the Lydians and Medes were
fighting.4 Yet, could the Milesian philosopher have predicted such a
special occurrence?
Strenuous efforts have been made to either support or deny the
prediction of Thales. Since the nineteenth century, when the first serious
1 Herodotus, Histories, I.74.2–3, trans. R. Godley (Cambridge Mass.: Harvard
University Press, 1920).
2 Dimitri Panchenko, ‘Thales's Prediction of a Solar Eclipse’, Journal for the
History of Astronomy, Vol. 25 (1994): p. 275.
3 Pliny the Elder, Naturalis Historia, II.53, trans. H. Rackham (Cambridge
Mass.: Harvard University Press, 1942).
4 All eclipse computations correspond to Fred Espenak and Chris O’Byrne,
NASA Goddard Space Flight Centre; this will be commented in detail later. The
battle took place somewhere in the Anatolia peninsula, which was almost
completely covered by the totality path.

Miguel Querejeta
Culture and Cosmos
7
attempts were made to pinpoint the moment of the famous eclipse,5 an
integral part of the debate has depended on whether calculations yielded
totality over Asia Minor for each of the possible dates; after all, the
words of Herodotus ‘the day was suddenly turned to night’ would make
little sense had the eclipse been only partial over the battlefield. Even
quite recently, authors have tried to justify the fact that the eclipse of
Thales should correspond to a variety of dates.6 However, it has been
made clear by Stephenson and Fatoohi that only the eclipse of 28 May
585 BCE could match the visibility required from Asia Minor.7
The complexity of the problem also stems from the fact that the
choice of the date of the eclipse has strong historiographic implications,
as intricate chronological issues are involved.8 This problem is to some
extent independent from the debate as to whether Thales could have
predicted the eclipse: we now know for sure that there was a total solar
eclipse in Asia Minor on 28 May 585 BCE, and this date is in accordance
with the one given by Pliny. The question of the prediction, on the
contrary, is extremely controversial. Some scholars, including Martin and
Neugebauer,9 have flatly denied the prediction, while others have
struggled to find a numerical cycle by means of which the prediction
could have been carried out. Most of these conjectures have already been
5 The first significant attempts correspond to Sir Francis Baily (1811), Sir
George B. Airy (1853), and Prof Simon Newcomb (1878). See John Stockwell,
‘On the eclipse predicted by Thales’, Popular Astronomy, Vol. 9 (1901): pp.
376–89.
6 The eclipse of 30 September 610 BCE has traditionally been considered instead
of the one in 585 BCE in terms of having some chronological advantages.
Panchenko points to the eclipses on 21 September 582 BCE and 16 March 581
BCE based on the assumption that Thales should have used the Exeligmos to
predict the eclipse. See Panchenko, ‘Thales’, pp. 275–88.
7 F. R. Stephenson and L. J. Fatoohi, ‘Thales’s Prediction of a Solar Eclipse’,
Journal for the History of Astronomy, Vol. 28 (1997): pp. 279–82.
8 See, for example, A. A. Mosshammer, ‘Thales’ Eclipse’, Transactions of the
American Philological Association, Vol. 111 (1981): pp. 145–55.
9 Thomas-Henri Martin, ‘Sur quelques prédictions d’éclipses mentionnées par
des auteurs anciens’, Révue Archéologique, Vol. 9 (1864): pp. 170–99. Otto
Neugebauer, The Exact Sciences in Antiquity, 2nd ed. (New York: Dover
Publications, 1969).

On the Eclipse of Thales, Cycles and Probabilities
Culture and Cosmos
8
refuted,10 but there are two of them which stand unchallenged for the
moment: the mechanism proposed by Willy Hartner,11 and a ‘false cycle’
suggested more recently by Dirk Couprie.12
The aim of this paper is to assess the validity of these two proposals,
and also to perform a statistical study analogous to the one carried out by
Willy Hartner for lunar eclipses, in order to know whether the same
results apply to the solar case. This will permit us to conclude whether it
is reasonable to defend that Thales made his prediction based on one of
the cycles which have been discussed in the literature so far.
The Hypothesis of Dirk Couprie
One of the two cycles that remain uncontested corresponds to a recent
study by Dirk Couprie.13 After refuting the proposal of Patricia
O’Grady,14 in his attempt to justify Herodotus’ claim, Couprie resorts to
a ‘false prediction’ by Thales. In his paper, the author suggests that
Thales could have deduced that solar eclipses come in clusters of three
events, judging by the data presumably available to the Milesian
philosopher. The pattern, consisting of three consecutive eclipses, would
span a total of 35 lunations (the time between eclipses in a cluster being
either 17–18 or 18–17 lunations), and these clusters would be separated
by much larger gaps (see Table 1).
10 For example, the eclipse prediction suggested in Panchenko, ‘Thales’, was
proved to be extremely unlikely by Stephenson & Fatoohi, ‘Thales’s Prediction’;
similarly, the prediction mechanism proposed by Patricia O’Grady has recently
been refuted by Dirk Couprie (see note 14).
11 Willy Hartner, ‘Eclipse Periods and Thales’ Prediction of a Solar Eclipse:
Historic Truth and Modern Myth’, Centaurus Vol. 14 (1969): pp. 60–71.
12 Dirk L. Couprie, ‘How Thales Was Able to “Predict” a Solar Eclipse without
the Help of Alleged Mesopotamian Wisdom’, Early Science and Medicine, Vol.
9 (2004): pp. 321–37.
13 Couprie, ‘Thales’.
14 Patricia O’Grady, Thales of Miletus. The Beginnings of Western Science and
Philosophy (Aldershot: Ashgate, 2002). She suggests that Thales used a cycle of
23 ½ months, but this method yields a much smaller probability of success
(23%) than initially calculated by O’Grady.

Miguel Querejeta
Culture and Cosmos
9
One of the most evident problems that this hypothesis poses is the
need for a long list of eclipse records, as the author himself
acknowledges. In particular, the author sets an arbitrary limit of
magnitude 0.5 to the smallest observable eclipse.15 However, even more
important than this is the problem of cloudiness, since an important
fraction of the eclipses making up the list may well have gone unnoticed
due to unfavourable weather conditions. Still, the possibility of all those
eclipses being recorded exists in principle, so the visibility issue cannot
be regarded as a conclusive counter-argument; there is an additional
objection that can be raised to this cycle, however, based on the fact that
the eclipse list is not exhaustive according to the criterium chosen by the
scholar.
The author assumes a limit in magnitude of 0.5 to the eclipses that
Thales could have observed, ‘unless he had a special reason to expect
one’,16 which justifies the inclusion of the eclipse of 9 May 594 BCE
(magnitude 0.46). However, Couprie consciously ignores the eclipse of
17 April 611 BCE, which had a magnitude of 0.45 at the moment of
sunset17; this would have permitted an individual to see virtually half of
the solar diameter eclipsed and, due to the proximity to the horizon, it
would have been possible to observe it with the unaided eye. Moreover,
Couprie admits records since 635 BCE, but makes no mention of the
eclipse of 17 June 633 BCE, which attained a maximum magnitude of
0.66 shortly before sunset (therefore, weather permitting, probably
observable). Similarly, the eclipse of 18 May 603 BCE (magnitude 0.50)
is missing from his list. If we include all these eclipses in the record that
Thales could have made himself, the ‘obviousness of the pattern of
clusters’seems to vanish (see Table 2).18
15 Magnitude is defined as the fraction of the Sun’s diameter obscured by the
Moon, expressed here in decimal units; it is sometimes expressed in digits, or
even as the area of the sun that is blocked by the lunar disk (obscuration). In any
case, increasing magnitude in terms of diameter (decimal or digits) also implies
an increase in the obscuration, so they could ultimately be seen as different
measures of the same thing.
16 Couprie, ‘Thales’, p. 331.
17 All magnitudes and local circumstances of eclipses according to NASA data
(Fred Espenak and Chris O’Byrne, NASA’s GSFC).
18 Couprie, ‘Thales’, p. 337.

On the Eclipse of Thales, Cycles and Probabilities
Culture and Cosmos
10
The Hypothesis of Willy Hartner
One of the most ambitious and interesting studies on the eclipse of
Thales was undertaken in 1969 by Willy Hartner.19 The first part of his
article is devoted to a statistical survey of lunar eclipses and their
predictability according to a number of cycles. The second part lists 29
solar eclipses which might have been observable from Miletus, and based
on the analysis of the repetition pattern, Hartner proposes that Thales
intended to predict the eclipse of 18 May 584 BCE. Such a prediction was
made in some vague terms due to calendrical difficulties, argues Hartner,
which would explain why the Milesian philosopher was acclaimed when
a total solar eclipse took place one year earlier than he expected.
The objections made to this hypothesis so far include the requirement
of a long and precise record of eclipses, as mentioned in the previous
section, as well as the lack of security in the prediction due to the
overwhelming number of ongoing cycles. In addition to this, it is
important to note that, in his detailed study, Hartner does not list all the
solar eclipses visible from Miletus in the time-period considered. One
would naturally think that he just sets a limit to what eclipses could have
been observed by considering their visibility magnitude. However, if we
use the excellent ephemerides now available from NASA, we can see
that Hartner’s ‘Table 3’ includes eclipses of magnitude down to 0.32 (10
November 687, 28 June 596, and 18 May 584 BCE all have magnitude
0.32), but ignores six eclipses of magnitude greater than 0.520 : for
example, the eclipse on 17 June 633 BCE reached a maximum magnitude
of 0.66 just before sunset; thus, weather permitting, it may well have
19 Hartner, ‘Eclipse Periods’.
20 Eclipses of magnitude more than 0.5 omitted by Hartner in the period
considered (magnitude in brackets): BCE 17 July 709 (0.67), 5 May 705 (0.54), 5
Mar 702 (0.53), 28 July 691 (0.66), 17 June 633 (0.66), 23 December 596 (0.61).
Moreover, the eclipses on BCE 17 April 611 (0.45) and 1 October 583 (0.36),
which attained those maximum magnitudes at sunset, could have been easily
observable (it is easier to gaze an eclipse of a given magnitude if the maximum
occurs near the horizon, because the atmosphere of the Earth blocks most of the
light from the Sun and, therefore, even a small eclipse can be noticed with the
unaided eye provided that it is not cloudy). The eclipse of 17 June 679 BCE,
which reached its maximum (0.48) at a rather low Sun altitude (18º), is also
worth mentioning.

Miguel Querejeta
Culture and Cosmos
11
been observable. The inclusion of these eclipses in the list completely
alters the ‘gaps’ that make Hartner suggest that Thales could have
deduced a certain number of cycles from these data. In spite of this,
Hartner’s probabilistic approach to lunar eclipse prediction remains of
considerable interest, and it would be valuable to perform a similar
statistical study for solar eclipses, taking their visibility into account.
Predictability of Solar Eclipses Using A Variety of Cycles
In the first part of his article, Willy Hartner calculates the probabilities of
a lunar eclipse being followed by another one after a certain number of
periods (some of them traditionally identified as ‘eclipse cycles’),
concluding that the triple Saros or Exeligmos ‘deserves the praise
unjustly wasted on the Saros’.21 It is important to note that conclusions
about the eclipse of Thales have been derived from these results; that is,
conclusions on the predictability of lunar eclipses have been extrapolated
to the prediction of solar eclipses.22 Consequently, it would be interesting
to undertake a similar study based on a statistical record of the solar
eclipses potentially visible from Miletus, analogous to what Hartner did
for lunar eclipses. We are going to calculate the percentages of those
solar eclipses that repeat after a number of cycles (those listed by
Hartner) in a given time-interval. It would also be good to quantify
whether the resulting percentages depend on the visibility limit that we
impose and, for this purpose, all results will be computed for three
different arbitrary magnitude limits (0.25, 0.50, and 0.75).
It is important to note that not all solar eclipses can in reality be
observed, as we have already pointed out. On the one hand, the
magnitude limit required for an eclipse to be recorded depends strongly
on the method used to observe it (naked eye, pinhole effect,
reflection…), and also on whether observers are carefully watching at the
sun because they expect an eclipse to happen. The latter has usually been
assumed to be true in the literature, and it has been explicitly stated by
Couprie, who suggests that Thales may have the habit of observing the
reflection of the sun on a liquid surface every new moon close to an
21 Hartner, ‘Eclipse Periods’, p. 60.
22 Hartner himself derives conclusions for the solar eclipse of Thales from these
lunar probabilities (Hartner, ‘Eclipse Periods’, p. 65), and so do Panchenko
(Panchenko, ‘Thales’, p. 280) and Couprie (Couprie, ‘Thales’, p. 322) in their
papers.

On the Eclipse of Thales, Cycles and Probabilities
Culture and Cosmos
12
Eclipse Season.23 On the other hand, a more crucial matter implies the
meteorological conditions necessary for an eclipse to be visible. Even if
we set a reasonable (but obviously arbitrary) limit to the minimum
observable eclipse magnitude, when we work out percentages as Hartner
did, we are at most obtaining an upper limit to the average probability of
repetition after each of the periods. This is because at most those eclipses
will be observed, but in all probability, many of them will pass unnoticed
due to cloudiness.
Using a JavaScript application available through the NASA website,
local circumstances can be retrieved for all eclipses of a given type
visible from the chosen location over a certain time-period. This
extremely powerful tool uses the best available corrections, so the
ephemerides can be considered most reliable.24 The circumstances of the
eclipses potentially observable from Miletus from 1000 BCE to 501 BCE
have first been obtained: we are not assuming that Thales had access to
eclipse records for such a long period, but this arbitrary length has rather
been selected in order to have a sufficiently large number of events to
work out statistics. The choice of a different geographical location25 or an
appreciably different historical period could lead to different results, as
the orbital properties of the Moon slightly change with time, and,
depending on the latitude, a different amount of eclipses occur in a given
time interval.
Results are shown in Table 3. Of course, this set of periods does not
list all the possible repetition patterns, but it is quite comprehensive, as it
contains all the significant multiples of less than 100 years, including
famous cycles like the Eclipse Seasons (6 lunations), Saros (223
lunations) or Exeligmos (669 lunations). We find that the Exeligmos
23 Couprie, ‘Thales’, p. 331.
24 URL: http://eclipse.gsfc.nasa.gov/JSEX/JSEX-index.html [accessed 2 June
2011]. This JavaScript calculator uses the same Besselian elements as the Five
Millennium Canon of Solar Eclipses: -1999 to +3000, and the values for ΔT are
calibrated using historical eclipses, based on the work by L. Morrison and F. R.
Stephenson, ‘Historical Values of the Earth’s Clock Error ΔT and the
Calculation of Eclipses’, Journal for the History of Astronomy, Vol. 35 (2004):
pp. 327–36.
25 Miletus: 27º20’ E, 37º30’ N, the same coordinates chosen both by Hartner
and Couprie, to avoid divergences for this reason; altitude: 10m over the sea
level.

Miguel Querejeta
Culture and Cosmos
13
provides the best results for solar eclipses as well, but even for the lowest
magnitude limit considered (0.25) the resulting percentage (58.5%) is
smaller than the one found by Hartner for lunar eclipses (76.2%), and it
reduces down to 22.7% when we require a minimum magnitude of 0.75.
Surprisingly, Hartner’s second best rated cycle (T*, 1074 lunations)
performs quite poorly for solar eclipses (8.5%, 2.3%, 0.0% for the
different magnitude limits, compared to Hartner’s 60.6%). It can also be
noted that periods marked by Hartner with an asterisk (cycles in which
consecutive eclipses occur in opposite nodes) clearly provide worse
results in the case of solar eclipses, as opposed to lunar eclipses, where
this distinction was not significant.
With this statistical study it has been shown that repetition
percentages for solar eclipses are always smaller than those obtained for
lunar eclipses. Moreover, our percentages do not take meteorological
difficulties into account, which are certainly not negligible; therefore,
true percentages would in reality be even smaller than the ones listed in
Table 3. As already noted in the existing literature, the eclipse preceding
28 May 585 BCE by an Exeligmos period was not visible from Miletus,
which discounts the possibility of a prediction based on this method. On
the contrary, one Saros before, a partial solar eclipse was visible from
Miletus26; judging by the percentages obtained, however, the cycle
cannot be considered a reliable method for predicting solar eclipses
(6.9% for a magnitude of 0.5), and thus seems unlikely as an explanation
for the prediction of Thales. Even if we are not in a position to
completely rule out the possibility of a prediction based on cycles, we
can state that, if such a cyclic prediction took place, the probabilities of
guessing right suggest that it should be seen as a lucky guess.
Conclusions
We have first considered the two cyclic approaches that stood
unchallenged (all the others had already been refuted). The conclusion is
that none of those conjectures can be regarded as serious explanations of
the problematic prediction of Thales: in addition to requiring the
existence of long and precise eclipse records, which clashes with the
meteorological visibility difficulties, both cycles that have been
examined overlook a number of eclipses which match the visibility
criteria and, consequently, the patterns suggested seem to disappear.
26 It is the solar eclipse of 18 May 603 BCE, which reached a maximum
magnitude of 0.83 in Miletus.

On the Eclipse of Thales, Cycles and Probabilities
Culture and Cosmos
14
Secondly, Hartner proposed a method to calculate repetition
probabilities for lunar eclipse cycles, and a similar technique has been
applied here to the solar case. The percentages obtained for each of the
periods are significantly smaller than those found by Hartner for lunar
eclipses, and our results diminish as we require higher magnitude limits.
Therefore, another important conclusion is that the probabilistic
calculations for lunar eclipses cannot be extrapolated to the prediction of
solar eclipses.
It has also been stressed throughout the paper that visibility plays a
key role in any attempt to explain the prediction by means of cycles. In
addition to the difficulty of setting a limit to what the smallest observable
eclipse is, cloudiness would add a random component that prevents
observers from regarding certain eclipses. As a consequence, all the
repetition percentages that we have calculated must be understood as an
upper limit to the probability of an eclipse repeating after a given period.
Therefore, and since the Exeligmos must be ruled out because the
preceding eclipse was not visible from Miletus, we can conclude that any
of the cycles considered implies a small probability of correctly
predicting a solar eclipse (in all of them, even for the smallest magnitude
limit of 0.25, failure turned out to be more likely than guessing right).
This means that, if Thales used a cyclic mechanism at all, his prediction
can hardly be considered fully scientific.
Date of solar
eclipse
Maximum
phase
Local time at
maximum
phase
Altitude of sun
at maximum
phase
Lunations
elapsed
since last
solar
eclipse
30 Sept 610
0.59
8.6 h.
+30º
317
13 Feb 608
0.76
15.2 h.
+21º
17
30 July 607
0.63
9.5 h.
+52º
18
9 July 597
0.73
5.0 h.
+3
123
23 Dec 596
0.61
16.7 h.
0º
18
9 May 594
0.46
8.3 h.
+36º
17
29 July 588
0.88
19.0 h.
+1º
77
14 Dec 587
0.75
10.9 h.
+28
17
28 May 585
0.97
17.9 h.
+13
18
Table 1: Dirk Couprie’s ‘Table 4’ with the alleged clusters of solar eclipses that
Thales could have observed at Miletus.

Miguel Querejeta
Culture and Cosmos
15
Date of
solar eclipse
Maximum
phase
Local time at
maximum phase
Altitude of
sun at
maximum
phase
Lunations
elapsed since
last solar
eclipse
17 June 633
0.66
19.2 h.
+2º
29
17 April 611
0.45
18.6 h.
0º
270
30 Sept 610
0.59
8.6 h.
+30º
18
13 Feb 608
0.76
15.2 h.
+21º
17
30 July 607
0.63
9.5 h.
+52º
18
18 May 603
0.50
8.2 h.
+36º
47
9 July 597
0.73
5.0 h.
+3
76
23 Dec 596
0.61
16.7 h.
0º
18
9 May 594
0.46
8.3 h.
+36º
17
29 July 588
0.88
19.0 h.
+1º
77
14 Dec 587
0.75
10.9 h.
+28
17
28 May 585
0.97
17.9 h.
+13
18
Table 2: What Dirk Couprie’s ‘Table 4’ would look like if we include all the
potentially observable eclipses that match his visibility criterium.

On the Eclipse of Thales, Cycles and Probabilities
Culture and Cosmos
16
Table 3: Resulting percentages for our study on solar eclipse predictability
assuming different magnitude limits (0.25, 0.50, 0.75), shown along with
Hartner’s probabilities for lunar eclipses and his notation for the cycles.
Asterisks refer to eclipses occurring in alternate nodes.
Hartner
notation
for cycles
Hartner
probability
in the
lunar case
Percentage
in the
solar case,
mag ≥ 0.25
Percentage
in the
solar case,
mag ≥ 0.50
Percentage
in the
solar case,
mag ≥ 0.75
6
lunations
N* (ecl.
seasons)
37.8 %
4.6 %
4.6 %
2.3 %
41
lunations
H*
45.5 %
3.8 %
2.3 %
2.3 %
47
lunations
K
46.3 %
22.3 %
18.4 %
9.1 %
88
lunations
B*
51.4 %
6.2 %
1.1 %
0.0 %
129
lunations
C
39.4 %
12.3 %
8.0 %
4.5 %
135
lunations
L*
53.3 %
3.8 %
1.1 %
0.0 %
223
lunations
S (Saros)
39.3 %
10.8 %
6.9 %
2.3 %
317
lunations
A
42.3 %
24.6 %
19.5 %
9.1 %
358
lunations
M*
42.7 %
0.8 %
1.1 %
0.0 %
446
lunations
D
33.7 %
8.5 %
4.6 %
0.0 %
669
lunations
E
(Exeligmos)
76.2 %
58.5 %
49.4 %
22.7 %
804
lunations
F*
52.7 %
5.4 %
1.1 %
0.0 %
939
lunations
G
48.5 %
34.6 %
33.3 %
22.7 %
1074
lunations
T*
60.6 %
8.5 %
2.3 %
0.0 %
1209
lunations
Q
48.5 %
20.8 %
14.9 %
6.8 %