HEADINGS :- / Discovery / Details of Event / Acknowledgements / 2nd Discovery / Lunar Eclipse June 20th, 3340BC / Lunar Eclipse Dec 14th, 3340BC / Criticisms of Solar Eclipse / New Moon Sighting Record / Interpretation of Petroglyphs & Eclipse Deduction / Delta T Overview / Lunar Acceleration Measurements / Scientific Modelling...... / Factors of Earth's Rotation........ / DU Program Compared to JPL Horizons / JPL Source Sheets / Sun & Moon Positions per JPL / Comparison of DU to JPL Reduced / Sun's Reduced Position / Doppelganger Experiment / Methodology / Criteria for Doppelganger Experiment / Doppelganger ....... Results / Summary Conclusions / Further Criticisms Raised / Weight of Evidence for Discoveries... / Implications for Neolithic Iconography Decipherment / Recommendations / Webography / Bibliography
Scientific Modelling, Delta T and the Principle of Uncertainty
When scientists try to measure back in time the effects of Delta T , they are faced with very difficult circumstances. Because no measurements are known very far back in time, eclipses, lunar occultations and planetary transits of the Sun become the only link into the distant past. Interpretations of recoverable records can present problems. For instance, interpretation can be hindered by fragmented remains, conflicting writing systems, loss of records, or conflicting accounts of eclipses. The further you go back in time the less the record survives to be interpreted. Initially parchments can be recoverable up to a certain time. Clay tablets from the Assyrian Empire and Babylonia are very fragile. Perhaps the only medium to record on is the impermeability of stone. This becomes the only record to survive over large tracks of time. The choice of stone for carving also determines its survivability. Currently Limestone is an extremely porous material which can deteriorate rapidly under the action of water. Witness the current state of affairs at Giza plateau in Egypt. The sphyinx's face is developing cracks because surface water is undermining its foundations and corners of the 3 main pyramids are crumbling away under the same action. In Ireland the Neolithics used a variety of hard stones and soft to pick dress their symbolism. Granite and Greywacke were the most durable. Inside Cairn L monument nearly all the stone work is Brown Sandstone, of relative durability. But the pillar is of a Blue Limestone quality. If the pillar was placed outside then weathering would have caused it to crumble long ago. All the interior workmanship is intact and protected by tons of rocks that generally keep the interior relatively dry. But this ability for symbolism to survive lends itself to interpretations because no 'dictionary' was left behind to decipher the stones.Now we come to the modelling of the behaviour of Delta T which means having to set up a Scientific model with arbitrarily choosen parameters. The available data is then 'tested' within their parameters and any data that does not 'fit' the limits is discarded. Unfortunately you get advantages and disadvantages with this method. In all liklihood, if a measurement could be made directly then it is chosen. Delta T 'modelling' is the perfect example of how the scientific method is used. Unfortunately a scientific 'model' is essentially superimposed over nature. It creates an artificial world in which theories can be tested. Because we are dealing with very difficult forces in action affecting the values of Delta T , inferences and suppositions are frequently made. In essence, Delta T modelling is analogous to the scientific physics discovery made by Werner Heisenberg back in about 1927 . He found out that in dealing with sub atomic particle properties, instrumentation could only accurately measure 2 of 4 properties at the one time. For instance, the two canonically conjugate variables , time and energy, could be accurately measured at the expense of imprecision for momentum and position of any sub atomic particle. He termed this "The Uncertainty Principle," or "Principle of indeterminancy." In much the same way, drawing a line through a set of scattered eclipses on a graph to gain an average Delta T formula will not include any specific eclipses that are not on that line. One measure is invariably at the expense of another!!! Assumptions have to be drawn in order to move the 'model' and its dataset along. Eclipses,occultations & transits present a value of Delta T that 'snapshots' the rate of rotation of the earth. Because this rotation is not a constant over time in order to model Delta T , the assumption is drawn up that the lunar orbital acceleration has to be a constant for the model to produce a parabola or curve .
Some of the Factors affecting the Rate of the Earth's Rotation
1. The Earth has a decelerating spin.
2. The Moon has an altering acceleration in its orbit.
3. The last ice age melt produced a shrinking of the Earth's equatorial bulge that forced an additional accelerative spin by " isostatic rebound".
4. The lunar tides, and to a lesser extent Solar tides, produce a friction against the Earth's rate of rotation.
5. Upper and lower earth crust mantle movements complicate the earth spin rate and have only been measured back approx. 250 years ago.
6. Earthquakes, weather patterns, near asteriod collisions also affect the gravitational influence of the Earth - Moon system and indirectly the earth's spin and lunar orbit.
7. Polar wobble and the Chandler wobble produce effects on the spin rate that are decadal but could be of longer duration.
8. Other unknown factors
Number 1 and 2 above have a counteracting affect on each other . Theoreticaly, if the earth slows down and the only factor is the moon then the moon accelerates and spins outwards in its orbit. By one estimate the moon has moved outward by some 400m, by another estimate its 80 m. By the law of the conservation of energy, 'angular momentum' or energy transference is passed to the moon. Numbers 3 and 1 were opposing effects and were sensitive in NORTHERN and Southern mid latitudes of the earth. They affected number 2 also. The last ice age produced a 'weight' of ice at the poles which produced an additive bulge at the equator and caused the earth to slow its spin rate down. After the ice melted then the bulge shrank and the earth tried to return to a near sphere again but that produced the opposite effect (faster spin rate) and probably not always a smooth one over time. 5000 years ago was closer to that ice melt than medieval times. Number 4 is probably the most complex one. It interacts on an opposing way to number 2 and number 1. Numbers 6 and 7 affect 1(directly) and 2 (indirectly). Number 8's effects are unknown. Add to all these complicated forces the fact that you cannot accurately measure half these forces back millennia ago. Therefore estimates and statistical analyses based on probabilites and mathematical modelling become the only scientific 'arm' that reaches out to the distant past. Another problem is the length of day variates over time and influences the Delta T value. There are also periodic effects underlining all of the above that science cannot yet know, never mind measure. Therefore when you produce a Delta T model you have to try to simplify things and the major components of the above factors are used to try to map out the underlying trend ,IF possible, to Delta T. One of the predominant factors is the lunar orbital acceleration(n-dot) , as I've mentioned before. Depending on who you quote , this can account for from between 33 - 50% of the effect on the Earth's rotation. It must be said that scientists have to pick a lunar orbital acceleration measurement and apply it over extended time as an average without knowing if indeed that measurement is correct. The current model used by scientists has a lunar orbital acceleration pick of -26.00"/cy² which is applicable to 2300BC if the acceleration was a constant over 2 millennia ago.(NOTE 3) You will know that PC planetarium programs adopt various lunar orbital acceleration measures. In essence, the eclipses in 3340BC are the only indirect measure of the lunar orbital acceleration in that epoch and they give a measure of -23.89461"/cy². Therefore something happened to the Moon's orbital acceleration which slowed down and by inference the earth's spin speeded up. But that is a very simplified conjecture. Other factors could easily be involved here. Therefore in the Fourth millennium BC the lunar orbital acceleration would have been different. The difference is very small, some 2 arcsecs rate over each century. Professors Stephenson and Morrison submitted a modelling analysis in 1995 to the Royal Society of London. The main trust of their paper was to measure the non-tidal component of the rate of rotation and drive a parabolic delta T curve through a series of eclipses between 700BC and 1620 AD.(NOTE 4) They arrived at the Delta T value of 31T² where T = (year-1820AD) or time in centuries before 1820AD. Kevin Pang and Kevin Yau of the JPL (Jet Propulsion Laboratory) in California found, together with a team, a Chinese eclipse in Sept. 1912BC. Their Delta T measure gives them 30 +/- 2.5 T².(note that the variance +/- 2.5 T² is very high; this is somewhat due to their eclipse not been known at an accurate geopgraphical location, among other factors). So the upper level of the variance could be evidence of a creep in rising delta t values back in time. My eclipses give a measure of 39.35 +/- 0.3 T² where T = (year-1820AD). (note the variance is very small with a precise geographical location for the recordings). This measure will be steeper than the 31T² curve and have a different tidal curve boundary to it other than 40T² because the lunar orbital acceleration is of a lower value than Professor Stephenson's model. However, the professors will readily admit a number of things about their modelling. No ONE Delta T curve will capture ALL eclipses over ALL epochs of time.(NOTE 5) The non-tidal component isolated by them shows scatter of the eclipses over time. Perhaps showing what a Delta T curve looks like, at least in principle, will help, see below.
You can see actual Delta T curves by clicking the links below from a German web site by Professor Bernd Pfeiffer of the University of Mainz
This graph shows timed solar and lunar eclipses. On the graph the highest placed dotted line is the tidal friction of the moon at 40 +/- 2T² Notice the vertical scattering of the eclipses.
Non Tidal component(Alternative Darsteelung) between -721BC and 1280ADThis graph shows what's called 'solution space' as vertical lines that give a range of time for the eclipse occurances in question.
Timescales Length Of Day(Zeitskalen) between 1600AD and 2000ADThis graph shows us how the length of day (LOD) variates over a small time scale(400 years). There are smaller sharper oscillations that make up this graph.,
All data(Ausschnitt) between 400BC and 1600ADHere we have both timed and untimed solar and lunar eclipses on the one graph. You can see readily the cubic spline dashed line that I mentioned before criss-crossing the full line at knotches.
An alternative account is given at
/www.blackwell-synergy.com/links/doi/10.1046/j.1468-4004.2003.44222.x/full/#h9
This is Professor Stephenson's Harold Jeffries lecture in Oct 2002 and gives a slightly more detailed account of the 1995 & 1997 papers without too much mathematical detail.
If that doesn't open simply scale back the URL to the links section and search for it there under the subheading 'Geophysics and Astronomy' April 2003. This presentation has all the graphs mentioned above from the German site but in English
Precision of Eclipse and Non-Eclipse Timings
Just how precise and therefore reliable are timings with regard to compiling datasets? Professor Stephenson et al in his R.S.L. 1995 scientific papers mentions that non-eclipses are of "considerably lower precision". He is referring to Mercury transits and lunar occultations from 1677AD to 1973AD (NOTE 6)as compared to the post 1955AD measurements with the introduction of the highly accurate Atomic clock (TAI). Throughout his work, the professor labels eclipses researched as having "fair precision" (1995 R.S.L. paper ; Harold Jeffries lecture 2002). Other scientists studying these eclipses label them " low precision" but nevertheless the only extendable record back in time. Qualitative statements are hard to evaluate unless some timing mechanisms are stated. Fortunately in the case of Lunar occultations (53,000 timings) between 1620 AD and 1955 AD we have a precision of one second in time for the period up to 1800 AD (Lunar limb contact with stars). After 1800 AD precision is ten times better at 0.1 seconds. What of solar and lunar eclipses themselves? In the case of the Chinese dataset from 400 AD onwards solar eclipses have an accuracy of 15 mins called a "KE" (NOTE 7). Prior to 400 AD no timings appear to be stated in the original Chinese Texts. For Babylonian eclipses a timing of 4 mins called an "US" was used as well as a "BERU" equal to 30 mins(NOTE 8) In the case of european eclipses no reliable timings are available until the medieval period and then there are inaccuracies in reporting such eclipses ; e.g. "about the 5th hour" ; "about midday" (NOTE 9). Arab eclipses were timed using a quadrant and astrolabes to determine luminary altitudes. This was more accurate than other geographically produced records. So solar and lunar untimed eclipses are used in conjunction with timed ones to bring the dataset quantity to approx. 500 back to 700BC. Compare this to the non-eclipses (53,000 timings ; lunar occultations) and 45 Mercury transits (NOTE 15) transits and you have a ratio of approx. 101 : 1 between non eclipsed datasets and eclipsed ones. Professor Stephenson admits that decadal fluctations in the earth's rate of rotation can be ascertained by the non-eclipse dataset. In fact, the lunar occultations are the best dataset from 1620 AD onwards prior to the introduction of atomic time (1955 AD) for determining Delta T. (NOTE 10). The question is the period of the non-eclipse dataset ranged over 300 years as opposed to the eclipse datasets going back 2300 years. In the case of a partial solar eclipse at sunset, modern quality astronomical programs take into account variables such as atmospheric refraction and parallax. For the 3340 BC solar eclipse we have a 'pictorial' snap shot in stone at sunset. Even if modern astronomical programs got the refraction measurements off it would only translate to approx. 2 - 5 percent of disc obscuration. I've already accounted for this with a Delta T variance of +/ - 5 mins.
Why labour this point? This is because the theory of lunar motion in the Digital Universe is the result of the scientists Chapront & Touze using a - 23.8946 " /cy² lunar orbital acceleration for their ELP2000-85 model which was based on Morrison and Ward's reappraisal of Spencer Jones 1939 AD work on lunar occultations and mercury transits between 1677 and 1927 AD. That ELP 2000- 85 is the basic of lunar motion in the Digital Universe as well as other programs. In other words I do not assume a lunar orbital acceleration for the 3340 BC Neolithic dataset. Chapront & Touze (1988 or 1991) ELP 2000-85 series gives an actual motion for the moon based on the above dataset and its accurate for that time period.
ACCURACY OF THE DIGITAL UNIVERSE (DU) COMPARED TO JPL'S HORIZONS EPHEMERIS
JPL's online HORIZONS ephemeris is very accurate. All of their ephemerides have this
unsurpassed accuracy to them. Two of their ephemerides, the DE125 and DE130 were used for the Voyager
unmanned probes sent to the edge of the Solar System. They needed accurate
co ordinates for the outer planets so the probes could get a close flyby. In 1995 JPL produced the
DE405/LE405 ephemerides that gave a positional accuracy for the Moon
to MILLIMETRES !!. That accuracy was slackened off in May-June 1997 when they
produced the DE406/LE406 'Long Ephemerides' back to 3001BC. They announced
an accuracy of the Moon to 1 metre and the planets to 25 metres. We are not
talking kilometres here but millimetres and metres. So this becomes the
standard to measure any planetarium program against. In pursuit of this
it was necessary to compare like with like.I've done this over 3 stages in the following pages.
1. Stage 1 . Compare the Du against JPL Horizons program on the Equatorial and Horizon
co ordinate systems.
2. Stage 2. Reduce the comparisons to the ecliptic co ordinate system (Geocentric Longitude & Latitude)
3. Stage 3. Find the final displacement of the Sun and Moon as in an eclipse
situation compared to the JPL Horizons program. This gves us the accuracy of the DU.
STAGE ONE(AZIMUTH & ALTITUDE)
This means matching precession, aberration, proper motion, nutation, co ordinate frames between the DU and JPL's program.The latter(JPL) cannot be altered but the DU is versatile enough for the task.1. Change the DU temp on ENVIRONMENTS SETTINGS to 10° C and 101.1 Kp(JPL's temp is set at 10° C ; 1010 Millibars Hg)
2. Deflag the Nutation in SETTINGS menu.
3. Use Epoch of 'DATE' not B1950 in ENVIRONMENTS SETTINGS . Latter gives huge discrepancies which are not true )
4. Use Delta T times in seconds in TIME SETTINGS Menu from Graphs on these pages
5. Set Loughcrew co ordinates at Lat 53.7441N and Long. 7.1325W , Alt = 0m, +0:00 offset from UT.
TABLE ONE EXPLAINED
In the above TABLE ONE the JPL 'Horizons Ephemeris' (JPLH) is compared to the Digital Universe (DU). The fraction of the Lunar orbital acceleration of the DU with that of JPLH in their respective lunar ephemerides is -23.8946 divided by -25.7376 = 0.9283927. I obtained my Moon Delta T times per Rob VGent's web site which has a Javascript Delta T calculator. By entering in - 23.8946 in the Lunar Acceleration Parameter box I could instantly get a Delta T time for JPL's Horizons program in values of minutes. You have to enter - 2999 for year 3000 BC as Rob has Delta T values for year zero. This is the reverse of Fred Espenak's web site.(see below)
ROB GENT'S DELTA T CALCULATOR RESULTS
0BC 3000 BC 2800 BC 2400 BC 2300 BC
1700 BC 1600 BC 1100 BC
JPL SOURCE SHEETS FOR DU COMPARISON
If you have difficulty in seeing each of these sheets , in IE go to VIEW at the top of browser, click it and a drop down list will appear. Look for the word 'text', highlight it and a side window opens, click LARGEST and you will get the full screen filled with the sheet. Apologies for not resoluting the images better but memory was scarce.
MOON POSITION AT LOUGHCREW CAIRN L PER JPL HORIZONS EPHEMERIS
You are looking for the top and bottom of these sheets and the following item values :=
AZI & ELEV r-apprnt (refracted apparent) and CT - UT = This is the Delta T calculated for
the dates , all Jan 1st, at 12 :00 :00 UT,Loughcrew Cairn L co ordinates . The JPLH Delta T formula is 31T²
with T = (year - 1820AD)/100 or time measured in Julian Centuries from 1820 AD.
1600 BC 1100 BC
SUN POSITION AT LOUGHCREW CAIRN L PER JPL HORIZONS EPHEMERIS
You are looking for the top and bottom of these sheets and the following item values :=
AZI & ELEV r-apprnt (refracted apparent) and CT - UT = This is the Delta T calculated for
the dates , all Jan st1, at 12 :00 :00 UT . The JPLH Delta T formula is 31T²
with T = (year - 1820AD)/100 or time measured in Julian Centuries from 1820 AD.
1600 BC 1100 BC
