Acronycal Risings in Babylonian Astronomy
 L H*  J M. S †
Babylonian observations of planets fall into two main types: (i) passages of
the planets by one of the so-called ‘‘Normal Stars’’ (reference stars distributed unevenly in longitude, but all near the ecliptic), and (ii) synodic phenomena such as first visibilities, stations, etc. For the outer planets (Mars, Jupiter
and Saturn) there are five of these synodic phenomena, and modern scholars
have conventionally denoted them by Greek letters. These ‘‘Greek-Letter
phenomena’’, as they have become known, are:
IGI
UŠ
aná ME-e
UŠ
ŠÚ
G
F
Q
Y
W
First appearance
First stationary point
‘‘Opposition’’
Second stationary point
Last appearance
For the inner planets (Mercury and Venus), Q ‘‘opposition’’ is of course replaced by the last appearance in the east (S) and the first appearance in the
west (X).
In addition to acting as useful shorthand, use of the Greek-Letter designations allows us to avoid the problem of the exact interpretation of these
phenomena. For example, W should probably be understood as the first date
on which a planet was not seen, rather than the last day on which it was seen
(Huber et al, 1982, p. 14). Nevertheless, it is important to attempt to identify
the precise meaning of these phenomena if we are to try to understand the
*Department of Physics, University of Durham, South Road, Durham, DH1 3LE, England.
†
Institute for the History and Philosophy of Science and Technology, Victoria College,
University of Toronto, 73 Queen’s Park Cres. E., Toronto, M5S 1K7, Canada.
C 2004: V. 46: . 145–162
C Blackwell Munksgaard 2004. Centaurus ISSN 0008-8994. Printed in Denmark. All rights reserved.
146
Louise Hollywood and John M. Steele
Babylonian observational record and, in particular, its role in the development of mathematical astronomy.
The identification of Q is not straightforward. True astronomical opposition occurs when a planet is at an elongation (difference in longitude) of
180æ from the sun. However, this is an event that cannot be directly observed
since only half of the ecliptic is visible above the horizon at any given time.
In principle at opposition a planet and the sun cross the opposite horizons
at sunrise and sunset, but at these moments the planet cannot be seen due
to the sky brightness. A planet needs to be a certain amount above the horizon and the sun a certain amount below it before the planet can be seen
with the naked eye. There is no exact method to calculate when this occurs
as it is dependent upon a number of factors such as the observer’s eyesight,
location, atmospheric extinction and refraction, etc, many of which are nonconstant.
Around opposition, however, there are two events which are observable:
acronycal rising and cosmical setting. Acronycal rising is the evening when a
planet is seen to rise for the last time after sunset. Cosmical setting is the
first time the planet is seen to set before sunrise. Both events are subjective.
For a few days after an acronycal rising the planet will still theoretically rise
above the horizon, but this will occur when the sky is too bright to make out
the planet and so when it is first seen, it will already be some distance above
the horizon.1
For an object on the ecliptic, acronycal rising will occur a few days before
the planet reaches opposition, and will therefore have an elongation (l첐ªlp)
less than 180æ. However, the situation becomes more complicated when the
object is not on the ecliptic. A positive latitude will make the object higher
above the horizon than the point on the ecliptic with the same longitude, and
so acronycal rising will occur earlier, at a lower elongation. On the other
hand, an object with a negative latitude will be lower with respect to the
horizon than the corresponding point of the ecliptic, and so acronycal rising
will occur later, at a greater elongation. For objects below the ecliptic by a
certain amount, such as Sirius whose ‘‘opposition’’ is also recorded, the order
acronycal rising – opposition – cosmical setting will be reversed, with acronycal rising happening after opposition (Neugebauer 1975, p. 1091). The extent
by which a planet’s latitude will change the date of acronycal rising, and
hence it elongation, depends also upon the time of year. At sunset in the
winter the ecliptic is inclined at quite a flat angle to the horizon and so the
Acronycal Risings in Babylonian Astronomy
147
effect of latitude is more pronounced than in the summer when the ecliptic
is closer to vertical.
Before going any further, it will be useful to provide an overview of the
main statements of the meaning of Q that have appeared in the literature.
Epping (1889), p. 113 initially interprets the phenomena as ‘‘opposition of
the outer planets with the sun’’, when listing the phenomena he wishes to
discuss:
b. Opposition der äußeren Planeten mit der Sonne.
But later (p. 135), when discussing opposition, he describes a position where
the planet is opposite the setting sun on the horizon:
Eine bemerkenswerthe Stellung am himmel nimmt ein Planet dann ein, wenn er der
Sonne gerabe gegenübersteht, oder, was dasselbe ist, wenn er beim Untergange der
Sonne über den horizont sich erhebt.
Kugler (1907), p. 15 also simply translates the phenomena as ‘‘opposition
with the sun’’, in a list of important appearances that demand attention:
Vor allem fesselten alle jene Erscheinungen ihre Aufmerksamkeit, die von der wechselnden Stellung der Planeten zur Sonne und Erde ... ihre Opposition mit der Sonne,
Ihr zweiter Stillstand, und ihr Verschwinden in den Sonnenstrahlen (heliakischer
Untergang).
But in Kugler (1909), p. 490 he translates
8 AN aná ME.E.A
as
8 Mars im akronychischen Aufgang (kurz vor der Opposition)
In his classification article, Sachs (1947), p. 274 lists Q as ‘‘opposition’’, but
places it in quotation marks. In Sachs (1952), p. 105 he describes records of
Sirius as comprising:
a triplet of dates for the heliacal rising (igi), ‘‘opposition’’ (actually apparent acronycal rising; aná ME (-E) (-A)), and heliacal setting (šú).
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Louise Hollywood and John M. Steele
The ‘‘opposition’’ of Sirius is written with the same phrase as used for Q of
the planets, and surely corresponds to the same phenomena.
The same year, Neugebauer (1952), p. 93 stated:
Disappearance and reappearance of the planets are phenomena close to the horizon
and it seems also ‘‘opposition’’ of a planet was defined as rising or setting at sunset
and sunrise respectively.
Later, in ACT (1955), p. 280 he summed up the assumption as:
All phenomena under consideration, with the sole exception of the stationary points,
are phenomena in the horizon. This also holds for Q which we simply call ‘‘opposition’’ but which, in all probability, is ‘‘acronycal rising’’, i.e. rising of the planet at
sunset.
Then in Neugebauer (1975), p. 399 he refers to a translation of Sachs’ within
a discussion of the procedure texts:
... Q is not the ‘‘opposition’’ in the strict sense of Greek or modern astronomy but
... it corresponds to the ‘‘akronycal rising’’ of the planet. The planet is then just
visible in the east shortly after sunset; the Babylonian term means in fact ‘‘opposition
in the east.’’ [Ana ME-a ina kur, or similar (Sachs).]
Most authors since Neugebauer have assumed that Q refers to acronycal
rising, often with a reference to one of the above publications. In this paper
we shall take a fresh look at the evidence in an attempt to evaluate this
common interpretation of Q.
Evidence from the texts of mathematical astronomy
A small amount of information concerning Q is provided by the texts of
mathematical astronomy.2 Q is regularly computed in the ephemerides of
the outer planets. For Jupiter and Saturn this is done in the usual fashion
using the appropriate System A or B schemes. For Mars, however, Q (and
the other retrograde phase Y) is instead calculated as a satellite phenomena of F.3 Four different schemes for determining these phenomena of
Mars were identified by Neugebauer.4 However, only for one of these,
called by Neugebauer S, is information fully preserved on the complete
Acronycal Risings in Babylonian Astronomy
149
retrograde arc, rather than just the part from F to Q. In scheme S the
arc from Q to Y is equal to 3/2 of the arc from F to Q. The fact that
Q is closer to F than to Y means that Q has an elongation from the sun
of less than 180æ (Neugebauer 1975, p. 459), supporting the hypothesis
that Q corresponds to acronycal rising.
Schemes for the subdivision of the synodic arc of the other planets are
known from several procedure texts. For example, ACT No. 813, a mixed
collection of Jupiter procedures, contains in section 2 a scheme for System A
where on the slow arc F to Q is ª4æ and Q to Y is ª6æ, and on the fast arc
F to Q is ª4;48æ and Q to Y is ª7;12æ (Neugebauer 1975, p. 449). Again, this
asymmetry in the division of the retrograde arc supports the identification of
Q as acronycal rising.
Further evidence is supplied by Swerdlow (1999, pp. 58–61), who investigated the elongations of Q from the mean sun as implied in ephemerides,
template texts and procedure texts. He concluded that Q falls short of the
mean opposition by about 3æ for Saturn, about 5æ, 6æ or 2æ for Jupiter (depending upon which scheme was used), and about 6æ or 7;30æ for Mars
(again, depending upon the scheme). As he notes, it is not clear whether these
precise numbers have any significance, but they nonetheless indicate that Q
occurs at a mean elongation of less than 180æ, again supporting the identification of Q as acronycal rising.
Evidence from the texts of non-mathematical astronomy
The non-mathematical astronomical texts (Astronomical Dairies, Planetary
Compilations, Goal Year Texts, Almanacs and Normal Star Almanacs) all
contain observations and/or predictions of Q for the outer planets (Sachs
1947; Hunger 1999). The Astronomical Diaries contain observations and predictions made on a day-by-day basis. Generally planetary phenomena are
recorded as observed, but occasionally predicted data was inserted in the
record instead. For example, whenever certain observations could not be
made due to bad weather, a computed value was entered followed by the
remark ‘‘I did not see it’’ or ‘‘I did not watch’’. Planetary Compilations are
simply collections of records for a specific planet. They were often arranged
in periods appropriate to the planet. Planetary data contained in the Goal
Year Texts was to be used in making predictions for a coming ‘‘goal’’ year.
150
Louise Hollywood and John M. Steele
The data was taken from a number of years previously corresponding to the
following characteristic periods:
Mars
Jupiter
Saturn
Mercury
Venus
47 years
79 years
71 years
83 years
59 years
46 years
8 years
for
for
for
for
conjunctions with Normal Stars
Greek-Letter Phenomana
Greek-Letter Phenomena
conjunctions with Normal Stars
It is possible, indeed likely, that all the data in the Goal Year Texts and
Planetary Compilations was taken directly from the Diaries.5
The Almanacs contain data about the moon, a planet’s Greek-Letter
phenomena and entries into zodiacal signs, the sun and Sirius. The Normal
Star Almanacs contain data concerning the planet’s Greek-Letter phenomena
and conjunctions with Normal Stars, the moon, the sun and Sirius. They both
contain predicted data that would presumably have been obtained by using the
Goal Year Texts, with appropriate corrections to the Goal Year Periods.
We have collected together all recorded entries for Q of a planet from these
sources that were available to us. For the Diaries and Planetary Compilations
we have used the editions by Sachs and Hunger (1988, 1989, 1996) and Hunger (2001). Data from the Goal Year Texts was read from the copies by Pinches and Strassmaier in LBAT (ΩSachs 1955). For the Almanacs and Normal
Star Almanacs, we have collected data from the copies in LBAT, Epping
(1889), Kugler (1900, 1907–1935), and editions of individual texts by Sachs
(1976), Sachs and Walker (1984), and Hunger (1999).6
All of the usable records are collected in the appendix. From the dates of
Q the difference in longitude with the sun was calculated using a program
designed by Kevin Yau and F. Richard Stephenson based upon the planetary
ephemeris of Bretagnon and Simon.7 Dates in the Babylonian calendar were
converted to the Julian calendar using the tablets of Parker and Dubberstein
(1956). Calculations were made uniformly for an Ephemeris Time (ET) of
20.00, which corresponds roughly to shortly after sunset in Babylon. It was
not considered necessary to make more precise estimates of the time of observation (eg by taking into account the variations in the Earth’s rotational
clock error (DT), or the time of sunset at Babylon), since we have no infor-
151
Acronycal Risings in Babylonian Astronomy
Fig. 1. Calculated elongations at Q for all Mars, Jupiter and Saturn.
mation about when during the course of the night Q was observed (although
if Q is indeed acronycal rising, then the observations take place shortly after
sunset). If the computations were made for the end of the night the elongations would be approximately 0.5æ greater.
All of the computed elongations range from 165–195æ. Occasionally we
have two records with conflicting information concerning the date of Q. In
the following, we have omitted these cases from our analysis, although including them would have made little difference to the statistics.
In figure 1 we examine the data by source. Overall the data is centred around
a little less than 180æ, but it is clear that the extent of the spread in elongations
varies depending upon the source. This is analysed in the table below:
Source
Diaries
Planetary texts
Goal year texts
Almanacs
Normal star almanacs
Average
Standard
Deviation
No. records
178.2
177.0
179.2
179.7
180.9
2.2
2.0
4.8
2.8
7.7
35
47
15
14
8
152
Louise Hollywood and John M. Steele
The three sources which generally contain observational data have very similar averages, as is to be expected if we assume that the Planetary Compilations and the Goal Year Texts were extracted from the observations in the
Diaries. There is a greater standard deviation for the Goal Year texts, but
this is probably partly caused by the smaller number of observations available from this source, and also by one particularly high point, an elongation
of 192æ for Saturn in SE 32. Although there is much less data available for the
texts which contain predictions, the Almanacs and Normal Star Almanacs do
seem to place Q at a somewhat greater elongation than the observational
material. The reason for this becomes clearer when we consider each planet
separately (see figures 2–4):
For Mars, the distribution is similar for all classes of text. The mean
elongation at Q is 176.5æ, with a standard deviation of 5.2æ. For Jupiter, the
mean elongation at Q is 177.5æ, almost identical to that of Mars, but the
spread in values is somewhat less, resulting in a standard deviation of 2.2æ.
As with Mars, the distribution is similar for all classes of text. For Saturn, the
mean elongation at Q is 180.5æ, with a standard deviation of 3.9æ, reflecting a
large spread in elongations. Furthermore, there are clear differences between
the data from different classes of text; this is especially obvious between data
from Astronomical Diaries and Normal Star Almanacs (although curiously
Fig. 2. Calculated elongations at Q for Mars.
Acronycal Risings in Babylonian Astronomy
153
Fig. 3. Calculated elongations at Q for Jupiter.
Fig. 4. Calculated elongations at Q for Saturn.
not Almanacs). In order to explain this we first have to look at how the
predictions were made.
The Goal Year Texts were presumably the source of the predicted data in
the Almanacs and Normal Star Almanacs, and ultimately any predicted data
154
Louise Hollywood and John M. Steele
that enters the Diaries due to bad weather preventing observation. To make
a prediction of a Greek letter event from data in a Goal Year Text, one simply
moves on the relevant period and adds a small correction to the date in the
Babylonian calendar, to find the date in the new Babylonian year. Occasionally, it is necessary to adjust this date by one month in order to take into
account intercalation. Indeed, it seems that at least some Goal Year Texts
allowed for this by adjusting the month of the recorded data when compiling
original observations, so the intercalation correction did not have to be made
when the text came to be used (Brack-Bernsen 1999). Hunger (1999) has
computed the necessary corrections to the Goal Year periods from modern
computation. On average they are π4 days for Mars (using the 79 year
period), 0 days for Jupiter and ª6 days for Saturn. A few texts are known
(e.g., Text E in Neugebauer & Sachs 1971 and LBAT 1515) which attest these
or similar corrections. However, Hunger (1999) has also shown by comparing
preserved Goal Year Texts and Almanacs/Normal Star Almanacs that the
correct correction was rarely applied in practice. For Mars he found the correction varied between 0 and π9 days, for Jupiter between ª1 and π1 days
and for Saturn between ª4 and ª13 days.
For Saturn, a difference in the applied correction of 1 day corresponds to
a change in elongation of about 1æ, since 1æ is roughly the mean daily motion
of the sun, and Saturn moves hardly at all over a few days. Incorrectly applied corrections to the Goal Year period for Saturn will therefore translate
directly to the elongation derived from dates of Q in Almanacs and Normal
Star Almanacs. This is presumably the cause of the very high (greater than
180æ) elongations for the Saturn data taken from Normal Star Almanacs. It
may simply be chance that the available Normal Star Almanacs all err in the
same direction (too small a day correction), whereas the Almanacs apply a
correction that is about right, and so result in elongations which are similar
to those found in observational texts. In this respect, it is worth noting that
several, though by no means all, of the Saturn data with elongations greater
than 180æ taken from observational texts are accompanied by the phrase ‘‘I
did not watch’’, indicating that these are predictions, presumably taken from
the Almanacs/Normal Star Almanacs. It is largely due to predicted data that
the mean elongation at Q for Saturn is marginally above 180æ, and as we have
seen this is an artefact of the way they were computed, and not a reflection of
observational practice. For Jupiter, the applied corrections are in good agreement with what they should be, and as a result the distributions for the
Acronycal Risings in Babylonian Astronomy
155
predicted and observed data are similar. There is too little data to draw any
similar conclusions for Mars.
There are two more issues that deserve comment as they explain why there
is a greater spread in elongations for Mars and Saturn than there is for
Jupiter, even when we disregard the predicted data. These are the effects of a
planet’s latitude and magnitude on the observed date of acronycal rising. As
discussed in the introduction, acronycal rising does not occur at a fixed distance from the sun. This is because it is a visibility phenomenon, and so
depends upon a number of factors such as climatic/atmospheric conditions,
the observer’s eyesight, etc. The variations in the factors will naturally produce some spread in the elongation at which acronycal rising will occur for
a given planet. Furthermore, the magnitude of a planet directly affects the
date of visibility, since clearly a bright object can be seen closer to the horizon
and when the sky is lighter, than a dim object. This is particularly relevant
for Mars, whose magnitude varies significantly, and to a lesser extent Saturn.
In this regard it is significant that there is a greater spread in elongations for
Mars and Saturn than for Jupiter, although the effect of magnitude variation
cannot be investigated quantitatively as there is insufficient data to isolate
magnitude effects from other factors.
The variation in a planet’s latitude will have a similar effect, since when
the planet is further away from the ecliptic, it will rise several days earlier or
later than when it is close to the ecliptic. The variation in the latitude of
Saturn is about twice that of Jupiter, and Mars’s latitude varies still further,
especially around opposition, so this may be one reason why there is less
spread in the distribution of elongations of Jupiter. Quantitatively, again, it
is hard to analyse the effect of latitude on the elongation at Q, since the
effect is also dependent upon the time of year. We might expect a correlation
between elongations of over 180æ and dates when the planet has negative
latitude. Although this is true most of the time for Mars and Jupiter (3 out
of 4 and 7 out of 8 cases respectively), it is clearly not always the case for
Saturn (only 8 out of 17 cases). In figure 5 we plot elongation at Q against
latitude. For the reason just stated it is hard to interpret such a plot. Nevertheless, two points can, we believe, be made: (i) as expected, there is some
correlation between elongation and latitude, with elongations of greater than
180æ more often occurring when the latitude is negative; however, (ii) for
Saturn the effect of latitude is less significant than other factors, in particular
when we are dealing with predicted data.
156
Louise Hollywood and John M. Steele
Fig. 5. The dependence of elongation at Q on planetary latitude.
Conclusions
All of the evidence considered in this paper leads to the not unexpected conclusion that the phenomena Q observed and predicted by the Babylonians
corresponds to the acronycal rising of the planet, not opposition. Both the
theoretical schemes of the Mathematical Astronomical Texts, and the observed data on the Non-Mathematical Astronomical Texts indicate that Q
occurs at elongations less than 180æ, and the differences in the spreads of
elongations for the three planets indicates that Q is a visibility phenomena.
These two factors inevitably indicate that Q is aconycal rising, as the only
obvious observable visibility phenomena with at an elongation a little less
than 180æ. Qualitative support for this conclusion is also provided by the
application of the so-called Uruk scheme to computing dates of Sirius
phenomena (Sachs 1952). This scheme predicts dates of Sirius’s Q (again
written aná ME-E-a) at elongations somewhat greater than 180æ, and this is
just what we would expect for a star with Sirius’s fairly large negative latitude.
One problem that remains is how exactly an acronycal rising was observed.
Due to extinction effects, a planet is never actually seen to cross the horizon;
instead it is first seen at a small distance above the horizon. This distance
will vary night by night due to changing atmospheric conditions. It is quite
Acronycal Risings in Babylonian Astronomy
157
possible that the Babylonian astronomers used more than one criterion (for
example, a combination of the height of the planet above the horizon when
first seen and measurements of the time interval between sunset and first
sighting of the planet) to judge when an acronycal rising had occurred.
Acknowledgements
We wish to express our thanks to Lis Brack-Bernsen and Teije de Jong for
their helpful comments and advice during the writing of this paper. John
Steele’s work was made possible through the awards of a Leverhulm Trust
Research Fellowship at the University of Durham and the E. P. May Fellowship at the University of Toronto.
References
Aaboe, A.
1987: ‘‘A Late Babylonian Procedure Text for Mars, and Some Remarks on Retrograde
Arcs’’, in King, D. A., and Saliba, G. (eds.), From Deferent to Equant: A Volume
of Studies in the History of Science in the Ancient and Medieval Near East in Honor
of E. S. Kennedy, New York, pp. 1–14.
Aaboe, A., Sachs, A. J.
1966: ‘‘Some Dateless Computed Lists of Longitudes of Characteristic Planetary
Phenomena from the Late Babylonian Period’’, Journal of Cuneiform Studies 20,
pp. 1–33.
Brack-Bernsen, L.
1999: ‘‘Ancient and Modern Utilization of the Lunar Data Recorded on the Babylonian
Goal-Year Tablets’’, in Actes de la VémeConférence de la SEAC, Warszawa-Gdansk,
pp. 13–39.
Epping, J.
1889: Astronomisches aus Babylon, Freiberg im Breisgau.
Huber, P. J., et al.
1982: Astronomical Dating of Babylon I and Ur III, Malibu.
Hunger, H.
1999: ‘‘Non-mathematical Astronomical Texts and Their Relationships’’ in N. M. Swerdlow (ed.), Ancient Astronomy and Celestial Divination, Cambridge, MA, pp. 77–96.
2001: Astronomical Diaries and Related Texts from Babylonia Volume V, Vienna.
Kugler, F. X.
1907–1935: Sternkunde und Sterndienst in Babel, Münster.
Neugebauer, O.
1952: The Exact Sciences in Antiquity, Princeton.
1955: Astronomical Cuneiform Texts, London.
1975: A History of Ancient Mathematical Astronomy, Berlin.
158
Louise Hollywood and John M. Steele
Neugebauer, O. and Sachs, A. J.
1971: ‘‘Some Atypical Astronomical Cuneiform Texts I’’, Journal of Cuneiform Studies
21, pp. 183–218.
Parker, R. A. and Dubberstein, W. H.
1956: Babylonian Chronology, Providence.
Sachs, A.
1948: ‘‘A Classification of the Babylonian Astronomical Tablets of the Seleucid Era.’’
Journal of Cuneiform Studies 2, pp. 271–290.
1952: ‘‘Sirius dates in Babylonian astronomical texts of the Seleucid period.’’ Journal of
Cuneiform Studies 6, 105–114.
1955: Late Babylonian Astronomical and Related Texts, Providence.
1976: ‘‘The Latest Datable Cuneiform Tablets’’, in B. Eichler (ed.), Kramer Anniversary
Volume: Cuneiform Studies in Honour of Samuel Noah Kramer, Neukirchen-Vluyn,
pp. 379–398.
Sachs, A., Hunger, H.
1988–1996: Astronomical Diaries and Related Texts from Babylonia Volumes I–III, Vienna.
Sachs, A., Walker, C. B. F.
1984: ‘‘Kepler’s View of the Star of Bethlehem and the Babylonian Almanac for 7/6 BC’’,
Iraq 46, pp. 43–56.
Swerdlow, N. M.
1999: ‘‘Acronychal Risings in Babylonian Planetary Theory’’, Archive for History of Exact Science 54, pp. 49–65.
Appendix
The following tables contain lists of all entries in Non-Mathematical Astronomical Texts
known to us which concern the phenomena Q. In the first column, a reference is given to
the source of the record. Diaries (D) are cited from their publication in Sachs & Hunger
(1988–1996); Planetary Compilations (P) by their text number in Hunger (2001); Goal Year
Texts (G), Almanacs (A) and Normal Star Almanacs (NSA) by their LBAT number. The
date column refers to the Babylonian calendar. The following abbreviations apply: AΩ
Alexander III, ArIIΩArtaxerxes II, ArIIIΩArtaxerxes III, DIΩDarius I, DIIIΩDarius III,
NEIIΩNebuchadnezzar II, PAΩPhilip Arrhidaeus, SEΩSeleucid Era
MARS
Month Day
lM
l첐
l첐ªlM Latitude Comments
Source
Year
D –276
D –229
D –143
SE 35
SE 82
SE 168
XI
XI
V
15
19
5
151.16 327.20 176.04
145.57 321.92 176.35
317.65 138.81 181.16
4.27
4.42
1.18
D –137
D –133
P 68
SE 174
SE 178
SE 8
X
XII
II
1
28
6
101.05 277.33 176.28
171.42 349.27 177.85
233.64 52.21 178.57
4.20
3.42
ª2.24
Text: 19?
Around ... I did
not watch
All day overcast
Around ...
159
Acronycal Risings in Babylonian Astronomy
ª3.85
3.43
4.56
P 69
P 69
P 76
SE 27
SE 31
SE 50
VI
IX
XI
12
20
19
351.10 172.51 181.42
82.61 256.69 174.08
136.98 314.72 177.74
P 76
P 79
A 1164/5
A 1174
G 1228
SE 52
SE 142
SE 234
SE 236
SE 18
XII
IX
VIII
IX
X
12
25
8
6
16
177.35
94.37
42.29
83.15
128.95
167.55
171.54
179.40
173.75
177.52
3.36
3.85
0.75
3.37
4.62
G 1265
SE 89
G 1300
SE 245
NSA 998
SE 55
NSA 1050 SE 187
V
II
II
VII
1
21
8
27
312.34 136.99 184.65
247.89 58.59 170.70
221.99 47.10 185.11
52.47 219.06 166.59
ª6.51
ª2.94
ª1.42
0.95
344.90
265.91
221.69
256.90
306.47
Around ... I did
not watch
I did not watch
Date partially
broken away,
could be 26
Ideal date
JUPITER
Month Day
lJ
l첐
l첐ªlJ Latitude Comments
Source
Year
D –567
NII 37
I
D –357
D –346
D –302/1
ArIII 1
ArIII 12
SE 9
XI
X
VII
15
20
4
145.66 321.96 176.30
119.60 296.29 176.69
5.44 182.88 177.44
1.63
1.18
ª1.70
D
D
D
D
D
–273
–253
–245
–218
–209
SE 38
SE 58
SE 66
SE 93
SE 102
XII
VII
IV
VIII
V
16
29
8
7
1
176.07
60.73
282.46
41.14
298.12
354.06
236.72
100.82
217.87
114.55
177.99
175.99
178.36
176.73
176.43
1.73
ª0.54
ª0.74
ª1.08
ª1.13
D –208
D –201
D –198
D –178
D –171
D –161
D –141
D –140
P 54
P 60
P 60
P 63
P 60
SE 103
SE 110
SE 113
SE 133
SE 140
SE 150
SE 170
SE 171
DI 19
ArII 18
ArII 19
ArII 41
ArII 41
V
XII2
IV
XII
VIII
V
I
I
VIII
V
VI
IV
IV
22
30
4
21
2
15
12
27
9
28
16
17
15
333.84
202.49
267.29
180.71
26.15
318.60
193.95
225.02
59.46
328.64
5.05
302.59
302.86
155.24
20.75
88.03
358.91
204.26
137.21
11.80
44.19
238.25
146.50
183.01
121.56
119.62
181.40
178.26
180.74
178.20
178.11
178.61
177.85
179.17
178.79
177.86
177.96
178.97
176.76
ª1.73
1.46
ª0.29
1.71
ª1.40
ª1.54
1.59
0.98
ª0.49
ª1.71
ª1.70
ª1.29
ª1.28
11,12 219.76
35.83
176.07
1.04
Text: [11th] or
12th
Previous entry
7th, next 16th
Around ...
Date (1st or
2nd) is broken
away, next entry
3rd.
I did not watch
Text: 30?
Around ...
Around ...
Around ...
Around ...
Around ...
Around ...
Aquarius
160
Louise Hollywood and John M. Steele
P
P
P
P
P
P
P
P
63
60
60
60
66
66
69
66
ArII 42
ArII 43
ArII 44
ArII 45
ArIII 1
ArIII 2
ArIII 4
ArIII 5
VI
VII
VIII
IX
XI
XII
I
II
5
21
8
22
15
27
12
27
339.29
15.67
50.57
83.63
145.66
175.85
206.52
238.59
156.53
192.24
227.53
260.96
321.96
352.22
23.87
56.10
177.24
176.57
176.96
177.33
176.30
176.37
177.35
177.51
ª1.78
ª1.57
ª0.79
0.20
1.63
1.74
1.34
0.57
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
70
70
70
70
70
70
72
72
70
72
72
72
78
78
78
80
82
82
82
82
82
82
82
82
ArIII 9
ArIII 10
ArIII 12
ArIII 14
ArIII 16
ArIII 17
ArIII 18
ArIII 19
DIII 1
DIII 2
DIII 4
DIII 5
Al 7
Al 11
Al 13
SE 12
SE 13
SE 14
SE 15
SE 21
SE 23
SE 23
SE 24
SE 24
SE 25
SE 26
SE 33
SE 114
SE 119
SE 120
SE 131
SE 163
SE 164
SE 165
SE 166
SE 167
SE 170
SE 171
SE 172
VII
VIII
X
XII
I
II
IV
IV
XI
XI
I
I
III
VII
X
X
X
XII
XIII
VI
IX
IX
X
X
XI
XII
VII
IV
X
XI
X
VI
VIII
VIII
X
XI
I
I
III
9
24
20
16
30
16
2
20
8
21
4
14
1
15
11
18
28
13
25
23
22
19
5
4
16
27
10
22
6
21
26
22
8
22
5
15
13
17
12
20.66
55.52
119.60
180.08
211.07
243.27
277.63
313.40
124.06
154.24
184.58
216.10
248.42
30.86
97.71
106.54
137.43
167.30
197.88
10.53
79.29
79.69
110.91
111.05
141.51
171.87
15.44
302.55
116.35
146.36
120.25
0.12
36.12
70.32
102.74
133.87
193.82
226.27
258.05
198.43
231.70
296.29
358.14
28.75
61.90
94.09
129.51
300.42
332.04
2.12
29.81
63.90
207.69
272.42
283.77
312.70
345.10
14.96
188.99
256.63
253.56
288.91
287.90
318.76
348.12
195.14
123.33
289.85
323.70
298.02
180.52
214.58
247.96
279.31
308.33
12.77
34.64
75.39
177.77
176.18
176.69
178.06
177.68
178.63
176.46
176.11
176.36
177.80
177.54
173.71
175.48
176.83
174.71
177.23
175.27
177.80
177.08
178.46
177.34
173.87
178.00
176.85
177.25
176.25
179.70
180.78
173.50
177.34
177.77
180.40
178.46
177.64
176.57
174.46
178.95
168.37
177.34
ª1.49
ª0.66
1.18
1.72
1.28
0.43
ª0.62
ª1.49
1.27
1.71
1.68
1.18
0.29
ª1.30
0.59
0.85
1.51
1.75
1.53
ª1.64
0.04
0.04
0.96
0.96
1.57
1.75
ª1.57
ª1.25
1.05
1.61
1.15
ª1.74
ª1.20
ª0.27
0.69
1.41
1.59
1.00
0.04
Text: 21?
Text: [1]2
Text: month I,
editor corrected
Around ...
I did not watch
I did not watch
Around ...
Around ...
Around ...
Until around ...
161
Acronycal Risings in Babylonian Astronomy
A 1148
A 1151
A 1160
A 1174
A 1195
G 1233
G 1249
G 1251
G 1253
G 1261
G 1280
G 1283
NSA 1052
SE 198
SE 201
SE 233
SE 236
SE 305
SE 35
SE 64
SE 69
SE 71
SE 87
SE 116
SE 120
SE 188
V
IX
V
VIII
VI
IX
II
VIII
X
I
VI
XI
VIII
28
11
3
24
21
8
3
3
2
3
27
22
11
339.24
84.85
318.20
65.36
348.63
84.07
215.92
30.98
97.68
192.77
15.78
146.23
46.52
160.16
259.45
138.10
245.67
170.09
259.79
32.61
209.57
276.33
18.65
193.92
324.69
221.86
180.92
174.60
179.90
180.31
181.46
175.72
176.69
178.59
178.65
185.88
178.14
178.46
175.34
ª1.75
0.15
ª1.52
ª0.42
ª1.77
0.18
1.19
ª1.30
0.59
1.58
ª1.60
1.61
ª0.97
Ideal date
Ideal date
SATURN
Month Day
ls
l첐
l첐ªls Latitude Comments
Source
Year
D –380
D –342
ArII 24
ArIII 16
X
I
26
21
111.22 287.47 176.25
203.35 20.12 176.77
0.90
2.68
D –333
DIII 2
IV
19
306.42 123.25 176.83
ª1.56
D –332
D –322
DIII 3
PA 1
V
IX
16
23
318.79 138.58 179.79
99.15 274.21 175.06
ª2.05
0.27
D
D
D
D
D
–277
–365
–232
–198
–165
SE 34
SE 48
SE 79
SE 113
SE 146
IV
IX
X
XII
I
6
18
27
10
1?
272.03 91.96 179.93
100.62 275.91 175.29
120.98 303.66 182.68
178.37 358.78 180.41
208.00 25.11 177.11
0.08
0.37
1.31
2.84
2.62
D –158
SE 153
IV
18
286.84 109.41 182.57
ª0.61
D –157
D –149
P 62
A 1122
A 1134
A 1135
A 1152
A 1185
A 1188/9
A 1195
G 1220
SE 154
SE 162
ArII 26
SE 128
SE 178
SE 179
SE 209
SE 282
SE 300
SE 305
SE 32
IV
VII
XI
VI
III
II
III
IX
IV
VI
II
11
28
20
10
1
23
1
4
16
21
29
298.83
46.49
137.10
342.38
236.66
247.84
254.24
79.41
286.29
348.61
248.58
ª1.18
ª2.15
2.01
ª2.67
1.76
1.29
1.02
ª0.82
ª0.49
ª2.73
1.16
120.75
227.28
318.08
165.07
58.79
69.98
75.44
257.74
103.12
170.12
79.06
181.92
180.79
180.98
182.69
182.13
182.14
181.20
178.33
176.83
181.51
190.48
Around ...
Clouds, I did
not watch
No date,
previous entry
18, next 20
Clouds crossed
the sky
I did not watch
Date of entry
broken away,
next 3rd.
Around ... I did
not watch
Around ...
162
G 1229
G 1236
G 1265
G 1291
NSA 1008
NSA 1010
NSA 1016
NSA 1020
NSA 1057
Louise Hollywood and John M. Steele
SE 46
SE 48
SE 109
SE 148
SE 96
SE 104
SE 107
SE 111
SE 194
VIII
IX
XI
II
V
IX
X
XII
X
30
18
6
19
10
3
13
2
6
72.17
100.62
128.69
230.34
309.46
59.01
102.00
153.58
82.56
250.93
275.91
309.41
48.55
129.49
242.68
279.64
342.64
272.39
178.76
175.29
180.72
178.21
180.03
183.67
177.64
189.06
189.83
ª1.07
0.32
1.62
1.99
ª1.66
ª1.65
0.37
2.48
ª0.57
Ideal Date
Ideal Date
NOTES
1. See Swerdlow (1999, p. 55).
2. The principle texts are published in Neugebauer (1955) and Aaboe & Sachs (1966). See
also the discussion in Neugebauer (1975).
3. The likely reasons for this are discussed by Aaboe (1987, p. 11).
4. See Neugebauer (1955, pp. 305–306), Aaboe (1987, pp. 9–13) and Neugebauer (1975,
pp. 458–460).
5. See Hunger (1999) however.
6. Before beginning this analysis it is worth noting that the data is limited by those tablets
that have survived (and published in some form) and is by no means a standardised
cross section. Consequently we have an uneven distribution over the years, and for the
Almanacs, Normal Star Almanacs and Goal Year Texts we have a very limited number
of relevant entries.
7. We thank F. R. Stephenson for generously making available his program.
8. For further cases of conflicting data in overlapping texts, see Hunger (1999).