Probable Visibilities of Venus at the Time of the Supposed Spin Rate Acceleration of the Earth MICHAEL G. READE The Data (1) The Venus table of the (Mayan) Dresden Codex indicates a 584-day synodic cycle for Venus, broken down into 8 days invisibility at inferior conjunction, 236 days visibility as morning star, 90 days invisibility at superior conjunction and 250 days visibility as evening star. (2) A. F. Aveni, in his Skywatchers of Ancient Mexico (University of Texas Press, 1980), has the following footnote (p.327): "It is curious that that the Babylonians also counted a three month disappearance interval ..." (quoted by Aveni from A. Pannekoek, A History of Astronomy (London, 1969), p. 33). (3) A portion of the Babylonian "Ninsianna" (or "Ammizaduga") tablets, frequently referred to as "the artificial insertion", contains a number of reports on Venus, all of which claim a 90-day disappearance at superior conjunction (Rose & Vaughan, Kronos V:4); the synodic period of Venus comes out at 587 days in this set of records, which appear to be artificially contrived ones, rather than actual observations. Rose and Vaughan argue (op. cit.) that they are actually a form of "smoothed average" of observational data cited in other parts of the tables, presumably intended for use for astrological purposes. The Dresden Codex tables are also suspected of being designed for use by astrologers and presumably present a not dissimilar "smoothed" motion of Venus, except that in their case the synodic period has been adjusted to its modern value (approx. 584 days). (4) Modern Venus has a 583.92-day synodic cycle, composed of 6½ days invisibility at inferior conjunction, 254 days visibility as morning star, 69½ days invisibility at superior conjunction and 254 days visibility as evening star (averaged values, as computed for the Panchasiddhantika article presented in SISR V:2 - q.v. for the visibility/invisibility criteria applied). (5) Varaha Mihira ("An Introduction to the Evidence of the Panchasiddhantika", SISR V:2), in his breakdown of the "strange synodic period" of Venus, shows a visibility as morning star of 235 days (compare with the 236 days of (1), above). It can be inferred that the corresponding invisibility at superior conjunction was 96 days and the corresponding invisibility at inferior conjunction 10 days. He says nothing at all about Venus as evening star, beyond that it had a subsequent and apparently symmetrical motion as an evening star. His whole Venus (synodic) cycle appears only to have been 575½ days, however (compare with (7), below), which would indicate a visibility as evening star of 234½ days (575½ - 10 - 235 - 96 = 234½). (6) The Babylonian "Ninsianna" observations (as reconstructed by Rose & Vaughan, Kronos II:2; also Pensée III; Kronos V:3, V:4 and VIII:l) include a morning-star visibility of 235 days followed by an evening-star visibility of 250 days (compare with (1), above). It occurred immediately after event 9 (the anomalously long invisibility at inferior conjunction). The duration of the invisibility between these two was only 66 days, however (event 10, superior conjunction). There was no actual disappearance of 90 days recorded in the Ninsianna observations (except as quoted in (3), above), the only ones at all close to this figure being the 89-day one of event 20 and the 99-day one of event 8b. [*!* Image] Modern orbits of Mercury, Venus, Earth, Mars to show conjunctions. (Orbits are drawn circular. The outer planets circle the Sun more slowly than the inner ones). Mars at conjunction. Sector within which conjunctions between Mars and Venus are possible. Mars and Venus are both invisible when in this sector. Venus at superior conjunction. Venus at greatest elongation as evening star. Venus at greatest elongation as morning star. Venus at inferior conjunction. Mars at opposition. Mars. Earth. Venus. Mercury. Sun.] (7) The article "Ninsianna & Ramesside Star Tables" (awaiting publication in SISR) examines Rose & Vaughan's reconstruction of the observations recorded on the Ninsianna tablets and claims that they fall into two groups: a first and earlier group which shows an average synodic period of 578.2 days, with a second and later group which shows an average synodic period of 584.75 days. It is further argued that the "break point" between the two groups probably lies between events 8a and 8b, and that event 8a was synchronous with the conspicuous celestial disturbance indicated by Months 3 - 5 of the Ramesside Star Tables (SISR IV:2/3; the Ramesside star tables show an accompanying acceleration in the spin rate of the Earth, such as would be consistent with the change in the synodic period of Venus found in the Ninsianna observations). "Ninsianna & Ramesside Star Tables" incidentally also includes evidence that the changes were more slurred than sharp and that, in some respects at least, the irregularities were spread over a period of years. ____________________________________________________ Visibilities of Venus _________________________________________________________________ morning star evening star Present day (a) 254 days 254 days Mayan 236 days 250 days Hindu 235 days ? days Babylonian (b) 235 days 250 days Notes: (a) These are average values. The deviation can probably be up to about 15 days on occasion but the pattern of variations is complex and the acceptable combinations of morning and evening star visibilities have not as yet been satisfactorily evaluated. (b) This is only one pair of values out of a large number of recorded ones but this pair is particularly significant because it follows immediately after Event 9 of the Ammizaduga tablets. This event indicated a very abnormal inferior conjunction of Venus. The Mayans also emphasize the specially villainous nature of Venus immediately following inferior conjunction. (c) It is still an open question what orbital changes, if any, are indicated by this apparent deviation from normality. The deviations must in any case be considered in conjunction with other deviations shown on the Ammizaduza tablets. ____________________________________________________ Conclusion We therefore have four sets of data - the Panchasiddhantika, the Dresden Codex, the Ninsianna tablets, the Ramesside star tables - all of which seem to relate to the same event. The Mayan and the Hindu data can also be related to one another, in the sense that their celestial arithmetic is remarkably similar; Hindu yugas and mahayugas, for instance, have essentially the same properties as Mayan tuns and katuns. Both societies also have a similar attitude to the astrological uses of astronomical observations. A hypothesis worth deeper study is that these habits originated on the Indian subcontinent and migrated across the Pacific, via Easter Island, to the central American mainland; it could, of course, also be that the migration was in the opposite direction, but it looks very probable that there must be some link between the two. None of these four versions of the troubled period surrounding the spin rate change can as yet be dated by any absolute means. Currently, the best hope of progress appears to lie in identification of the "noteworthy event" recorded by Varaha Mihira and shown as occurring 60 days before superior conjunction of Venus. A potentially viable speculation is that it marks the heliacal setting of Sirius, at the start of a period when Venus threatened possible interference with Orion (= Osiris), possibly even a clash between Sirius itself and Venus, which at least the Egyptians would have seen as potentially catastrophic (possibly upsetting the rising of the Nile and the ensuing growing season). If this hypothesis is verifiable, it offers a potential astronomical dating of the event (look for the years in which Sirius set heliacally 60 days before a superior conjunction of Venus - they recur once in every 240-year period, approximately). Discussion The moment of "heliacal setting", as recognized by the ancients, is unfortunately difficult to determine with any certainty. "Heliacal setting" occurs when Sirius, which is chasing the Sun across the sky and steadily overtaking it, finally catches up with it and is lost to sight behind it. Possibly the best guide as to how the ancients determined the moment of final disappearance is given by the Egyptian claim that Sirius disappears into the "Duat" (the underworld) for 70 days. This claim suggests that Sirius would have had about 15.5° greater altitude than the Sun (with respect to the horizon for an observer in 25.7° N. latitude at c.750 BC) at both heliacal setting and rising (= the moment of reappearance of Sirius on the other side of the Sun, ahead of it instead of behind it). It could be, for instance, that Sirius is last seen when about 6° above the horizon, with the Sun 9.5° below the horizon. The situation when Sirius is close to heliacal setting is that the deeper the Sun dips below the horizon, the darker becomes the night sky and the more easily is Sirius seen. As Sirius dips towards the horizon, however, its brilliance slowly dims, and at some point its rate of fading will become greater than the rate of darkening of the night sky (at which point it disappears). The same sequence of events applies in reverse at heliacal rising but there can be no guarantee that the height of Sirius above the horizon at heliacal rising will be exactly the same as its height at heliacal setting, though the two should be very similar (they are unlikely to be identical as there is a difference of date between the two events which particularly affects the angle and rate of ascent or descent of the Sun; the horizontal separation of Sirius and the Sun, as measured along the horizon, is also different, which has a slight effect on the brightness of the sky directly behind Sirius). When the Sun is at a fixed (small) height below the horizon, the change in altitude of Sirius from one night to the next will be approx. 0.9° and one has also to assess whether this change is enough to make it possible for an observer to identify the precise day of disappearance or reappearance with any real certainty. In view of the potential effects of a slight change in weather conditions on the darkness of the sky and the brightness of Sirius, it appears doubtful whether the reproducibility of the determinations from one year to the next could be very good, especially as Sirius is glimpsed only briefly on both occasions (at the last dusk before disappearance and at the first dawn of reappearance). The obvious way round this difficulty for the observers of the time would be to set up markers which would indicate the bearing and altitude of Sirius at the expected, or "official", moments of disappearance and reappearance; particularly the altitude marker would assist the observer to recognize whether Sirius had arrived at the proper spot or not (NB the bearing of Sirius when at a fixed altitude does not change from night to night but on the last night before disappearance Sirius would only show very briefly at this one spot). If the proposed critical altitude of 6° is accepted as a reasonable starting point, the bearings of the two markers, as seen from the observing position, would be S. 67° W. and S. 67° E. for heliacal setting and heliacal rising respectively (247° & 113° true). The function of a "Djed" pillar, particularly, seems never to have been satisfactorily established and it could be that it is such a marker. Does any archaeologist know of a potential observatory site with two such "markers" which could function as described? The precise bearings would be slightly modified if (a) the critical altitude of Sirius proved actually to be rather greater or rather less than 6°, (b) the observatory was in a different latitude from 25.7° N. or (c) the estimated date of 750 BC was 250 years or more in error (due to the effect of the precession of the equinoxes on the declination of Sirius). Any departure from the Egyptians' ''official disappearance interval" of 70 days would also show up in the form of modified bearings for the markers and it is therefore desirable that the purpose of the markers should, if possible, be confirmed from some other source (e.g. it is known that Djed pillars are in some way connected with the heliacal rising of Sirius - see Brugsch's Thesaurus). The angle of sight (above the horizontal) from the eye of the observer to the top of the marker is of particular interest, for this is what one would principally rely on for computation of the precise date of the event, though the combination of altitude and bearing makes assurance doubly sure. It must also be observed that a difference of altitude of 15.5° between the Sun and Sirius at heliacal setting and rising is remarkably large, larger than seems reasonable, though it appears to be inescapable if the 70-day disappearance claim is accepted. Observations made in England suggest that a 9° difference of altitude, producing a 56 day disappearance in latitude 25.7° N., would be more likely. This would result in bearings of about S.68.5° W. and S.68.5° E. (248.5° and 111.5° true) for the markers. Even if all the uncertainties in the above evidence should eventually be resolved and even if it should eventually be proved beyond all doubt that all four sets of data refer to the same event, a caution is needed that astronomical dating of an event which occurs in the middle of a prolonged disturbance of normal celestial motions can probably be challenged as unreliable. Readers may like to be weighing up the implications of this uncertainty, which may or may not prove resolvable in the long term. ____________________________________________________ Canadian SIS Seminar: Haliburton, 3rd & 4th September 1983 If you would like to attend this Seminar please contact Frank Wallace (publisher/treasurer CSIS) at Haliburton Highlands Secondary School, P.O. Box 390, Haliburton, Ontario K0M 1S0, Canada. ____________________________________________________ Proposed 10th Anniversary Tour of Egypt, 28 August 1984 A reminder to those members still contemplating making a reservation on this tour, there are still a few places available. Please contact Derek Shelley-Pearce at the Workshop editorial address (see title page) as soon as possible. _________________________________________________________________ \cdrom\pubs\journals\workshop\vol0502\05prob.htm