2021258a0Nature202493919640627125812610028-0836196410.1038/2021258a0ukNatureNatureNATUREnatureNature is a weekly international journal publishing the finest peer-reviewed research in all fields of science and technology on the basis of its originality, importance, interdisciplinary interest, timeliness, accessibility, elegance and surprising conclusions. Nature also provides rapid, authoritative, insightful and arresting news and interpretation of topical and coming trends affecting science, scientists and the wider public./nature/journal/v202/n4939issueJournal homeArchiveCurrent issueAdvance online publicationPrivacy policySubscribeNature Publishing GroupCurrent issue2021258a0Stonehenge: A Neolithic Computer
AU  - HAWKINS, GERALD S.Boston University and Harvard-Smithsonian Observatory, Cambridge, Mass.DIODOKUS in his History of the Ancient World[ast], written about 50 B.C., said of prehistoric Britain: "The Moon as viewed from, this island appears to be but a little distance from the Earth and to have on it prominences like those of the Earth, which are visible to the eye. The account is also given that the god [Moon ?] visits the island every 19 years, the period in which the return of the stars to the same place in the heavens is accomplished. . . . There is also on the island both a magnificent sacred precinct of Apollo [Sun] and a notable temple . . . and the supervisors are called Boreadae, and succession to these positions is always kept in their family".
I am indebted to the British archaeologist R. S. New all for directing my attention to this classic work. The statement of Diodorus is secondhand and has sometimes been dismissed as a myth, but there is a possibility that it refers to Stonehenge.
The Moon rises farthest to the north when it appears over stone D as seen from the centre of Stonehenge2, similar to the rising of the midsummer Sun over the heel stone. In a period of 18-61 years the extreme moonrise will shift from D to the heel stone to F and then return to J). The extreme moonrise thus swings from side to side in the avenue because of the regression of the nodes. When we consider a particular moonrise, such as the nearest full moon to the winter solstice, which we will call 'midwinter moonrise', then the cycle takes either 19 or 18 years.
The position of the Moon has been computed using first-order terms3 from 2001 to 1000 B.C. and the azimuth of moonrise has been determined for each winter solstice during this period. A sample of the results from 1600 to 1400 B.C. is shown in Fig. 1. Mrs. S. Rosenthal assisted with the programming of the I.B.M. 7094, and I thank the Smithsonian Astrophysical Observatory for the donation of 40 sec of machine time for this problem.
With midwinter moonrise the cycle is primarily one of
19 years with 38 per cent irregularity. For example, the Moon rises over F in 1671, 1652, 1634, 1615, and 1596 B.C. The intervals are 19, 18, 19 and 19 years respectively. Actually, from 2001 to 1000 B.C. the winter Moon is over F 52 times, and there are 32 intervals of 19 years and
20 of 18 as shown in Table 1. Similarly the cycle is primarily one of 19 years for moonrise over D at the winter solstice (Table 1).
The winter Moon rises over the heel stone with twice this frequency. For example, in 1694, 1685, 1676 and 1666 B.C. the intervals are 9, 9 and 10 years. Over the period 2001 to 1000 B.C. the '10' irregularity occurs with a frequency of 33 per cent. However, if we consider second intervals, 1694 to 1676 and 1685 to 1666 B.C., then the cycle is again 19 years with 18 occurring as an irregularity as shown in Table 1.
This cycle would also govern the return of the Moon to the other important alignments such as 94-91, and the trilithon positions. Even the moonrise along 92-93 at the time of the summer solstice would be governed by this 19, 19, 18 cycle. The Sun would return to the trilithon and heel stone at the winter and summer solstice each year. Thus the 19-year cycle was the main periodicity and seems to account for celestial objects returning to their positions as Diodorus implies. A rigid 19-year cycle gradually becomes inaccurate, however, and the winter moon deviates from the heel stone (Fig. 1) unless a correction is made every 56 years.
Eclipses of the Sun and Moon also follow this cycle. An eclipse of the Sun or Moon always occurs when the winter Moon rises over the heel stone; actual winter eclipses4 from 1600 to 1400 B.C. have been indicated in Fig. 1. It should be noted that not more than half of these eclipses were visible from Stonehenge, and so moonrise over the heel stone primarily signals a danger period when eclipses are possible2.
Now I cannot prove beyond all doubt that Stonehenge was used as an astronomical observatory. A time machine would be needed to prove that. Although the stones line up with dozens of important Sun and Moon positions the builders of Stonehenge might somehow have remained in ignorance of this fact. The statement of Diodorus might be a meaningless myth. But perhaps I can reduce the doubt to a shred by showing how other features of Stonehenge are explained by the astronomical theory.
If we take second intervals between the years when the Moon is over the marker stones there is no clear periodicity; in Table 1 the Moon is over D and F every 37 or 38 years. However, a surprising condition exists for the next interval in extreme azimuthsit is almost always 56 years ! Similarly, winter moonrise over the heel stone and eclipses also occur exactly 56 years apart on 84 per cent of all occasions (Table 1). This means that the winter Moon will return to its position over a certain stone every 56 years, and there are many such cycles which will become due in the span of a human lifetime. For example, during 20 years of observation the Moon would take up the ten positions which I have noted2 in both the sarsen circle and station stones. Each of these occurrences would have been a part of a sustained 5 6-year cycle and therefore could have been predicted by a person with knowledge of the cycleknowledge "kept in their family" as Diodorus says.
Table l.
Interval (years)
9
10
18
19
37
38
54
55
56
INTERVAL IN YEARS BETWEEN WINTER MOONRISE OVER STONES D, F AND THE HEEL STONE
Frequency of interval (stone F)
0
0
0
20 32(62%)
39 (77%) 12
0
8 42(84%)
Frequency of interval (stone D)
0
0
0
20
33 (62%)
40 (77%) 12
0
8 43 (85%)
Frequency of
interval (heel stone)
2
70(65%) 35
40
66(62%)
80(77%) 24
1
15
86 (84%)
The number 56 is of great significance for Stonehenge because it is the number of Aubrey holes set around the outer circle. Viewed from the centre these holes are placed at equal spacings of azimuth around the horizon and, therefore, they cannot mark the Sun, Moon or any celestial object. This is confirmed by the archaeological evidence; the holes have held fires and cremations of bodies, but have never held stones. Now, if the Stone-henge people desired to divide up the circle why did they not make 64 holes simply by bisecting segments of the circle32, 16, 8, 4 and 2 ? I believe that the Aubrey holes provided a system for counting the years, one hole for each year, to aid in predicting the movement of the Moon. Perhaps cremations were performed in a particular Aubrey hole during the course of the year, or perhaps the hole was marked by a movable stone.
Fig. 1. The azimuth of winter moonrise from 1600 to 1400 B.C.
Stonehenge can be used as a digital computing machine. One mode of operating this Stone Age monument as a computer is as follows:
Take three white stones, a, 6, c, and set them at Aubrey holes number 56, 38 and 19 as shown in Fig. 2.
Take three black stones, x, y, z, and set them at holes 47, 28 and 10.
Shift each stone one place around the circle every year, say at the winter or the summer solstice.
This simple operation will predict accurately every important lunar event for hundreds of years. For example, to the question: "When does the full Moon rise over the heel stone at the winter solstice ?", the answer is: "When any stone is at hole 56". (Hole 56 is a logical marker because it lines up with the heel stone as viewed from the centre.) In Table 2, I have given the critical years as predicted by the Stonehenge computer for the period 1610 to 1450 B.C. with the stones set so that V was at hole 56 in 1610. This period was chosen because 1600 B.C. is the earliest year for which eclipses have been computed4. Table 2 shows the remarkable accuracy of the Stonehenge computer. The correct year was predicted on 14 occasions out of 18 and the maximum error was only one digit. It also gave the years when the nearest full Moon to mid-summer set through the great trilithon (55-56). Incidentally, a stone was at hole 28 at this time, lining up with the great trilithon.
The stones at hole 56 predict the year when an eclipse of the Sun or Moon will occur within 15 days of midwinter the month of the winter Moon. It will also predict eclipses for the summer Moon. In 1500 B.C. the winter solstice occurred on January 6, Julian calendar, and so the 30 days between December 22, 1501, and January 21, 1500, were the period of the winter Moon. Similarly, the summer Moon and other seasons in 1500 B.C. occurred 15 days late by our present Gregorian calendar. Table 2 gives actual eclipse data showing how Stonehenge scored 100 per cent success in predicting winter and/or summer eclipses. When more than one eclipse occurred, only one is listed in Table 2.
To summarize the mode of operation for the reader, the six movable stones give intervals of 9, 9. 10. 9, 9, 10, . . . years after 1610 B.C. The a, 6, c stones give intervals of 18. 19, 19, . . . years. The Stonehenge cycle keeps in step with the Moon because it gives an average period of 18-67 years and the regression of the nodes of the Moon's orbit is close, 18-61 years. It keeps in step with eclipses because the metonic cycle of 19 years and the saros of 18 years are both eclipse cycles. The metonic cycle has not been previously recognized as an eclipse cycle, probably because it runs for only 57 years or so. It is, however, a remarkable cycle because eclipses repeat on the same calendar date. The lunar eclipse of December 19. 1964, for example, follows the lunar eclipse of December 19, 1945.
Fig. 2. Stonehenge computer ; schematic plan
Table 2. WINTER MOONRISE OVER THE HEEL STONE AND ECLIPSES AT THE SUMMER AND WINTER SOLSTICES
Stonehenge
cycle Year B.C.
1610
1601
1592
1582
1573
1564
1554
1545
1536
1526
1517
1508
1498
1489
1480
1470
1461
1452
Moon over heel B.C.
1610
1601
1591
1583
1573
1564
1554
1545
1536
1527
1517
1508
1498
1489
1480
1471
1461
1452
Lunar eclipses
Solar eclipses
No data available4 JNTo data available4
Jttl. 14, '92 Dec. 24, '92
Dec. 30, '83 
 Jan. 4, '73
Jan. 10, '64 
 Jan. 4, '54
Jan. 10, '45 
 Jan. 14, '36
Jul. 16, '27 Jan. 5, '27
Dec. 31, '18 
 Jan. 5, '08
Dec. 31, '99 
 Jan. 6, '89
Jan. 10,'80 Jim. 21,'80
Dec. 22, '71 Jul. 12, '71
 Jun. 21, '61
Jan. 1, '52 Jul. 12, '52
Table 3. WINTER MOONRISE OVER STONE F, AND ECLIPSES OF THE HARVEST AND SPRING MOON
Stonehenge Moon
cycle over F
Year B.C. B.C.
1597 1596
1578 1578
1559 1559
1541 1540
1522 1522
1503 1503
1485 1485
1466 1466
1447 1447
Lunar eclipses
Apr. 13, Oct. 6, '97 Apr. 13, Oct. 7, 78
Mar. 25, '03
Apr. 4, Sep. 28, '85
Apr. 5, Sep. 29, '66
Solar eclipses Mar. 18, '96
Mar. 29, Sep. 22, '59 Apr. 9, Oct. 2, '41 Apr. 9, Oct. 3, '22 Apr. 9, Oct. 3, '03 Apr. 19, Oct. 13, '85
Mar. 20, '47
When does the winter Moon rise over stone F, and set along 93-91?; when does the summer Moon rise over 91 as seen from 93 ?; when does the equinox5 Moon rise and set along 94-O, and when do eclipses occur at the equinoxes? Answer: When a white stone is at hole 51. A comparison of the Stonehenge prediction and the actual dates is given in Table 3. Again the accuracy is very satisfactory.
When does the winter Moon rise over stone J9, and set along 94-91 ?; when does the summer Moon rise over mound 92 as seen from 93 ?; when does the equinox Moon rise and set along 94-C, and when do eclipses occur at the equinoxes? The answer to all these questions is: When a white stone is at hole 5. A sample run (Table 4) shows the accuracy of the stone machine.
Needless to say, Tables 2, 3 and 4 also predict the appearances of the moonrise and moonset in the trilithon and archways of the sarsen circle, because this later construction repeats the 10 lunar-solar alignments of the station stones.
Table 4. WINTER MOONRISE OVER STONE D, AND ECLIPSES OF HARVEST AND SPRING MOON
Stoueheuge Moon
cycle over D
Year B.C. B.C.
1605 1606
1587 1587
1568 1568
1549 1550
1531 1531
1512 1512
1493 1494
1475 1475
1456 1457
Lunar eclipses
Solar eclipses
jS"o data available4
Apr. 13, Oct. 7, '87 Apr. 7, Oct. 1, '87
Mar. 23, '68 Apr. 7, '68
Mar. 23, '49 
Apr. 3, Sep. 28, '31 
 Mar. 20, Oct. 12, '12
 Mar. 19, Sep. 24, '94
 Mar. 30, Sep. 24, '75
 Mar. 30, Sep. 23, '56
In what years will eclipses occur between the solstice and equinox ? In terms of our calendar, take the months of April and October as an example. When any stone is at holes 3 or 4, eclipses occur during these months. The sector between 51 and 5 has been marked appropriately in the diagram so that it predicts the eclipse seasons according to our present-day calendar.
One remaining requirement was to be able to determine which full Moon was nearest to the solstice or equinox. The average time between one full Moon and the next is 29-53 days and the Stonehengers w^ould need to count that interval. A movable stone in the 30 archways of the sarsen circle would be sufficient. If it were moved by one position each day, full Moon could be expected wThen the stone was at a particular archway, such as 30-1. The stone would require resetting by [plusmn] 1 position every two or three months to stay in time with the somewhat irregular Moon. As the solstice or equinox approached (shown by solar observations), the Stonehenger could decide which full Moon was going to be the critical one. The sarsen circle could also have been a vernier for predicting the exact day of an eclipse. A lunar eclipse occurs when the Moon stone is in archway 301; a solar eclipse when the Moon stone is in 15-16.
A complete analysis shows that the stone computer is accurate for about three centuries, and then the Moon phenomena will begin to occur one year early. This wrould be noticed by the Stonehengers and could have been corrected simply by advancing the six stones by one space. The process is known to-day as resetting or recycling, and is used by all modern computers and logic circuits. A simple rule to add to the operating instructions would be to advance all six stones by one hole when the Moon phenomena are a year earlier than the prediction of a particular stone, say stone a. This is not a critical adjustment. If the error was not noticed with stone a, because of clouds for example, the error could still be corrected with the following stones, x, b, y, etc. The adjustment becomes due once every 300 years or so, in 2001, 1778, and 1443 B.C., for example.
Precession does not affect the accuracy, and the change of obliquity of the ecliptic and Moon's orbit also have very little effect. In 1964, for example, stone a is at 56. The full Moon rises over the heel stone on December 19, will be eclipsed at 2.35 a.m., and will set along 94-G. The next winter eclipse is also visible at Stonehenge, and is marked by stone x, 9 years later on December 10, 1973. The Stonehenge computer will function until well beyond A.D. 2100, when it will require resetting by one hole. It will then function for at least another 300 years before further resetting is required.Diodorus of Sicily, Book II, 47 (Harvard Univ. Press, Cambr., 1935).Hawkins, , G. S., Nature200, 306 (1963).ArticleISIExplanatory Supplement to the Astronomical Ephermeris (H.M.S.O., London 1961).Van den Bergh, , G., Eclipses - 1600 to - 1207 (Tjeenk, Willink and Zoon, Holland, 1954).Newham, , C. A., The Enigma of Stonehenge (private publication, 1964).