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Joe Keller

USA
957 Posts

Posted - 12 Mar 2010 :  12:04:44  Show Profile  Reply with Quote
"Electronic Telegram No. 939
Central Bureau for Astronomical Telegrams
INTERNATIONAL ASTRONOMICAL UNION

SUPERNOVA 2007bm IN NGC 3672
H. Navasardyan, S. Benetti, A. Harutyunyan, and M. Turatto, Istituto Nazionale di Astrofisica and Osservatorio Astronomico di Padova

...type-Ia supernova...intense (EW about 0.26 nm) Na I D
interstellar absorption doublet. ..."


Here is a third kind of evidence of abnormal light effects near Barbarossa. First I found, in the literature, the exceptionally strong "interstellar" absorption lines of Theta Crateris and 61 Leonis. Then I found, in the literature, the exceptionally abnormal apparent radial velocity profile of NGC 3672 (see previous post). Now we have the "intense" sodium "interstellar" absorption line of the 2007 supernova in NGC 3672.

Update March 13, 2010:

Patat et al, Science 317:924+, 2007, show the Na I D2 line (shorter wavelength line of the Na I D doublet; twice as strong as D1) for SN 2006X, a "normal" type-Ia supernova in NGC 4321 in the Virgo cluster. This line (Patat, Fig. 1, p. 924) is only 50 km/sec (redshift equivalent) wide at the top (i.e. 589.0nm*50km/s / 300,000km/s = 0.10nm) and only 32 km/s wide at the lowest part shown (normalized flux 0.4). Roughly, the trapezoidal shape probably extends to the bottom (normalized flux 0.0) so this line averages 35km/s wide, i.e. 0.07nm.

Thus the Equivalent Width (EW) of the Na I D2 line for SN 2006X (at the authors' several times, between 2wk and 4mo) is 0.07nm, about a quarter of the "Na I D" (D2?) EW of 0.26 for SN 2007bm in NGC 3672. This is further evidence of abnormally strong "interstellar" absorption near Barbarossa.

Edited by - Joe Keller on 13 Mar 2010 21:55:57
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Joe Keller

USA
957 Posts

Posted - 13 Mar 2010 :  14:49:15  Show Profile  Reply with Quote
In 2008 another supernova, 2008gz, occurred in NGC 3672.
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Stoat

United Kingdom
964 Posts

Posted - 14 Mar 2010 :  07:38:30  Show Profile  Reply with Quote
Hi Joe, i was having a look at the electron again, in terms of the Schwarzchild radius. The equation is a parabolic capture orbit. So if an electron were transparent to light, that light couldn't escape at about a radius of 1E-57 metres. We have g/r_s (r/c)^2 = 0.5

r_s is the Schwarzchild radius
g is local gravity at the Compton wavelength radius

A rough working out, to a couple of decimal places, for g gives a value that I reckon is the square root of barh.

Now if we have particles which can travel much faster than the speed of light, and to these an electron is transparent, then the Schwarzchild radius is going to be much smaller again. These particles could go into orbit at about 1E-91 metres radius. Another very rough calculation and it still looks like g is going to be the square root of barh.

Perhaps we can work out the mass of an orbiting graviton about the gravitational Schwarzchild radius of a particle?

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Joe Keller

USA
957 Posts

Posted - 19 Mar 2010 :  16:52:43  Show Profile  Reply with Quote
Dogs and the Younger Dryas

Above, I wrote about using sled dogs in another Younger Dryas. Also, dogs seem first to have appeared at the Younger Drayas c. 13,000 yr ago.

Kristen Webb and Marc Allard, in the journal "Mitochondrial DNA", Feb. 2010 (I have access only to the abstract) say:

"...studies commonly choose the mitochondrial control region as the locus for which to evaluate the domestic dog. ...Of the most commonly cited evolutionary research, only a single study has adequately surveyed the domestic dog population..."

From the abstract alone, I don't know which study this is, that Webb & Allard say is statistically adequate. Anyway, archaeologists say that from C14 dating, apparently the oldest evidence of domestic dogs is in the Middle East and Europe c. 14,000 yr ago. This figure is inherently biased upward: if I find three sites measured as 12,000, 13,000, and 14,000 yr old, the likeliest true figure for the oldest site, isn't 14,000, because the site whose measurement error is most positive is likeliest to be the "oldest" site. (Error bars on C14 dates reflect only some of the error; they omit the often larger, but harder to estimate, "systematic" errors involved.)
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Joe Keller

USA
957 Posts

Posted - 20 Mar 2010 :  11:45:15  Show Profile  Reply with Quote
(email sent last night, March 19, 2010)

Dear Prof. *******:

...Would you email or landmail me a copy of your Ph.D. thesis? I am a graduate of Harvard College, B. A., Mathematics, 1977.

I think that the 6000 year duration of creation, told by early Christians, is explained spuriously by them according to the accidental correlation, "God made the World in 6 days", "to God a day is as 1000 yr", 6x1000=6000. The truth is, that there is a real, physical, cataclysmic Earth cycle of approx. 6000 yr. Early Christians preserved this true knowledge but gave it a spurious numerological/textual explanation.

I post everything I know about this, to Dr. Tom Van Flandern's messageboard at www.metaresearch.org, under my name, Joe Keller. Here is a summary:

1. From lake varves, Brauer et al (2008) determined that the onset of the "Younger Dryas" was 12,683 years before 2012AD (exactly). The Younger Dryas phenomenon includes a mysterious "black layer" throughout much of N. America, which might signify a holocaust due to comet impacts. Almost all large animals in N. America suddenly became extinct at the time of this "black layer", as did the human "Clovis Culture".

2. Phoenix-like, human progress continued. The dog was domesticated ~13,000 yr ago and agriculture is thought to have begun at about that time.

3. Jantz & Owsley (2001) found that roughly 6000 yr ago, human cranial diversity in N. America drastically decreased. Published European data somewhat support similar change in Europe.

4. Last year I discovered by careful standard astronomical almanac calculations, that Arcturus rose heliacally at Giza at the summer solstice of ~4329BC. I applied Prof. Eduard Meyer's "Sothic dating" concept to the famous "Sothic" date of Thutmose III. I found that if this date of Thutmose III, is "1 Thoth" in the "official (360 day) calendar", and a reasonable assumption is made for the summer solstice in the "seasonal calendar", then "1 Thoth" in 4329BC, is the summer solstice, the heliacal rising of Arcturus at Giza. Therefore it is reasonable to suppose that the (now lost) Egyptian calendar began in 4329BC.

5. Phoenix-like, advanced human civilization appeared shortly after the cataclysm at that time.

6. The famous Mayan time interval, 5125 yr, though made by them into a conveniently remembered calendar, really is advanced astronomical knowledge: a common multiple of the orbital periods of Jupiter, Saturn, *and* Uranus.


Sincerely,
Joseph C. Keller, M. D.
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Joe Keller

USA
957 Posts

Posted - 23 Mar 2010 :  00:27:59  Show Profile  Reply with Quote
13,000 and 6,500 years ago

According to Randles & Warrington, "UFOs: a British Viewpoint", p. 18, fig. 1 (citing Aime Michel and Gordon Creighton), "typical" central European cave art c. 14,000 yr ago, depicted four-armed humanoids (?) and domed saucers leaving tracks. Alleged UFO art exists for many dates, however.

Jack Hough, Journal of Geology 58:254-260, 1950, p. 258, fig. 2, shows that according to seafloor sediment cores from the 2nd Byrd expedition, the Ross Sea at 70 S latitude was almost perfectly free of icebergs from 6000 to 15,000 yr ago. I found this reference in Charles Hapgood, "Maps of the Ancient Sea Kings".

*********

"The 'Chronicle' [of disputed authorship] accounts 65 generations from the creation of the world to the birth of Christ; whereas the 'Commentary on Daniel' [known to be by Hippolytus] gives 60. ...[the 'Chronicle'] in presenting the patriarchs from Adam to Christ, gives a list which probably originally contained only 60 names."

- Prof. David G. Dunbar, Ph.D. thesis, pp. 42-43 (electronic text obtained from Biblical Seminary, of Hatfield, Pennsylvania).

What follows, is not discussed in the above thesis, but it occurs to me, that as a period of time, one "patriarch" might more have resembled one "lifetime" than one "generation". This is so, with the Dalai Lamas and other similar Buddhist successions.

The 1st Dalai Lama was born in 1391 and the 14th in 1935, averaging (1935-1391)/13 = 42 yr per Dalai Lama. The 15th probably will be born no sooner than 2010, which gives, alternatively, at least (2010-1391)/14 = 44 yr. Multiplying 65 patriarchs x 44 yr gives 2860BC as the time of creation. Multiplying 65 x 70 yr gives 4550BC. Jewish and Christian tradition, according to the above thesis, was 5500BC or 5502BC. (Usher's chronology gave 4004BC.)

These numbers are comparable to the date, 4328 or 4329BC, I found from studying the "Sothic" date of Thutmose III.
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Stoat

United Kingdom
964 Posts

Posted - 30 Mar 2010 :  05:33:33  Show Profile  Reply with Quote
Hi Joe, have you tried getting an image form these guys? http://adsabs.harvard.edu/abs/1996DPS....28.1002P

Off topic a bit, the Schwarzschild equations. g / r_s ( r / c )^2 = 0.5
where g is surface grav or a body.
r_s is the Schwarzschild radius
r is the radius of the body
c is the speed of light
Change c for b, the speed of gravity and multiply that 0.5 by the ratio of the speed of light squared divided by the speed of gravity squared, with my proposed speed of gravity that would be
g / r_s ( r / b )^2 = 0.5 * 6.626E-34 (h as a pure dimensionless number)

It gives us the same answers for orbits but there's no time dilations to speak off.

Another thought here, you remember that we talked about the Reimann conjecture? Now, that's one hell of a nut to crack. So I thought, if we have gravity having an exponential fall off, and that doesn't show because of the huge distances involved with a very high speed of gravity, Something suggested by MOND. We also have the very real phenomena of negative refractive index, which means looking at "imaginary" solutions. I also have that problem of, is the speed of gravity, such that the ratio c^2 / B^2 is h or barh (again these are dimensionless numbers, as we are talking refractive indices)

So, we have e, i (or j) and pi in the Lorentzian where there's a phase change at the speed of light. Euler's famous equation springs to mind e^(i / pi)

Not sure, it might be an easier job to look at that.

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Stoat

United Kingdom
964 Posts

Posted - 30 Mar 2010 :  06:12:16  Show Profile  Reply with Quote
To save a bit of time writing down a load of formulae, here's a couple of links. the first one is on Euler. Note that animated graphic, i thnk we can do something with that.
http://en.wikipedia.org/wiki/Euler's_identity

The second is on the Schwarzschild radius, where it gives the formulae for orbits.
http://en.wikipedia.org/wiki/Schwarzschild_radius

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Joe Keller

USA
957 Posts

Posted - 10 Apr 2010 :  23:21:53  Show Profile  Reply with Quote
Barbarossa & "excursions" (less than flips) of Earth's magnetic pole

JA Jacobs, Royal Astronomical Society Quarterly Journal 27:328-350, 1986, lists three (sometimes doubtful) magnetic excursions and their dates:

Laschamp excursion 45,400 +/- 2500 BP
Mono Lake excursion 24,500 BP
Gothenburg flip 12,350 BP

Let's add 2012-1986=26yr to these times, and divide by the 6339.5 yr period of Barbarossa's orbit:

Laschamp is 7.17 periods
Mono Lake is 3.87 periods
Gothenburg is 1.95 periods

That these three would be as close to integers as they are, is significant at p=0.88%.
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Stoat

United Kingdom
964 Posts

Posted - 29 Apr 2010 :  04:31:37  Show Profile  Reply with Quote
Hi Joe, I'd like to pick your brains on this for a moment. I'm still looking at the Dirac cosmology and how it might relate to the "speed" of gravity. We've got.
e^2 = 1/137 * barh c aprox (m_o / 137m_e) m_e c^3 t / (4pi n t^3 c^3 /3)^0.5

Now this is in cgs units, which I'm not used to but for people used to SI units note that there's no 4pi epsilon_0

e = 4.8E-10 erg^0.5 cm^0.5
bah = 1.5E-27 erg sec
m_e = mass of electron
t = 1.06E-40

Now that m_o is taken to be the mass of the pion by Dirac and co. That's about 273 times the mass of an aelctron. So the ratio of m_o / 137 m_e is about 1.99

So let's say that the speed of gravity is either h = c^2 /b^2 or barh = c^2 / b^2 where b is the speed of gravity. Replace the c^3 with the speed of gravity and the barh = c^2 / b^2 value is very close. So just make that 1.99 ratio equal to two.

I still think I'm missing something here, it's that damn 2pi i can't account for.






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Stoat

United Kingdom
964 Posts

Posted - 01 May 2010 :  14:51:39  Show Profile  Reply with Quote
Em, I just noticed that barh is wrong in that paper, must have been a printer's typo. It should be 1.057E-27 erg sec
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Stoat

United Kingdom
964 Posts

Posted - 02 May 2010 :  05:47:01  Show Profile  Reply with Quote
I've just realized that I've got t wrong as well. I was taking t as being the age of the universe in atomic units. From the Dirac cosmological model we can work out t from the equation, G = 1 / 6 pi rho t^2

Taking G as 6.7E-8 erg cm g^-2
rho = 4E-31 g cm^-2 (the mean density of the universe)
Then t = 1.4E 18 seconds. That makes the Dirac universe about three time bigger than current estimates.

What I think we should explore is the idea that both G and barh vary with time. We can have an expanding universe in G decreases over time, or we can have an expanding universe where barh increases. A steady state universe would have both happening.

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Joe Keller

USA
957 Posts

Posted - 02 May 2010 :  16:46:39  Show Profile  Reply with Quote
quote:
Originally posted by Stoat

Hi Joe, ... Now that m_o is taken to be the mass of the pion by Dirac and co. That's about 273 times the mass of an aelctron. So the ratio of m_o / 137 m_e is about 1.99 ...



Nice work! This is a clue that the mass of the pion depends on some simple formula involving the fine structure constant.

In 2004, I modeled the heavy leptons, and mesons and baryons, as "electric black holes" using Weyl's idea, that the electric field could be treated as a very strong gravitational field, and general relativity applied. The muon is the simplest of these; the tauon was like a heavy muon with a certain special property. The mesons and baryons had to be modeled as two- or three-layer onions of charge (each layer a quark). In each case the "singularity surface" was at a quark (i.e. layer) boundary.

For the pion, for example, the mass assumes the smallest possible wave-mechanical spherical gaussian distribution and the innermost half of the mass is assigned 1/3 or 2/3 charge, the outermost, likewise 1/3 or 2/3 charge, always with a fixed charge/mass ratio in the substance of each quark, either of the same sign or opposite sign, so the charge adds to 0 or +/-1.

Edited by - Joe Keller on 02 May 2010 16:48:19
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Stoat

United Kingdom
964 Posts

Posted - 03 May 2010 :  07:04:13  Show Profile  Reply with Quote
I wonder if we are sometimes using the number two in our equations when we should be using that mass of a pion divided by 137 times the mass of an electron?

Mass of pion 9.109534E-31 kg times 263.13 = 2.39699E-28 Divide that by 137 times the mass of electron to get 1.9206 Divide that into the number two, 1.0413

Now if we say that barh = c^2 / b^2 where b is the speed of gravity then we can also look at
barh = v^2 /c^2 They are vastly different in scale but proportionate. Then the velocity we get, is going to be something like 1E-9 something very very cold.

We can also pop the equation r = 2Gm /c^2 into the lorentzian equation, where r is equal to barh. The mass we get here is 7.09673E-8 So what's that in terms of the Planck mass? Let's try dividing it by pi. That's 2.2589E-8 Now that's a little high, so divide that by the Planck mass, which is 2.17644E-8 and that gives us 1.03792 which compares fairly nicely with that value of 1.0413 that we got earlier.

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johnboy

5 Posts

Posted - 04 May 2010 :  06:38:18  Show Profile  Reply with Quote
This question is to Joe Keller: Sorry it is three years late. But the topic is still open, so I guess it's OK. On your post of 12 Feb 2007 you said:

"The CMB dipole is caused by the sun's retrograde, small cool brown dwarf, 0.019 solar mass, mag +18 companion at 360 AU distance in the positive dipole direction."

This was in the context of several posts dealing with the effect of various known (Neptune) and hypothetical objects on the temperature anisotropies in the CMB. You went on to discuss how the orbits of the objects should cause a shift in the direction of the various multipole moments of the CMB.

Now you also mentioned, unless I misread your intent, that the source of the CMB was a shell at about 53 AU, where phenomenon of a hitherto unsuspected nature was at work.

If this is the case,attempting to demonstrate that the CMB is sourced at this distence by fitting the data on movement of the direction of the multipoles to the gravitational effect of a hypothetical object, while feasible, is more complicated then it needs to be.

If the CMB is coming from a source at ~50 AU it seems to me that the dipole directions would show a MAJOR parallax simply by using the Earths orbital baseline of 2 AU. Wouldn't the parallex be 2x arctan(1/52)=2.2 deg?
This seems to me to be a very much simpler and unambiguous way to determine if the CMB is coming from such a close source.

Apologies in advance if you already addressed this issue in another post. I only have read the first 4 pages of the 47 total.
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Maurol

Argentina
37 Posts

Posted - 04 May 2010 :  08:16:31  Show Profile  Reply with Quote
Hi all,
Some of you might be interested in the following paper:
Dark Fluid: Towards a unification of empirical theories of galaxy rotation, Inflation and Dark Energy
http://arxiv.org/abs/0804.1588

The math is extremely hard to understand, at least to me, but the general idea is similar to something I've expressed here in the past: gravity could be a force without a material cause, while accumulation of matter is just its consequence.

Best regards,
Mauro
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Joe Keller

USA
957 Posts

Posted - 12 May 2010 :  22:22:50  Show Profile  Reply with Quote
quote:
Originally posted by johnboy

...If the CMB is coming from a source at ~50 AU it seems to me that the dipole directions would show a MAJOR parallax simply by using the Earths orbital baseline of 2 AU. ...



Good point! The parallax would be as much as +/- 1 degree, but the (+) and (-) local frequency extrema (i.e., "poles") would be shifted in the same direction, that is, rotated by angles opposite in sign. So, to some order of approximation, the overall best fitting dipole would remain the same. Maybe investigators have missed unexplained same-direction shifts of the (+) and (-) CMB poles, occurring near December and June.
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Joe Keller

USA
957 Posts

Posted - 12 May 2010 :  22:34:44  Show Profile  Reply with Quote
quote:
Originally posted by Maurol

Hi all,
Some of you might be interested in the following paper:



Thanks for alerting me to this and giving me this helpful reference.
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Joe Keller

USA
957 Posts

Posted - 13 May 2010 :  00:33:32  Show Profile  Reply with Quote
The Berlin Gold Hat (see: Wikipedia) is an eclipse record

Geoff Stray's "Beyond 2012" mentions the four or more extant gold cylinders, a.k.a. "gold hats" because there is some evidence that they were worn ceremonially, found in modern times in Germany & France, and maybe Switzerland & Ireland, dating from 1000-1300 BC. The best preserved is the "Berlin Gold Hat", whose provenance is uncertain, but probably southern Germany or Switzerland.

The Berlin Gold Hat has 20 rings with numbers, in a simple, rudimentary number system, that have been straightforwardly decoded as:

44,42,75,38,90,57,105,57,95,60,100,60,105,90,38,66,126,138,162,235.

The total is 1783, so, this is a 1783-year record of total solar eclipses at some location or locations. To find the expected frequency of total eclipses at any given midlatitude location, I consulted Stephenson & Houlden, "Atlas of Historical Eclipse Maps: East Asia", 1986. This book shows calculated partial & total solar eclipse tracks in or near China, since 1500BC. From 1500BC to 316AD, the capital Chinese city conveniently marked on the maps, was one of five northern Chinese cities all between about 35 and 40deg N lat. During this time, totality encompassed the then capital nine times, so at 35-40 N lat, whether in China or in Europe, total eclipses occur at a given location roughly once every 200 years.

This is indeed the average time interval near the end (physically, the bottom) of the Berlin Gold Hat. Apparently, near the end of the recordkeeping, the declining civilization, possibly pre-Celtic and Stonehenge-related, which produced the hat, had a poor communication network and knew only of local eclipses. Earlier, the civilization recorded eclipses over a larger region, so the intervals were shorter.

Only 1/18 of the numbers should be divisible by 18, but 4/20 of them are. The most reliable eclipse cycle is the Saros cycle, 223 synodic months = 18.0 years. The Saros cycle is very close to whole numbers of synodic, draconic and anomalistic months, so, the new moon recurs at the node and at perigee. The time of day is acceptable:

223 synodic months in Saros cycle * 5 = whole# + 0.63day
" * 7 = whole# + 0.28day
" * 9 = whole# + 0.93day

(I used the linear extrapolation estimates for ancient month length and day length, given by Wikipedia; this estimated change in day & month length, affects the above results by no more than 0.04 day)

So, it is likely that a collection of eclipses separated by 5, 5, 7 & 9 Saros cycles could be seen from the same point on Earth, especially if the 5-cycle eclipses were in the summertime.

Only 1/19 of the numbers should be divisible by 19, but 5/20 of them are. Nowadays a less reliable eclipse cycle is the Metonic cycle, 235 synodic months = 19.0 years: its numbers of draconic and of anomalistic months are, on the average, less exactly whole. The time of day again is acceptable:

235 synodic months in Metonic cycle * 2 = whole# + 0.39day
" * 3 = whole# + 0.08day
" * 5 = whole# + 0.47day (thus probably summertime eclipses)

Thus eclipses separated by 2, 2, 3, 3 & 5 Metonic cycles likely could be seen from the same point on Earth, if the 2- and, especially, 5-cycle eclipses were in the summertime.

As an extra check, I wrote a BASIC computer program to find whether it is possible to have two eclipses X +/- 1 yr apart. For all 20 values of X on the Berlin Hat, there was at least one time interval T, with X-1 < T < X+1, such that T was a whole number of synodic months, and within 0.02 months (7.2deg; equivalent to 0.7deg from the ecliptic) of a whole number of mean draconic half-months. This was however also true for 98 of the first 100 integers and 190 of the first 200.

For all 20 values of X, at least one of its values of T that was satisfactory vis-a-vis the node, also was good vis-a-vis the perigee (that is, nearly a whole number of anomalistic months, so both eclipses could be near perigee). Even the poorest performer had a value of T only 0.24 anomalistic month different from a whole number. By contrast, only 82 of the first 100 integers, and 161 of the first 200 integers, had any value of T for which the number of anomalistic months was within 0.25 of a whole number. Only 15 of the 20 Berlin Hat numbers are different, but even allowing for the duplicates, the chance that all 15 nonduplicate Berlin Hat numbers would lie among the best 82%, vis-a-vis perigee, is 0.82^15 = p = 5%.

If the Berlin Hat record ended ~1200BC when the hat most likely was (deliberately and carefully) buried, then its record began ~3000BC. My guess is that the Berlin Hat record began shortly after 4328BC, ended shortly after 4328 - 1783 = 2545BC; then the hat was stored aboveground for ~1300yr before burial.

Is there a location (preferably but not necessarily in northwest Europe) where total eclipses (preferably but not necessarily consecutive) occurred 162 +/-1, then 235 +/-1 yrs apart? (These last two intervals on the hat are likeliest to represent the hatmakers' one remaining observatory.) The answer to this question, could both place and date the hat.

Edited by - Joe Keller on 13 May 2010 10:22:51
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Joe Keller

USA
957 Posts

Posted - 13 May 2010 :  17:32:11  Show Profile  Reply with Quote
Where do the tracks of these total eclipses intersect?

NASA's online list of long (>6min) total solar eclipses starts at 4000BC. Since eclipse tracks tend to be roughly west to east (Luna moves faster than the surface of Earth) the likeliest eclipses to be seen in Europe, are those near Europe's latitude, and with their "point of greatest eclipse" not too far away in longitude.

Two such eclipses are calculated at Julian calendar dates April 26, 2806 BC, and May 24, 2407 BC. These are 399 yr apart, which is within the range (162+/-1)+(235+/-1)=397+/-2 implied by the bottom two rings of the Berlin Hat. The point of greatest eclipse for the earlier eclipse, is 35N 11W, and for the later, 28N 27W. The earlier track is, at widest, 298km and the later, 271km.

The first eclipse on the Berlin Hat, would have been about 1783 years before the last, 2407 BC, eclipse: that is, 4190 BC. The top ring of the Berlin Hat is blank (see Wikipedia article). If the top ring said 138 yr, that would give a "zeroth" eclipse at 4328 BC.

The 18th ring of the hat, says 138 yr. The sum of the first 18 rings, is 1386 yr = 10*138.6. There is an eclipse cycle of 1714 synodic months = 138.58 Julian yr = 1860.026 draconic months = 1836.92 anomalistic months. So, it is plausible that the blank, "zeroth" ring, would have said 138 yr.

If, perhaps from Prof. Espenak or Prof. Meeus, the track of these two eclipses could be learned, then the intersection point would tell us the location of the observatory used for the last entries on the Berlin Hat.
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