Naked Eye Astronomy, Patrick Moore, W.W. Norton, New York, 1965:177.Secondly, this paper is neither a cozy seasonal piece nor is it an exercise in de-bunking. It is a non-denominational discourse on the subject for open minds.
"Though Uranus is so remote (1,783 million miles from the Sun at its mean distance), it is distinctly visible to the naked eye when best placed.
The maximum apparent magnitude is 5.7. and keen-sighted people will be able to make it out once they know where it is."
Celestial Objects for Common Telescopes, Rev. T.W. Webb, Dover, New York, 1962:221.
"Uranus, being visible in clear weather to the naked eye, will easily be caught up in the finder by the help of an almanac."
THE SKY - A User's Guide, David H. Levy, Cambridge University Press, Cambridge, 1991:134.
"It is incorrect to limit the number of naked-eye planets to five, since at its maximum brightness of magnitude 5.5, Uranus can be seen without optical aid by a keen-eyed observer."
Thirdly, the biblical "Star of Bethlehem" has been subject to various interpretations, but in 1979, after an extensive analysis astronomer David Hughes1 concluded that the most likely candidate was a trio of Jupiter-Saturn conjunctions which took place in the constellation of Pisces in 7 BC. More recently (1995), another astronomer suggested that the phenomenon could also be explained by the double occultation of Jupiter by the moon in 6 BC.2 Though neither configurations remotely resemble a single "star" or planet, these detailed and otherwise scholarly treatments have been well received, but the fact that the visible major superior planet Uranus was also in Pisces during the period in question does not appear to have been given sufficient attention, although it was apparently suggested in the present context by Stasiuk 3 in 1981.
Discovered fortuitously by William
Herschel with the aid of a
in 1781, this faint, astronomically significant single object is
undoubtedly visible to the naked eye,4,
as Wagner  has pointed out, it is almost surprising that the
was not detected in antiquity.5
But that is not all; Uranus also fulfills eight of the eleven
for the Star of Bethlehem listed by Hughes
twelfth concerns a contradictory bright object). Moreover, Babylonian
- long skilled in observing planetary risings and settings etc., -
have been natural, if not prime candidates for the incidental discover
of a faint outer planet moving in essentially the same orbital plane as
Mars, Jupiter and Saturn. From this viewpoint the discovery of Uranus
Babylonian observers is feasible enough, although whether the complete
orbit was ever fully determined remains another matter altogether. But
in any case, what concerns us here is the motion of Uranus in the
of Pisces during the interval 9 BC to 7 BC, when and where the planet
overtaken by both Jupiter and Saturn. No doubt a series of important
between the latter pair did indeed take place during this time, but
occurrences are not that uncommon, and say what one will, it remains
that ancient observers would confuse the regular and long-established
of two known major planets with a single and apparently transient
Thus Uranus seems to be both a logical and reasonable choice, albeit perhaps an unpopular one...
THE BIBLICAL STAR OF BETHLEHEM
According to the sparse information provided in the Gospel of St. Matthew:
"After Jesus was born in Bethlehem of Judea during the time of King Herod,On learning that the expected location was Bethlehem, King Herod is then said to have:
Magi from the east came to Jerusalem, and asked,
' Where is the one who has been born King of the Jews?
We saw his star in the east and have come to worship him.' "
[Matthew 2-1, 2-2].
"called the Magi secretly, and found out from them the exact time the star appeared"After the latter group departed for their country of origin, Herod next:
"gave orders to kill all the boys in Bethlehem who were two years old and under in accordance with the time he had learned from the Magi,"
OBSERVATIONS OF URANUS AT
But why the subsequent move to Bethlehem? One might suggest here that there could have been a number of reasons both scientific and political. Observations of Uranus could undoubtedly have been made in Mesopotamia and elsewhere, and perhaps they were. But initially, they would know very little because of the relatively slow sidereal motion exhibited by the object (approximately 4 degrees annually) and further complications that would arise from refraction and the relative faintness of the object itself. This in turn, however, may have generated a requirement for additional procedures--procedures that may have involved local meridian transits made at or near opposition. Locations suited to such purposes may or may not have included Bethlehem, but an elevated site above a valley running essentially north to south would certainly be useful for meridian transits (essentially at opposition) to augment any and all other observations carried out on the horizon, i.e., the Babylonian characteristic synodic phenomena known as the "First Appearance in the East," the "Stationary Points"and the "Last Appearance in the West," etc. None of the latter are as simple-minded or as primitive as most modern commentators on the subject would have the casual reader believe. The terms "East" and West" in this context incorporate both diurnal and seasonal components, and even the most rudimentary analysis of Babylonian methodology shows that the procedures not only accounted for the apparent retrograde and forward motions of the planets, they also simultaneously described direct and varying sidereal progress into the bargain. For further information on this topic see Figure 1 below and the additional details provided in: Babylonian Planetary Theory and the Heliocentric Concept.
Figure 1. The Babylonian Synodic Phenomena for Earth and Jupiter
Figure 2. Saturn and Uranus rising in the East at Babylon, March 9 BC
Thus, perhaps aware of the importance of the "Star" to Israel (or perhaps totally oblivious of it and concerned only with obtaining data), the Babylonians after the March 9 BC sighting may have embarked on a journey to Jerusalem, as Hughes suggests. But why Jerusalem, and why ultimately Bethlehem? Here we return to the problems that arise from observing relatively faint objects on the horizon. Arriving there by early September 9 BC in time for a near opposition meridian transit of Uranus, the Babylonians may have proceeded on to Bethlehem where the planet culminated "overhead" at the place of Christ's birth. This scenario could explain two difficult and related biblical passages, namely that: "the star which they saw in the east went before them," (albeit by only two degrees or so of sidereal motion) and that at the opposition meridian transit the "star" therefore: "stood over where the young child was," [Matthew 2-9]. This explanation requires that the birth occurred in 9 BC and that the disastrous meeting with Herod took place during a further visit two years later; which would at least synchonise with Herod's order to kill all boys who were two years old or under.
The suggested initial observation at Bethlehem [35 13E, 31 42N] in 9 BC may also have been both fortuitous and incidental to the visit. However, successive meridian transits of the planet at Bethlehem on, say September 5, 9 BC, and September 9, 8 BC, and again on September 13, 7 BC might have helped to provide:
(1) Confirmation of motility in the same direction and approximately the same plane as the known planets.If Babylonian astronomers were indeed in Jerusalem [35 15E, 31 47N] and Bethlehem again on September 9, 7 BC, and they "were overjoyed" when they saw the star [Matthew 2-10] it might have been, as Hughes has suggested, because they had regained the planet after losing track of it while en route from Mesopotamia, or alternatively, because they were about to obtain confirmatory data concerning the motion of the object in question. In terms of technique, near-midnight meridian transits of a faint object such as Uranus might even be preferred or be a necessary addition to the more usual observation of characteristic phenomena on the horizon. Either way, what can be said in this context is that if an observer was facing south at the northern outskirts of Bethlehem on or around the dates in question, then Uranus might indeed be seen to culminate, or "stand over" one specific location on one special date. The relative positions of Jupiter, Saturn and Uranus, the risings and settings, and the near-midnight meridian transits of the latter at Bethlehem (Israel: 35 13E, 31 42N) on September 5st, 9 B.C., September 9th, 8 B.C., and September 13th, 7 B.C. are thus of special interest. In particular, a local "midnight" meridian transit of Uranus around these dates might indeed be considered to culminate, or "stand over" Bethlehem (and possibly over one location of great significance) if the observer is located just north of the town and facing south.
(2) A synodic arc corresponding to a synodic period for Uranus in the region of 369-370 days.
(3) Eight degrees or so of sidereal motion for Uranus during the +738-day interval between the first and third transits.
BABYLONIAN PARAMETERS FOR URANUS
The Babylonian fundamental period relationships for the three known superior planets appear to have depended on the selection of two integer periods (called here T1 and T2) close to mean sidereal periods (or multiples thereof) for which small, convenient corrections for longitude of opposite sign were determined. The frame of reference for these corrections was provided by some 33 "normal" or "Goal-Year" Stars distributed along and around the ecliptic. Period relations for Jupiter are given in Section 1 of ACT 813 as follows (translator: A. Sachs):7
"Compute for the whole zodiac (or: for each sign) according to the day and the velocity.The Babylonian's appear to have possessed two sets of initial corrections to cope with both the fast and the slow arcs; the second correction in longitude given above (5;00 degrees) concerns the former; for the slow arc the correction was the 4;50 degrees above in association with the 71-year period relation. The full set of periods for Jupiter are given in ACT 813, Section 20, 2 namely intervals of 12, 71, 83, 95, 166, 261, and 427 years (7,7) producing a final integer period relationship to which corresponded 36 sidereal revolutions, 391 synodic periods and a total sidereal motion for the 427-year interval of 36 x 360 degrees (3,36,0).
In 12 years you add 4;10, in 1,11 years you subtract 5, in 7,7 years the longitude (returns) to its original longitude."
"[7,7, years (corresponds to) 6,31 appearances ] 36 rotations, 3,36,0 motion. 33,8,5 (is the) mean value of the longitudes."In Neugebauer's terminology (ACT, pp. 282-283), the relationship is expressed as: N Years = II synodic "appearances" and Z sidereal "rotations" of 360 degrees, although the use of "rotation" in this context is hardly appropriate. The mean synodic arcs for both Jupiter and Mars were rounded at the third sexagesimal place (in the present case 33;8,45 rounded from: Zx360/II = 33;8,44,48,29,... degrees). The number of synodic arcs (II) can be obtained from the relation: II = N - Z with the final period determined by addition such that the corrections in longitude finally cancel out.
T1 = 81 Years, = 80 synodic arcs and 1 sidereal revolution of 360 degrees -10;00 degreesThis hypothetical example supplies a final integer period relationship for Uranus of 583 years as follows:
T2 = 85 Years, = 84 synodic arcs and 1 sidereal revolution of 360 degrees + 7;30 degrees
T1 = 81 Years, 80 synodic arcs, 1 revolution of 360 degrees -10;00 DegreesThe resulting mean values for Uranus based on a final period of 583 years are therefore:
T2 = 85 Years, 84 synodic arcs, 1 revolution of 360 degrees + 7;30 Degrees
T3 = 166 Years, 164 synodic arcs, 2 revolutions of 360 degrees -2;30 degrees (T1 + T2)
T4 = 251 Years, 248 synodic arcs, 3 revolutions of 360 degrees+5;00 degrees (T2 + T3)
T5 = 417 Years, 412 synodic arcs, 5 revolutions of 360 degrees+2.30 degrees (T3 + T4)
FN = 583 Years, 576 synodic arcs, 7 revolutions of 360 degrees with 0;00 degrees correction (T3 + T5)
Mean Sidereal Period = N/Z = 583/7 = 83.28571428 YearsOther possibilities include final integer period relations of 249 years (3 sidereal revolutions), 420 years (5 sidereal revolutions), and also 565, 586, 587 and 589 years (all 7 sidereal revolutions):
Mean Synodic Period = N/II = 583/576 = 1.01215277 Years
Mean Synodic Period = 583 x 12;22,8 Months / 576 = 12;31,9,8,20 Mean Synodic Months
Mean Synodic Arc (u) = N x 360 / II = 7 x 360 / 576 = 4;22,30 degrees
N = 589 Years, Z = 7, II = 582, T = 84.14285... Years, u = 4;19,47,37,43,...
T1 = 82 Years (360 - 9;10)
T2 = 85 Years (360+ 3;40)
N = 587 Years, Z = 7, II = 580, T = 83.85714... Years, u = 4;20,41,22,45,...
T1 = 81 Years (360 - 12;15)
T2 = 85 Years (360+ 4;54)
N = 586 Years, Z = 7, II = 579, T = 83.71428... Years, u = 4;21,08,23,37,...
T1 = 83 Years (360 - 3;00)
T2 = 84 Years (360+ 1;12)
N = 565 Years, Z = 7, II = 559, T = 80.71428... Years, u = 4;30,58,03,52,...
T1 = 80 Years (360 - 3;10)
T2 = 81 Years (360+ 1;16)
N = 420 Years, Z = 5, II = 415, T = 84 Years, u = 4;20,14,27,28,...
T1 = 81 Years (360 - 12;45)
T2 = 86 Years (360 + 8;30)
N = 249 Years, Z = 3, II = 246, T = 83 Years, u = 4;23,24,52,40,...
T1 = 81 Years (360 - 8;40)
T2 = 84 Years (360 +4;20)
SYSTEM A PARAMETERS FOR URANUS
Based on modern aphelion and perihelion distances, Babylonian System A synodic arcs for Uranus might perhaps center around 4;20 for the mean value with 4;2 degrees and 4;40 degrees for "Slow" and "Fast" arcs distributed over 200 and 160 degrees respectively, as applied in the case of Saturn. Or alternatively, around 4;00 and 5;00 degrees with a corresponding mean synodic arc (u) closer to 4;30 degrees, etc.
Finally, for a mean synodic arc of precisely 4;31 degrees the corresponding time would be 12;31,26,39,41,20 months (k = 11,12,19,50,40); more rounded values would be 12;31,26,40 months for k = 11;12,20 r or perhaps 12;31,26 months for k = 11;12 r.
III. HYPOTHETICAL SYSTEM B VELOCITIES FOR URANUS
BASIS: THE 583-YEAR INTEGER PERIOD RELATIONSHIP FOR URANUS:
N = 583 YEARS, II = 576 SYNODIC ARCS, Z = 7 SIDEREAL REVOLUTIONS
P = Number of mean synodic arcs per sidereal revolution = 360/u
Sidereal Period T = P + 1
d = Increase/decrease in velocity (degrees) and time (tithi) per synodic arc = 0;1,10
Amplitude of Synodic Arcs = 1/2Pd = 0;48 (1/4Pd = 0;24)
m = Minimum Synodic Arc ( u - 1/4 Pd) = 3;58,30 degrees
u = Mean Synodic Arc: [(7 x 360 )/576] = 4;22,30 degrees
M = Maximum Synodic Arc (u +1/4Pd) = 4;46,30 degrees
IV. HYPOTHETICAL SYSTEM B TIMES FOR URANUS
(a) SYNODIC FACTORS IN TITHIS (Synodic Arc + k3 = Synodic Arc + 11;12,4,10,r Abbreviated value: +11;12 r )
(m) = 15;10,51,40 r Minimum Synodic Arc (abbreviated value: 15;10,30 )
(u ) = 15;34,34,10 r Mean Synodic Arc (abbreviated value: 15;34,30 )
(M) = 15;58,16,40 r Maximum Synodic Arc (abbreviated value: 15;58,30 )
(b) SYNODIC PERIODS [ IV (a) Values/30 + 12 Mean Synodic months]
(m) = 12;30,21,43,20 mean synodic months
(u ) = 12;31,9,8,20 mean synodic months (369.699569 days)
(M) = 12;31,56,33,20 mean synodic months
It seems possible that the Babylonian astronomers may have had more than one purpose for visiting Bethlehem, related, perhaps, to the continued observation or investigation of the phenomenon in question. Perhaps we will never know, but Babylonian planetary theory dates from at least 500 BC 9 and the visual magnitudes of Uranus (M) range from below the conservative limit for naked-eye observation (M = + 5.8) to as high as + 5.3. Thus the Babylonians could certainly have encountered the planet before, which would at least have prepared subsequent observers for a faint, transitory celestial object, although reacquisition might still have required fortuitous circumstances. However, a favorable situation actually prevailed just prior to the commencement of the Seleucid Era between 312 and 311 BC as noted below. Even so, the extinction angle,10 low visual magnitudes and the slow orbital motion of Uranus would likely complicate Babylonian observations of the characteristic planetary phenomena, although observations of meridian transits augmented by the use of ziqpu stars 11 (which culminate simultaneously with others which rise and set) could perhaps have helped compensate for these difficulties.
THE MOVING FISH STAR
An earlier Babylonian text does in fact contain a cryptic reference to a moving "star" in the constellation of Pisces, i.e., "If the Fish Star approaches the Acre Star...," with the latter star considered to be a member of the adjacent constellation Pegasus.12 The same source also includes additional material in a similar unusual context, i.e.,
"the 56th. Tablet of the astrological series enma Anu dEnlil which treats principally the relations of a star called bibbu to other heavenly bodies, bringing in especially the planets Jupiter, Venus, and Mars."THE STAR THAT "BISECTS THE HEAVENS"
"When the stars of Enlil have disappeared the great faint star, which bisects the heavens and stands, is mul dMarduk-nibirumul SAG.ME.GAR; he (the god) changes his position and wanders over the heavens."If the last part refers to Jupiter alone, it is an odd, if not redundant statement, although it might possibly relate to intermittent sightings of the "star" in question, especially if it occurred while observing this bright major planet. A similar statement is also provided by a Babylonian astrolabe:13
"The red star, which when the stars of the night are finished, bisects the heavens and stands there whence the south wind comes, this star is the god Nibiru-Marduk."The accepted explanation for the faintness of Jupiter in the first context is that the reference pertains to the early morning, but this hardly explains why this one bright, wandering planet should be included in a star list at all, nor does it explain the two references to bisecting the heavens, although this could conceivably refer to observational techniques applied in the case of especially faint objects. In particular, a local "midnight" meridian transit of might indeed be considered to "bisect the heavens" and culminate, or "stand over" Bethlehem (and possibly over one location of great significance) if the observer is located just north of the town and indeed facing "from whence the south wind comes."
THE SELEUCID ERA
Next, the Seleucid Era - a Babylonian astronomical era of unknown significance - begins with Month 0, Year 0 in April 310 BC (311 BCE). In fact, Uranus was occluded three times by Jupiter around this time, i.e., on September 23, 312 BCE, January 2, 311 BCE ( Uranus at opposition and nearly at its brightest, M = +5.4 ) and April 29, 311 BCE, i.e., April 310 B.C. Those with astronomical software can observe from the location of Babylon (Iraq: 44 25E, 32 33N) the positions of both planets, the perceptible parallax exhibited by Uranus with respect to Jupiter between the dates given and the planet's later motion (at its brightest) along the ecliptic through the constellation of Leo.
Lastly, it is worth noting that Jupiter/Saturn alignments occur in basically 20-year and 60-year cycles. Neither are particularly rare and neither deserve the degree of importance ascribed to them by those who favour the notion that such alignments unequivocally represent the "Star of Bethlehem." More important by far for astronomers would surely have been the actual detection or re-acquisition of a new "star" or planet in the constellation of Pisces. This occurrence raises another issue, however, namely that while Jupiter and Saturn return to Pisces in a little more than 900 years, the Jupiter-Uranus return occurs approximately twelve years later, i.e., towards the end of the following 12-year sidereal period of Jupiter.
Since this paper is a non-denominational discourse on the subject for open minds it may be pointed out that in addition to 7 BC, Jupiter/Uranus alignments in Pisces also occur in 919 AD; see, for example, the risings in the east on April 20, 919 AD. This latter date is provided for those who wish to embrace the far-reaching implications that attend the revised chronologies proposed by A. T. Fomenko.14
For further information on this complex topic see the latter's:"Empirico-statistical analysis of narrative materials and its applications to historical dating", his New Chronology of the World History, and more recently (2005) the comprehensive analysis of the matter provided by Florin Diacu.15
Deferring biblical aspects to biblical scholars and matters astrological to astrologers, questions remain regarding supporting evidence for the present hypotheses and the level of Babylonian astronomy in general. Firstly, because of the relatively low visual magnitudes of Uranus it is possible that the orbit could not be completely determined. Secondly, although no unambiguous references to an additional planet are apparent in the historical record, there nevertheless remain enigmatic statements and parameters of unknown significance in both earlier Babylonian material and the astronomical cuneiform texts of the Seleucid Era. Thirdly, it is far from certain whether the information provided in the latter represents the state of Babylonian astronomy per se, or the remnants of a much larger corpus of knowledge. The very existence of these texts was unknown until the last century, what has been reclaimed can hardly be considered sequential or self- explanatory, and a number of Babylonian parameters still remain unincorporated and unexplained. Complex issues arising from precession, the various types of months, and the definition of the "year" represent merely the luni-solar component of Babylonian astronomy. Others issues arise from the limited number and uneven distribution of the extant planetary texts. In fact, sufficient gaps and uncorrelated parameters remain to suggest that Babylonian astronomy was quite likely more developed than is normally assumed. Included here are unexplained parameters and operations in the planetary texts and uncorrelated corrections for both the solar velocity16 and the zodiac 17 in the lunar material. One might also consider the implications of the extensive range of the Babylonian period relations, synodic phenomena in association with varying, direct, and retrograde velocity, closed orbits, lines of apsides, and not least of all, an unexplained and strangely ignored "mathematical problem" concerning a "trapezoid," "area, "length," and unknown terminology which occurs in two astronomical "procedure texts" for Jupiter.18 Until these matters are addressed more adequately, it would surely be premature to dismiss the capabilities of Babylonian astronomers, or their possible naked-eye detection of Uranus, conventional wisdom, conventional chronology and the status quo notwithstanding.
Copyright © August 31, 1996, John N.Harris, M.A. (Cmns).
1. Hughes, D. The Star of Bethlehem, (Walker and Company, New York, 1979) 199.
2. Molnar, M. Quarterly Journal of the Royal Astronomical Society, Vol 36, (1995) 109.
3. Stasiuk, G. The Planetarium, Quarterly Journal of the International Planetarium Society, Vol 10, (1981) 16-17, according to the Executive Editor of this Journal (John Mosely of the Griffiths Observatory).
4. Levy, D H. THE SKY - A User's Guide, (Cambridge University Press, Cambridge 1991) 134.
5. Wagner, Jeffrey K. Introduction to the Solar System, (Holt, Rinehart and Winston, Orlando 1991) 334.
6. Hughes, D. The Star of Bethlehem, (Walker and Company, New York, 1979) 202-203.
7. ACT 813, Section 1, Astronomical Cuneiform Texts, (Lund Humphreys, London 1955) 404.
8. ACT 813, Section 21, Astronomical Cuneiform Texts, (Lund Humphreys, London 1955) 414.
9. Van der Waerden, B. Science Awakening II, (Oxford University Press, New York, 1974) 67.
10. Thom, A. Megalithic sites in Britain, (Oxford University Press, New York, 1974) 161-163.
11. Horowitz, W. "Two New Ziqpu-Star Texts and Stellar Circles,"Journal of Cuneiform Studies, Vol 46, (1994) 89-98.
12. Gadd, J. "Omens Expressed as Numbers," Journal of Cuneiform Studies, Vol 21. (1967) 56.
13. Van Der Waerden, B. Science Awakening II, (Oxford University Press, New York, 1974) 66-68.
14. Fomenko, Anatoli. T. Empirico-Statistical Analysis of Narrative Material and its Applications to Historical Dating, (Kluwer Academic Publishers. Netherlands 1994)
15. Diacu, Florin. The Lost Millennium: History's TimeTable Under Siege, (Alfred A. Knopf Canada, Toronto 2005)
16. ACT 200, Sections 7, 9, Astronomical cuneiform Texts, (Lund Humphreys, London, 1955) 193-195, 198.
17. ACT 202, Section 2, Astronomical Cuneiform Texts, (Lund Humphreys, London 1955) 242-244.
18. ACT 813, Section 5, Lines 1-4 and ACT 817, Section 4, Lines 1-12, Astronomical Cuneiform Texts, 405, 430-431.
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