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KRONOS Vol II, No. 2

ANALYSIS OF THE BABYLONIAN
OBSERVATIONS OF VENUS
Copyright (c) 1976 by Lynn E. Rose and Raymond C. Vaughan.

*This paper is an expanded version of one that was first presented on June 19 1974 before the international symposium - Velikovsky and the Recent History of the Solar System - held at McMaster Univ., Hamilton, Ontario.

A number of fragmentary tablets written in cuneiform describe the appearances and disappearances of "Ninsianna". It has usually been claimed that Ninsianna is the planet Venus. It has usually been claimed also that these observations cover approximately twenty-one years and that they are to be assigned to the twenty-one year reign of King Ammizaduga of the First Babylonian Dynasty. Such questions as whether the tablets date from the time of Ammizaduga are not dealt with here, since they have already been discussed in the paper, "Babylonian Observations of Venus"; that paper also included a preliminary report on our investigation of the tablets.

The tablets provide a dated sequence of those periods during which Ninsianna is not visible. For example, we may be told that Ninsianna disappears in the west on such-and-such a date, remains absent for so many months and/or days, and reappears in the east on such-and-such a date. This phenomenon resembles the invisibility of an inner planet (one whose orbit lies closer to the Sun than does that of Earth) at the time near inferior conjunction, when the planet is passing between Earth and the Sun. Or we may be told that Ninsianna disappears in the east on such-and-such a date, remains absent for so many months and/or days, and reappears in the west on such-and-such a date. This phenomenon resembles the invisibility associated with superior conjunction, when the planet is passing around the far side of the Sun.

The precise patterns of invisibility that these ancient tablets report might be used in calculating just what orbits and motions of Venus and of Earth would have produced such observations. But the patterns of motion given on the tablets do not fit the present observed motions of Venus. Neither the lengths nor the spacings of the invisibilities are compatible with the present orbits of Earth and Venus. Thus there are two principal approaches that one might take. Uniformitarians, who believe that the orbits of the planets have remained substantially unchanged for thousands, millions, or even billions of years, will take it upon themselves to "correct" what they perceive as the "scribal errors" of the tablets. Velikovskians, who have reason to suspect that the orbits of the planets involved may have been changed within historical times, will try to take as many as possible of the data at face value, and then determine the orbits that might have produced such data.

The uniformitarians who deal with the Ninsianna data frequently stress the complexity and difficulty of their task. But in general the task of the catastrophists who study the Ninsianna data is considerably more difficult. For at least the uniformitarians can assume that a careful retrocalculation of Venus' orbit will show what actually happened several thousand years ago, and that the ancient observations can be "corrected" so as to fit that retrocalculation. This may mean wholesale rewriting of the ancient records, but the uniformitarians carry out that rewriting with unshakeable confidence, since they already "know" what happened anyway. The catastrophists, on the other hand, do not know exactly what happened, and are relying on the ancient records in an effort to find out what did happen. They do not have retrocalculation to use as an aid in interpreting ancient records, because they see retrocalculation as the question-begging procedure that it is.

The catastrophists must consider many more possibilities than the uniformitarians consider. An enumeration of some of these possibilities may seem to present a rather bleak picture and offer little hope of a solution, but let us proceed with such an enumeration anyway, so as to obtain a familiarity with the problems.

If we lack the uniformitarians' prior "knowledge" of the orbits that Earth and Venus were following several thousand years ago, how can we tell whether ancient observations of Venus from Earth have been reported correctly? If the ancient reports were complete and undamaged and entirely consistent, we could simply compute the orbits of Venus and Earth that would have caused such observations. In spite of a widespread view to the contrary, it would be relatively easy to narrow down the approximate kind of orbits that would cause such-and-such observations. If absolute precision is sought, then the problem becomes extremely difficult, even insoluble. But we are not seeking absolute precision. We would be satisfied if we could show that Earth and Venus were on orbits with eccentricities specified within a couple of hundredths and semimajor axes specified within a couple of hundredths of an astronomical unit and perihelia offset specified within a couple of degrees. This is far short of the level of precision that is commonplace in modern astronomy, but it must be remembered that we are not seeking anything like that level of precision. Indeed, our major immediate goal is simply to determine whether the Ninsianna data do or do not prove that Earth and Venus were on orbits definitely different from their present orbits.

Unfortunately, the data are not in such a form that we can proceed directly to such a computation of the orbits. For one thing, most readings of the data include some data which conflict with any proposed set of orbits. The units in which the data are expressed are not fully understood, in that we do not know how long a day or a month or a year was at the time of the observations. We do not know how many days there were in a month, or how many months there were in each year, or how many days there were in a solar year. We do not know whether or how many intercalary months or other intercalary units were inserted at various places. We do not know which of various conflicting readings on different tablets should be relied upon and which should be rejected. And in trying to make decisions about these questions, we have no technique such as retrocalculation to rely upon.

Thus we are faced with the necessity of considering many possible interpretations of the data simultaneously. Where one tablet tells us that Ninsianna disappeared on the 25th and another tablet suggests that the disappearance was on the 15th, we must work with both of these reports, and reserve judgement on which is correct and which is incorrect. In some cases there are conflicting reports even about the month in which an appearance or a disappearance occurred, and we must then consider both of these alternative reports.

There is some question about whether the so-called Years 19 through 21 really were situated in that relation to Years 1 through 17. (The numbering of the years is entirely a modern convention; all we really have to go on is that the observations occur on some tablets in a sequence that appears to be chronological. But Years 19-21 do not occur in the same sequence as Years 1-17. There is a lengthy and extraneous insertion after Year 17 and before Year 19. It is only assumed by modern writers that 19-21 came after 1-17 originally,with a gap for the missing Year 18. But it might just as well be the case that 19-21 came long after 1-17, or even before 1-17.) Such considerations provide us with still more alternative possibilities that must be investigated.

Our intention has been to consider what orbits would produce the observations of Years 1-8, with various alternative readings, with and without intercalary months in various places; to consider what orbits would produce the observations of Years 9-17, with various alternative readings, with and without intercalary months in various places, and with and without Years 19-21 placed after Years 9-17; and finally to consider what orbits might have produced just the 19-21 sequence itself (even though 19-21 may be too short a sequence to permit any effective analysis), with various alternative readings, with and without intercalary months in various places.

Such considerations leave us with an enormous variety of options and alternatives, whose permutations run well into the thousands. Then we are faced with another large number of permutations of the proposed orbital parameters, even though some of the parameters are more important than others: ratio of Earth and Venus periods; inclination of orbital planes; perihelion offset; and individual eccentricities for both planets. If the perihelion offset is to be considered down to the degree, there are 360 possibilities to be considered. If the eccentricities are to be measured to the nearest hundredth, then, even with the arbitrary elimination of eccentricities above, say, 0.3, we are still left with a total of nearly one thousand eccentricity pairs to be considered for the two planets.

The permutations of the interpretations of the data must be one-by-one compared to each of the many permutations of the orbital parameters. The amount of work is enormous, even for a computer. We have chosen so far a combination of computer calculation, computer graph-plotting, and visual comparison of the orbital graphs with other graphs representing the ancient reports. We are not yet fully satisfied with our method. Thus far, we have emerged with a multiplicity of fits that are not too bad, and none that are excellent. Nearly every one of the reported invisibilities can be explained individually - on the basis of one or another set of orbits. But we have not found any one set of orbits that will simultaneously explain all of the reported invisibilities. For one set of orbits, one report will look suspicious; and for another set of orbits, another report will look suspicious.

The one report that presents the greatest difficulty is the invisibility of 9 months 4 days in Year 9. The tablets as a whole suggest a situation in which the orbits of Earth and Venus are roughly coplanar; in which the orbit of Venus lies entirely inside the orbit of Earth; and in which the ratio of the period of Venus to the period of Earth is approximately 0.615. Under these conditions, it would not be possible -- with Keplerian kinematics -- to have Venus remain invisible for three-fourths of an Earth year. It is tempting to suppose that an Earth-Mars collision might have disrupted living conditions and polluted Earth's atmosphere to such an extent that Venus would not have been observed for 9 months 4 days; but that is a highly speculative matter.

Aside from the invisibility of 9 months 4 days in Year 9, we find that the available fits between reported invisibilities and computed invisibilities lead us into a matter of statistics: what kinds of orbits and what ranges of orbital values work best and involve the least discrepancy with the reports? We can give a very rough answer: Earth orbits with eccentricities ranging up to about 0.2; and Venus orbits with somewhat lower eccentricities, ranging up to about 0.15. We can also say that the present orbits of Earth and Venus do not work at all, as the uniformitarians have already found. It is necessary for the uniformitarians to reject thirty or forty percent of the reports in order to make the tablets fit the present orbits. We, on the other hand, would not want to reject more than one or two of the reports in any case, and we would do that very reluctantly and very tentatively.

If Earth and Venus were moving in perfectly circular orbits, with their orbits lying in exactly the same plane, Venus' periods of invisibility at inferior and superior conjunction would follow a very regular pattern. The short invisibilities at inferior conjunction would each have a nearly uniform duration; the longer invisibilities at superior conjunction would likewise have a nearly uniform duration; and all intervals between invisibilities would be nearly equal. The pattern of invisibilities, plotted on a linear time scale, would look something like this:

[*!* Image]

INSERT KII2_07.TIF HERE

[Labels: INFERIOR CONJUNCTION; SUPERIOR CONJUCTION; One synodic period]

If Venus' orbit were then tilted slightly, so that it no longer lay in the plane of Earth's orbit, the pattern of invisibilities would become less and less regular as the orbital inclination increased. The same general effect would be seen, although the details would be different, if the orbits ceased to be perfectly circular: the pattern would become less and less regular as the orbital eccentricities increased.

By deliberately varying such factors as inclination and eccentricities, it is possible to compute patterns of invisibilities for a great many different pairs of hypothetical orbits of Earth and Venus. The work that we have been doing has been directed toward finding a match between one of these computed patterns and the pattern of invisibilities recorded on the Ninsianna tablets. The tablets, which contain a number of alternative readings, show a pattern like this (broken up into segments here, to fit the page):

[*!* Image]

INSERT KII2_08.TIF HERE

The shorter vertical lines separate the months, and the longer vertical lines separate the years; the two specially marked months are intercalary months.

The Ninsianna pattern is definitely less regular than the pattern that would be expected from today's orbits. On the other hand, it is nowhere near as irregular as some of the computed patterns that we have worked with.

Of the many factors that affect the pattern of invisibilities, four of the most important are the eccentricity of Earth's orbit, the eccentricity of Venus' orbit, the inclination of the orbits to each other, and the ratio of the orbital periods. The effects of these four variables are not completely independent; however, there are certain features that are characteristic of the different variables. The two eccentricities and the inclination of the orbits predominate in determining the short-range regularity of the pattern of invisibilities. The long range repetitiveness of the pattern depends primarily on the ratio of orbital periods.

The present ratio of the period of Venus to the period of Earth is approximately equal to the decimal value .6152. The ratio of periods implied by the Ninsianna tablets is roughly the same value. This can be shown, and the nature of the long-range repetitiveness can be illustrated, by using slightly different ratios of integers to approximate the ratio of orbital periods. For example, the ratio 5/8, the ratio 8/13, and the ratio 19/31 are all close to the present ratio of periods:

PV /PE = .6152
5/8 = .6250
8/13 = .6154
19/31 = .6129

where PV is Venus' orbital period and PE, is Earth's orbital period. In other words, eight periods of Venus are roughly equal to five Earth years; thirteen periods of Venus are almost exactly equal to eight Earth years; thirty-one periods of Venus are nearly equal to nineteen Earth years.

There is a fixed relationship between the orbital periods of two planets and their mean synodic period. Using the same three ratios, and assuming that Earth and Venus revolve around the Sun in the same direction, the relationship works like this:

8PV ~ 5PE ~ 3S
13PV ~ 8PE ~ 5S
31PV ~ 19PE ~ 12S

where S is the mean synodic period of the two planets. The convenient feature of the relationship between the orbital periods and the mean synodic period, when expressed in the above manner, is the fixed relationship among the coefficients of PV, PE,, and S in each equation:

8 - 5 = 3
13 - 8 = 5
31 - 19 = 12

It now becomes possible to obtain a rough value for the ratio of periods implied by the Ninsianna tablets. For example, consider the span of time from the first year of the tablets to the seventeenth year: the invisibility of Venus recorded in the seventeenth year occurs 16 years and one month after the invisibility in the first year. By

9 counting the invisibilities, it can be seen that the invisibility in the seventeenth year is the 20th invisibility after the first-year invisibility. If there are two invisibilities per synodic period (i.e., one invisibility at inferior conjunction and one at superior conjunction), then ten synodic periods have elapsed during those 16-1/12 years:

16-1/12 PE ~ 10S

Both sides of the equation can be multiplied by 12 in order to obtain integers for both coefficients:

193PE ~ 120S

The fixed relationship among the coefficients of PV, PE, and S then provides:

313PV ~ 193PE ~ 120S
PV/PE ~ 93/313 = .6166

The value of .6166 for the Ninsianna ratio of periods should be considered only a rough approximation, but it does indicate that the ratio of periods was close to the present value of .6152.

Consider now what the pattern of conjunctions and associated invisibilities would be like if the ratio of periods were exactly 5/8, so that 8PV = 5PE = 3S. For the sake of illustration, assume that Venus and Earth have circular orbits. Imagine that an inferior conjunction (which is an alignment of the two planets on the same side of the Sun) occurs when the planets are at the points labeled zero on their orbits:

[*!* Image]

INSERT KII2_10.TIF HERE

Venus will of course be invisible from Earth for several days due to the glare of the Sun.

The two planets continue to move around their hypothetical circular orbits, and, when half a synodic period has gone by, there will be a superior conjunction (which is an alignment of the two planets on opposite sides of the Sun). The original equation 8PV = 5PE = 3S can be divided by six to give the length of half a synodic period: 1-1/3 PV = 5/6 PE = 1/2 S. In other words, the superior conjunction occurs 1-1/3 periods of Venus or five-sixths of an Earth year after the inferior conjunction. Venus, having travelled one full revolution plus an extra 1/3 revolution, has reached the point on its orbit marked 1. Earth has travelled only 5/6 of a revolution, and has reached the point on its orbit marked 1:

[*!* Image]

INSERT KII211A.TIF HERE

Venus, as seen from Earth, is again obscured by the glare of the Sun, with the invisibility at superior conjunction usually starting about a month before the conjunction and lasting about a month afterward.

As the planets continue to revolve, each conjunction occurs 1-1/3 periods of Venus, or five-sixths of an Earth year, or one-half synodic period, after the previous conjunction. If the consecutive numbering of conjunctions is continued, the even numbers will refer to inferior conjunctions and the odd numbers will refer to superior conjunctions.

The positions that each planet has occupied at inferior or superior conjunction are shown after one, two, and three synodic periods in the diagrams below. As long as the ratio of periods is exactly 5/8, there are only three points on Venus' orbit that Venus can occupy during a conjunction; Venus thus returns again and again to the same three points for its conjunctions. Earth, on the other hand, can occupy six different points before repetition begins:

[*!* Image]

INSERT KII211B.TIF HERE

From a strictly mathematical point of view, Venus' motion can be compared to an arithmetic modulo 3; Earth's can be compared to an arithmetic modulo 6.

For a 5/8 ratio of periods, the pattern of conjunctions would thus be exactly repetitive after each interval of 8PV = 5PE = 3S. Furthermore, the pattern of invisibilities accompanying the conjunctions would also be exactly repetitive, at least as far as the orbital factors were concerned. The idea of exact repetition of invisibilities is complicated somewhat by terrestrial uncertainties such as the weather and such as the possibility that the precise interval of repetition would not be an integral number of days, so that the position of a given observer would not be the same each time, due to the rotation of Earth. Nevertheless, the orbital causes of invisibility would be exactly repetitive after five Earth years if the ratio of periods were 5/8. This is true for highly eccentric orbits as well as for circular orbits. Highly eccentric orbits would produce a highly irregular pattern of invisibilities within the span of five Earth years, but the same irregular pattern would be repeated every five years. In this way, the orbital eccentricities and inclination predominate in determining the short-range pattern, while the ratio of periods predominates in determining the long-range pattern.

Now, consider briefly what the pattern of conjunctions and invisibilities would be like if the ratio of periods were exactly 8/13, so that 13PV = 8PE = 5S. There is not much difference between 5/8 and 8/13, but the slight difference between them is enough to change the long-range repetitiveness. The 5/8 ratio produced exact repetition after three synodic periods. With an 8/13 ratio of periods, Earth and Venus would have undergone conjunctions at the following places on their orbits after three synodic periods:

[*!* Image]

INSERT KII2_12.TIF HERE

Exact repetition of the pattern would not begin, for the 8/13 ratio, until five synodic periods had elapsed; and the pattern would then be exactly repetitive after each interval of 13PV = 8PE = 5S:

[*!* Image]

INSERT KII213A.TIF HERE

Finally, for the ratio 19/31, repetition would begin after twelve synodic periods; and the pattern would then be exactly repetitive after each interval of 31PV = 19PE = 12S:

[*!* Image]

INSERT KII213B.TIF HERE

An idea that is related to the exact repetitiveness of the pattern of invisibilities is the continuity of the pattern when conditions are almost, but not quite, the same. Thus, while the pattern of invisibilities for a 19/31 ratio of periods is derived from conjunctions occurring at only 24 points on Earth's orbit, it gives a representative picture of the invisibilities that can be expected for conjunctions occurring at every point around Earth's orbit, for any ratio of periods close to 19/31, as long as other factors such as eccentricity are kept the same.

The astronomical criteria for the visibility or invisibility of Venus can be understood in the following way: For Venus to be visible in the sky, the Sun must be roughly five and three-quarters degrees, or more, below the horizon. The sky will then be dark enough for Venus, if it is above the horizon, to be seen. This minimum required angle of the Sun below the horizon is termed the arcus visionis.

Another way of expressing the criteria for visibility is in terms of the imaginary celestial sphere. The path of Venus as seen from Earth, the apparent motion of the Sun, and the horizon seen by an observer on Earth, can all be projected onto the celestial sphere; their relative positions can then be calculated using spherical trigonometry, involving two dimensions instead of three.

The horizon seen by any observer on Earth forms a great circle on the celestial sphere. (A great circle is any circle on a sphere that divides the sphere into two equal halves.) At any instant, two different great circles can be defined on the celestial sphere such that: one is the horizon of the point on Earth which has the same latitude as Babylon and which has the Sun, at that instant, 5-3/4 below its western horizon; the other is the horizon of the point on Earth which has the same latitude as Babylon and which has the Sun, at that instant, 5-3/4 below its eastern horizon.

These two great circles divide the celestial sphere into four zones, labeled A, B, C, and D in the diagram below. Zone A contains the north celestial pole; zone B lies to the east of the Sun; zone C lies to the west of the Sun; and zone D contains both the Sun and the south celestial pole. The two great circles follow the Sun's apparent motion across the celestial sphere. Their position relative to the Sun and their orientation relative to the north celestial pole vary, but only very slightly, through the year. At all times, each great circle remains 53/4 from the Sun, while the point of intersection of the two circles that lies directly north of the Sun is never more than 10-3/4 nor less than 9 from the Sun. (The values 10-3/4 and 9 are based on the present 23-1/2 obliquity of the ecliptic and the present 32-1/2 latitude of Babylon.) In other words, the four zones A, B, C, and D remain relatively stable during the course of the year as they move, in unison with the Sun, across the celestial sphere.

[*!* Image]

INSER KII2_14.JPG HERE

The visibility of Venus (or, in principle, any equally bright celestial body in the vicinity of the Sun) depends on which of the four zones it is located in, relative to an observer on Earth. If Venus were in zone A at any time, it would then be visible from the latitude of Babylon both at dusk and at dawn. In zone B, Venus is visible from the latitude of Babylon at dusk, but not at dawn, whereas in zone C it is visible at dawn, but not at dusk. Finally, whenever Venus is in zone D, it cannot be seen at all with the naked eye from the latitude of Babylon. Zone D can thus be termed Venus' zone of invisibility.

As seen from Earth, an inner planet such as Venus moves back and forth, making one cycle per synodic period, between its greatest elongation east of the Sun, occurring somewhere in zone B, and its greatest elongation west of the Sun, occurring somewhere in zone C. Conjunctions occur twice per synodic period as the planet passes through either zone A or zone D. The planet normally passes through zone D, so that the conjunction is accompanied by invisibility; however, with appropriate orbits, there could be conjunctions without any invisibility as the planet passed from zone B to zone C (or vice versa) through zone A.

If the orbits of Venus and Earth lay in exactly the same plane, all conjunctions would be accompanied by invisibilities, as Venus would necessarily pass directly in front of or directly behind the Sun at every conjunction. The different possible paths that Venus could follow through the zone of invisibility would look like this:

[*!* Image]

INSERT KII2_15.JPG HERE

The different angles of Venus' passage through the zone would be due to the inclination of Earth's axis to the plane of its orbit. Because of the repetitiveness of invisibilities accompanying each type of conjunction when Earth returns to the same point on its orbit, the different paths of Venus through the zone of invisibility would be tied to the seasons.

The present orbits of Earth and Venus are not in the same plane; they are inclined approximately 3-1/2 to each other. As a consequence, Venus usually passes somewhat to the north or south of the Sun at conjunction:

[*!* Image]

INSERT KII2_16.JPG HERE

The 3-1/2 inclination of the orbits is measured at the Sun; however, as seen from Earth, Venus can be as much as 8-1/2 above the ecliptic. It is thus possible for Venus to pass within one degree of the vertex of the zone of invisibility. A slight increase of the present inclination of the orbits would be enough to cause Venus to pass occasionally through zone A rather than zone D, producing occasional gaps in the pattern of invisibilities. Such missing invisibilities would occur first at inferior conjunction; a considerably larger inclination would be needed to produce missing invisibilities at superior conjunction.

The fact that there are no missing invisibilities at inferior conjunction in the sequence recorded on the Ninsianna tablets suggests that the inclination of the orbits at the time of the Ninsianna observations was not greater than, say, four degrees at the most.

The effect of different orbital eccentricities on the pattern of invisibilities is a more complicated problem than the effect of different inclinations. We have spent a lot of time developing a rather abstract general method of generating the patterns for different eccentricities. It is fairly simple, however, to establish a rough upper limit on the eccentricities.

A planet whose orbit is circular moves with a constant angular velocity around the Sun. As the eccentricity increases, the angular velocity is no longer constant, but varies as the planet moves around the orbit, with a maximum value at perihelion and a minimum value at aphelion. As this happens with Venus or Earth or both, the pattern of invisibilities is affected greatly, with both the length and spacing of invisibilities becoming less regular as the eccentricities increase.

With relatively low eccentricities, the angular velocity of an inner planet such as Venus is greater at all times than the angular velocity of Earth. As the eccentricities increase, however, the angular velocity of Earth when it is at or near perihelion will begin to be greater than Venus' angular velocity at or near aphelion. It thus becomes possible for a triplet of inferior conjunctions, or a triplet of superior conjunctions, to occur in succession when Earth is near perihelion as the two planets jockey back and forth for the lead. Such a triplet of conjunctions could be accompanied by one, two, or three invisibilities. Venus' path through the zone of invisibility would resemble one of the three following possibilities:

[*!* Image]

INSERT KII217A.JPG HERE

As an example of the effect of increasing eccentricity on the pattern of invisibilities, a segment of the pattern for a Venus-Earth orbital period ratio of 19/31 is shown below. The first line shows the pattern when both eccentricities are zero; the second line is for both eccentricities equal to 0.1; etc. The planetary perihelia are aligned in all four cases. The dotted lines show the continuity that could be expected for intermediate values:

[*!* Image]

INSERT KII217B.TIF HERE

The apparent lack of multiple invisibilities in the Ninsianna pattern is one indication that the eccentricities of Earth and Venus could not have been more than, say, 0.3 at the time of the observations.

In our work on the tablets, we are within sight of some sort of completion point. It is not clear yet whether we will actually perform a full computer search of the many orbital variables and the many interpretations of the tablets to find the best ultimate fits, or whether we will have to be satisfied with just writing the program, if the amount of computer time required turns out to be prohibitive. In any event, it is clear that there will be no single clear-cut orbital solution. The next step in this area would seem to be an analysis of the many late-Babylonian astronomical tablets, to see if they show any small but systematic inconsistencies with the present orbits of Earth and the other planets, particularly with regard to eccentricities.

APPENDIX

The Translation that follows is a conflation and reconstruction of the various Ninsianna tablets, no one of which is complete, and represents our best estimate of what the original series of Ninsianna observations might have contained. Where the tablets give alternative readings, or no reading at all, our choice has been based upon considerations that will be explained in detail in a Commentary (not included here). For ease of reference, year numbers have been added in the left margin, but the tablets themselves do not number the years or provide any other labels for them.

Table I gives the actual data from those tablets that list the invisibilities of Ninsianna in chronological order, and Table II gives the actual data from those tablets that list the invisibilities of Ninsianna in order of the months of disappearance. In Tables I and II, an expression such as "E 19 (5m16d) VI 25 W" for Year 12 means that Ninsianna disappears in the east on the ninth day of the first month, Nisan, remains absent from the sky for five months and sixteen days, and appears in the west on the twenty-fifth day of the sixth month, Ulul. The expression "VI*" refers to second or intercalary Ulul.

The twelve months of the normal Babylonian year were:

I Nisan
VII Tesrit
II Ayar
VIII Arahsamna
III Sivan
IX Kislev
IV Tammuz
X Tebit
V Ab
XI Sabat
VI Ulul
XII Adar

It will be seen that the Translation is in fairly close agreement with the data that are given in Tables I and II, except that where the data are inconsistent or incomplete we have had to make choices or reconstructions. We have proposed significant changes only in the cases of Year 8b and Year 16b, where we think that the intervals of invisibility might have become transposed. Our scenario for this proposed transposition is outlined in Table III.

A Bibliography is appended, including not only serious studies of the tablets but also a number of pronouncements by writers, including noted astronomers, who do not seem to have been very familiar with the tablets.

TRANSLATION

Year

1    In the month Sabat, on the 15th day, Ninsianna disappears in the went;
      for 3 days she remains absent from the sky;
    in the month Sabat, on the 18th day, Ninsianna appesrs in the east;
      catstrophes of kings;
    Adad brings rains, Ea brings streams; king to king greeting send

2    In the month Arahsamna, on the 11th day, Ninsianna disappears in the east;
      for 2 months 8 days she remains absent from the sky;
    in the month Tebit, in the 19th day, Ninsianna appears in the west;
      the harvest of the land is successful

3   In the month Ulul, on the 23rd day, Ninsianna disappears in the west;
      for 20 days she remains absent from the sky;
    in the month Tesrit, on the 13th day, Ninsianna appear in the east
      hostilities occur in the land; the harvest of the land is successful.

4   In the month Tammuz, on the 2nd day, Ninsianna disappears in the east;
      for 2 months 1 day she remains absent from the sky;
    in the month Ulul, on the 3rd day, Ninsianna appears in the west;
      the heart of the land is happy

5a  In the month Ayar, on the 2nd day, Ninsianna disappears in the west;
      for 16 days she remains absent from the sky;
    in the month Ayar, on the 18th day, Ninsianna appears in the east;
      rains and floods occur; the harvest of the land is successful

5b  In the month Kislev, on the 25th day, Ninsianna disappears in the east;
      for 2 months 4 days she rem ins absent fro the sky
    in the month Sabat, on the 29th day, Ninsianna appears in the west;
      the harvest of the land is successful

6   In the month Arahsamna, on the 28th day, Ninsianna disappears in the west;
      for 3 days she remains absent from the sky;
    in the month Kislev, on the 1st day, Ninsianna appears in the east;
      hunger for grain and straw occurs in the land; desolation is wrought

7   In the month Ab, on the 21st day, Ninsianna disappears in the east;
      for 2 months 11 days she remains absent from the sky;
    in the month Arahsamna, on the 2nd dey, Ninsianna appears in the west;
      rains occur in the land; desolation is wrought

8a  In the month Tammuz, on the 25th day, Ninsianna disappears in the west;
      for 7 days she remains absent from the sky;
    in the month Ab, on the 2nd day, Ninsianna appears in the east;
      reins occur in the lend; desolation is wrought.

8b  In the month Sabat, on the 25th day, Ninsianna disappears in the east;
     [for 3 months 9 days she remains absent from the sky;
    in the month Sivan, on the 4th day, Ninsianna appears in the west;
     . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .]*.

 *The bracketed material was eventually lost or deleted, and was replaced
by the year formula, "YEAR OF THE GOLDEN THRONE", which is usually thought
to have been a year formula for Ammizaduga. 

9   In the month Sivan, on the 11th day, Ninsianna disappears in the west;
      for 9 months 4 days she remains absent from the sky;
    In the month Adar, on the 15th day, she appears in the east;
      king to king greetings [or: declaration of war] sends.

10  In the month Arahsamna, on the 10th day, Ninsianna disappears in the east;
      for 2 months 6 days she remains absent from the sky;
    in the month Tebit, on the 16th day, she appears in the vest;
      the harvest of the land is successful
11  In the month Ulul, on the 26th day, Ninsianna disappears in the west;
      for 11 days she remains absent from the sky;
    in the month second Ulul, on the 7th day, she appears in the east;
      the heart of the land is happy

12  In the month Nisan, on the 9th day, Ninsianna disappears in the east;
      for 5 months 16 days she remains absent from the sky;
    in the month Ulul, on the 25th day, she appears in the west;
      the heart of the land in happy

13a In the month Ayar, on the 5th day, Ninsianna disappears in the vest;
      for 7 days she remains absent from the sky;
    in the month Ayar, on the 12th day, she appears in the east;
      the harvest of the land is successful

13b In the month Kislev, on the 21st [?] day, Ninsianna disappears in the east;
      for 2 months [and days?] she remains absent from the sky;
    in the month Sabat, on the 21st day, she appears in the west;
      the harvest of the land is successful

14  In the month Tesrit, on the 10th day, Ninsianna disappears in the vest;
      for 1 month 16 days she remains absent from the sky;
    in the month Arahsamna, on the 26th day, she appears in the east;
      rains occur in the land; desolation is wrought.

15  In the month Ab, on the 20th day, Ninsianna disappears in the east;
      for 2 months 15 days [or 3 months 15 days] she remains absent from the sky
    in the month Arahsamna [or the month Kislev], on the 5th day, she appears in
    the west; rains occur in the land; desolation is wrought.

16a In the month Tammuz, on the 5th day, Ninsianna disappears in the west;
      for 15 days she remains absent from the sky;
    in the month Tammuz, on the 20th day, she appears in the east;
      rains in heaven and floods in the streams occur

16b In the month Adar, on the 25th day, Ninsianna disappears in the east;
      for 2 months 7 days she remains absent from the sky;
    in the month Sivan, on the 2nd day, she appears in the vest;
      disaster of the Umman-manda 

17  In the month Adar, on the 11th day, Ninsianna disappears in the vest;
      for 4 days she remains absent from the sky;
    in the month Adar, on the 15th day, she appears in the east;
      king to king greetings sends; the harvest is successful; the heart of
the land is happy

18? . . . . . . . . . . . . . . . . . . . . . . . . . . 
      . . . . . . . . . . . . . . . . . . . . . . . . . . .
    . . . . . . . . . . . . . . . . . . . . . . . . . .
      . . . . . . . . . . . . . . . . . . . . . . . . . . .

19  In the month second Ulul, on the 2nd day, Ninsianna disappears in the vest;
      for 15 days she remains absent from the sky;
    in the month second Ulul, on the 17th day, Ninsianna appears in the east;
      a defeat occurs in a distant land; in the palace a maid

20  In the month Sivan, on the 25th day, Ninsianna disappears in the east;
      for 2 months 29 days she remains absent from the sky;
    in the month Ulul, on the 24th day, Ninsianna appears in the vest;
      the heart of the land is happy

21a In the month Nisan, on the 26th day, Ninsianna disappears in the west;
      for 7 days she remains absent from the sky;
    in the month Ayar, on the 3rd day, Ninsianna appears in the east;
      hostilities occur in the land; the harvest of the land is successful

21b In the month Tebit, on the 28th day, Ninsianna disappears in the east;
      for 2 months she remains absent from the sky;
    in the month Adar, on the 28th day, Ninsianna appears in the west;
      king to king declaration of war sends
22? 23?  11th day, .. .. .. .. .. .. .. the west;


TABLE I

INVISIBILITIES OF NINSIANNA LISTED IN CHRONOLOGICAL ORDER

Year
     K. 160, Obverse                   K. 2321 + K 3032, Obverse         W. 1924. 802, Obverse
1                                      W             (3d)            E   W XI 15   (3d)   XI 18  E
2                                      E             (2m7d)          W   E VIII 11 (2m7d) X 19   W
3                                      W             (20d)           E   W VI 23   (20d)  VII 13 E
4                                      E             (2m1d)          W   E VII 2   (2m1d) VI 3   W
5a                                     W             (15d)           E   W II 2    (18d)  II 18  E
5b                                     E IX   10[+?] (2m4d)  XI   16 W   E IX 25   (2m4d) XI 29  W
6                                        VIII 20[+?) (3d)    IX   1      W VIII 18 (3d)   IX 1   E
7    E         (    )      VIII 2      E V    21     ( 11d)  VIII 2  W   E         (2m11d)
8a   W IV   25 (7d)        V    2      E W IV 25     (     ) V    2  E             (7d)
8b   E XII  25 (    )                  E XII  25     (     )
9    W      11 (9m4d)      XII  15 E   W III  11     (9m   ) XII  15 E
10   E VIII 10 (2m6d)      X    16 W   E VIII 10     (     ) X    16
11   W VI   26 (11d)       VI*  7  W
12     I    9  (5m16d)     VI   25 W       Rm.     II 531:
13a  W II   5  (7d)                E          2[+?]  (     )      12
     E      20 (     )
13b  E         (16d)       XI   21 W     X    21     (     ) XI   11
14   E VII  10 (1m15[+?]d) VIII 26 W     VII  10     (     ) VIII 25 W
15   E V    20 (2m15d)     VIII 5  W   E V    21     (     ) IX   5  W
16a  W      5  (15d)            20 W   W VIII 4      (     ) IV   20 E
16b  E XII  25 (3m9d)      III  20 W   E XII  15     (     )         W
17     XII  11 (4d)

     K. 160, Reverse                   B. M.  41688
19   W VI*  1  (15d)       VI*  17 E          1      (     ) VI* 14
20   E III  25 (2m6d)      VI   24 W          25 (     )     VI  14
21a  W I    27 (7d)        II   3  E          17[+10?]           28d [?]
21b  E         ( )         XII  28
22? 23?                                "11th day,          the west"

TABLE II

INVISIBILITIES OF NINSIANNA LISTED IN ORDER OF MONTHS OF DISAPPEARANCE

Probable
Year

     Rm. 134               K: 7072                       B. M. 42033:
12   I  8  (5m17d) VI 25     I       (     ) VI   24        I  (5m18d)
21a  I  26 (6d)        E     I    26 (     ) II   3  E      I  17[+10?] ( )          E
5a   II 2  (  )            W II   2  (     )               II  2 "28 days" "15 days" E
13a?                                                     W II  3[+2?]
9?                                                             3[+2? +12?]
20?
?
     S. 174
16a? 8a?  W
                      K. 2321 + K. 3032, Reverse:
15        E        W
7         E                                          W
3         W                W VI   23 (20d)   VII  13 E
                                                            W. 1924. 802, Reverse:
11                         W VI   26 (12d)   VI*  8  E
14                         W VII  11 (1m17d) VIII 28 E      VII ( ) VIII 27
6                          W VIII 28 (5d)    IX      E
2                          E         (2m8d)  X    19 W
10                                   (2m8d)  [X?] 16 W
13b                        E   1[+?] (2m )           W
5b                         W         ( m4d)  XI   28 E
21b                        E         (2m)
1                          W         (3d)    XI   28
16b? 8b?                   E         (2m7d)          W
17                         W         (4d)            E

TABLE III

THE CHRONOLOGICAL LISTINGS THE LISTINGS BY MONTHS

8b 16b Bb 16b
XI 25
(3m9d)
III 4
XII 25
(2m7d)
III 2
XI 25
(3m9d)
III 4
XII 25
(2m7d)
III 2
v v v v
XI 25
( )
XII 25
( )
III 2
XI 25
(3m9d)
XII 25
( )
v v v v
25 XII 25
III 2
XII 25[1]
(3m9d)
XII 25
( )
v v v
II 25 [2]
( )
XII 25
( )
III 20[3]
XII 25
(3m9d)
[4]
v v v
II 25
YEAR OF THE
GOLDEN THRONE [6]
XII 25
(3m9d) [5]
III 20
v v v
as on:
X 160, Obverse,
and K. 2321 + K.
3032, Obverse
as on:
K 160, Obverse [7] [8]
lost?
W 1924 802, Reverse? [9]
[1] The similar and probably adjacent entries on the listing by months have confused, and XI 25 has been read as XII 25
[2] The missing month of disappearance has been erroneously "corrected" or "recovered" fro- the listing by months.
133 III 2 has become III 20
[4] Two different but probably adjacent disappearances on XII 25 have been erroneously conflated into one
[5] The missing interval has been erroneously "recovered" from the listing by months.
[6] The year-formula has been inserted in Year 8b
[7] lb II 531, a variant of K 160, Obverse, gives the disappearance in Year 16b as XII 15 rather than as XII 25
[8] The original interval for 16b has survived, according to this interpretation, in only one place on K 2321 + K 3032, Reverse
[9] Although none of the surviving fragments of the listing by months contains this reading, this is a reading that might once have appeared on W 1924 802 Reverse, in as much as the section of W 1924 802, Reverse, that vould have contained disappearances in month XII has not survived.

MATHEMATICAL VARIABLES

The following independent quantities must be treated as variables (or as constants) in making a comparison between the pattern of invisibilities reported on the Ninsianna tablets and computed patterns of invisibilities of Venus. The thoroughness of the comparison depends on how many are treated as variables. Not included in the list are observational uncertainties such as weather; uncertainties concerning the relationship among the calendar units (year, month, and day), including the number and location of intercalary months; and uncertainties in the Ninsianna data, where different dates can often be read or inferred for the same event.

1. Ratio of the orbital periods of Venus and Earth.

2. Orbital eccentricity of Venus.

3. Orbital eccentricity of Earth.

4. Inclination of Venus' orbit to the ecliptic (the ecliptic = the plane of Earth's orbit, without implying any relationship to the present ecliptic).

5. Heliocentric longitude of Venus' ascending node with respect to vernal equinox.

6. Venus' argument of perihelion.

7. Heliocentric longitude of Earth's perihelion with respect to vernal equinox.

8. Initial positioning of Venus with respect to Earth.

9. Initial positioning of Earth with respect to the calendar.

10. Ratio of the mean calendar year to the orbital period of Earth.

11. Obliquity of the ecliptic.

12. Terrestrial latitude of Babylon.

13. Arcus visionis (= angle of the Sun below the horizon which makes the sky dark enough for Venus to be seen on the horizon).

BIBLIOGRAPHY

Baity, Elizabeth Chesley. "Archaeoastronomy and Ethnoastronomy So Far", Current Anthropology, XIV (1973), 389431. "Comments" by eighteen scholars, 431438. "Reply" by Baity, 439449.

Bosanquet, R. H. M., and Sayce, A. H. "The Babylonian Astronomy: No. 3. The Venus Tablet", Monthly Notices of the Royal Astronomical Society, XL ( 1880), No. 9, 565-578.

Cant, Gilbert. "New Theory Attacked. Rubbish! Say the Scientists", New York Post Home News, April 2, 1950.

de Camp, L. Sprague. Review of Worlds in Collision, in Astounding Science-Fiction, September, 1950, p. 140.

Doermann, Humphrey. "Shapley Brands 'Worlds in Collision' a Hoax", Harvard Crimson, September 25, 1950.

Edmondson, Frank K. "'Worlds in Collision' Is Blasted", Indianapolis Star, April 9, 1950.

Edmondson, Frank K. "A Hoosier Astronomer Calls Velikovsky Book 'Annotated Claptrap' ", Louisville Courier-doumal, April 23, 1950.

Hommel, F. "Ur Dynasty Tablets", Assyriologische Bibliothek, XXV (1920), 197-199.

Huber, Peter J. Review (in German) of John D. Weir, The Venus Tablets of Ammizaduga, q.v. Unpublished as of early 1974.

Huber, Peter J. "Early Cuneiform Evidence for the Planet Venus", read at the American Association for the Advancement of Science Annual Meeting, San Francisco, February 25, 1974. Unpublished.

Kaempffert, Waldemar. "The Tale of Velikovsky's Comet", New York Times, April 2, 1950. Kaempffert, Waldemar. Letter to the Editor (under the heading, ". . . A Collision of Author and Reviewer"), New York Times Book Review, May 7, 1950.

Kugler, Franz Xaver. Im Bannkreis Babels. Munster in Westfalen: 1910. Pp. 147-148.

Kugler, Franz Xaver. Sternkunde und Stemdienst in Babel. Munster in Westfalen: Aschendorff, 1907-1935. 3 vols. II, Teil II, 257-311.

Landau, Joseph. "Did The Sun Really Stand Still for Joshua?", Louisville Courier-Joumal, April 2, 1950.

Langdon, Stephen H. The Illustrated London News, October 10, 1925, p. 666.

Langdon, Stephen H., Fotheringham, John K., and Schoch, Carl. The Venus Tablets of Ammizaduga Oxford: Oxford University Press, 1928.

Larrabee, Eric. "The Day the Sun Stood Still", Harper's Magazine, January,1950, pp. 23, 24. Larrabee, Eric. "Larrabee Rebuts", The Reporter, April 11, 1950.

Miller, Robert Cunningham. "Star Dust", Pacific Discovery, March-April, 1950, p. 3.

Neugebauer Otto. The Exact Sciences in Antiquity. Second edition. New York: Dover 1969. Pp. ;00, 139.

North, John. "Venus, by Jupiter!", London Times Literary Supplement, June 25, 1976.

Pannekoek, Antonie. A History of Astronomy. New York: Interscience Publishers, 1961. Pp.33-35.

Payne-Gaposchkin, Cecilia. "Nonsense, Dr. Velikovsky!" The Reporter, March 14, 1950. p.40.

Payne-Gaposchkin, Cecilia "Payne-Gaposchkin Stands", The Reporter, April 11, 1950. Pensee, "Velikovsky's Challenge to Science", IVR VII, Spring, 1974, pp. 32-33.

Prescott, Orville. "Books of the Times", New York Times, April 3, 1950.

Rawlinson, Henry C., and Smith, George. The Cuneiform Inscriptions of Western Asia (Often referred to as "W.A I.") Vol. III: A Selection from the Miscellaneous Inscriptions of Assyria London: R. E. Bowler, 1870. Plate 63.

Rose, Lynn E. "Babylonian Observations of Venus", Pensee, IVR 111, Winter, 1973, pp. 18-22. (Reprinted in Velikovsky Reconsidered.) Rose, Lynn E. Reply to Ms. van Lieshout, Pensee, IVR V, Fall, 1973, pp. 3940.

Rose, Lynn E., and Vaughan, Raymond C. "Velikovsky and the Sequence of Planetary Orbits", Pensee, IVR VIII, Summer, 1974, pp. 27-34. (Reprinted in Velikovsky Reconsidered.) Sachs, A. J., with the cooperation of Schaumberger, J. I.ate Babylonian Astronomical and Related Texts Copied by T. G. Pinches and J. N. Strassmaier. Providence, Rhode Island: Brown University Press, 1955. Nos. 1560-1563.

Sarton, George. Introduction to the History of Science. Publication No. 376 of the Carnegie Institution of Washington. Baltimore: Williams and Wilkins,1927. 1,71.

Sayce, Archibald H. "The Astronomy and Astrology of the Babylonians, with Translations of the Tablets Relating to These Subjects", Transactions of the Society of Biblical Archealogy, III (1874), 145-339, especially 316-339.

Schiaparelli, Giovanni, "Venusbeobachtungen und Berechnungen der Babylonier", Das Weltall, 6. Jahrgang, Heft 23, 7. Jahrgang, Heft 2 (1906).

Schiaparelli, Giovanni. Scritti Sulla Storia della Astronomia Antica. Bologna: Nicola Zanichelli Editore, 1925-1927. 3 vols. 1, 5-27 contains "Osservazioni e Calcoli dei Babilonesi", the Italian original of the Das Weltall paper. III, 125-233 contains "Osservazioni ed Effemeridi sui Fenomeni del Pianeta Venere Scoperte fra le Rovine di Ninive, ed Oggi Conservate nel Museo Britannico", which was written in 1904 or 1905 but never published during the author's lifetime. III, 123-124 contains excerpts from Schiaparelli's letter of January 24, 1907, on these subjects.

Science News Letter, "Theories Denounced", February 25,1950.

Science News Letter, "Retort to Velikovsky", March 25, 1950. Stecchini, Livio C. "Astronomical Theory and Historical Data", in The Velikovsky Affair, edited by Alfred de Grazia, Ralph E. Juergens, and Livio C. Stecchini. New Hyde Park, New York: University Books, 1966. Pp. 146-152.

Stern, Mort "Did Comets Strike The Earth?", Little Rock Gazette, April 16, 1950.

Stewart, John Q. "Disciplines in Collision", Harper's Magazine, June, 1951, p. 63.

Time Magazine, "Venus on the Loose", March 13, 1950.

Ungnad, Arthur. Die Venustafeln und das Neunte Jahr Samsuilunas (1741 V. Chr.). In Mitteilungen der Altorientalischen Gesellschaft, XIII. Band, Heft 3. Leipzig: Verlag von Otto Harrassowitz, 1940.

van der Waerden, Bartel L. "On Babylonian Astronomy 1: The Venus Tablets of Ammisaduqa", Ex Oriente Lux, X (1948), 414424.

van der Waerden, Bartel L. Erwachende Wissenschaft, Band 2. Die Anfange der Astronomie. Groningen: P. Noordhoff LtdL, 1966. Basel and Stuttgart: Birkhauser Verlag, 1968. pp. 34-52.

van der Waerden, Bartel L. Science Awakening II: The Birth of Astronomy, with contributions by Peter Huber. Leyden: Noordhoff International Publishing, and New York: Oxford University Press, 1974. Pp. 50-59.

van Lieshout, M. G. Letter to the Editor, Pensee, IVR V, Fall, 1973, pp. 38-39.

Vaughan, Raymond C. "A Configuration and Phase Space for Keplerian Planetary Motion". Unpublished.

Velikovsky, Immanuel. Worlds in Collision. New York: Macmillan, 1950. Pp. 198-200.

Velikovsky, ImmanueL Letter to the Editor (under the heading, "Dr. Velikovsky vs. Mr. Kaempffert . . ."), New York Times Book Review, May 7, 1950.

Velikovsky, Immanuel. "Answer to My Critics", Harper's Magazine, June, 1951, pp. 53-54.

Velikovsky, Immanuel. "Answer to Professor Stewart", Harper's Magazine, June, 1951, p. 65.

Velikovsky Reconsidered. Garden City, New York: Doubleday, 1976. Pp. 58, 73-86, 92, 110-132, 250.

Virolleaud, Ch. L'Astrologie Chaldeenne. Paris: Librairie Paul Geuthner, 1905-1913. 13 Fascicules. Fascicules 3 and 7: Nos. IV, XII, XIII, XIV, and XV. Fascicules 9 and 10: Nos. XXXVII, XLI, XLII, and LIV.

Virolleaud, Ch. "Fragments Astrologiques", Babyloniaca, 111(1910), 285. S. 174.

Virolleaud, Ch. "Etudes Astrologiques", Babyloniaca, VI ( 1912), 253. K. 11840.

Weir, John D. The Venus Tablets of Ammizaduga. Istanbul: Nederlands Historisch Archaeologisch Instituut in Het Nabije Oosten, 1972.

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