Let us take a closer look the chaotic dynamics of planetary formation; thus, a clear indication that the initial conditions cannot be predicted with accuracy (as we have seen, a mere 15 meters difference in the data will have catastrophic consequences upon the calculations).
OFFICIAL SCIENCE INFORMATION
Four stages of planetary formation
Initial stage: condensation and growth of grains in the hot nebular disk
Early stage: growth of grains to kilometer-sized planetesimals
Middle stage: agglomeration of planetesimals
Late stage: protoplanets
For the crucial stages, the initial and early stages, prediction becomes practically impossible.
As if this wasn't enough, we have absolute proof that in the age of modern man planet Earth underwent sudden pole shifts (heliocentrical version), thus making null and void any integration of the solar system/Lyapunov exponents calculations which do not take into account such variations of the system's parameters:
http://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1635693#msg1635693http://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1546053#msg1546053Ammizaduga Venus tables which show that the orbit followed by Venus in the past was markedly different from that observed in the present.
http://www.skepticfiles.org/neocat/ammi.htmCharles Ginenthal (Sagan and Velikovsky) has a great deal to
say about the Ammizaduga tablets, pp 281 - 284, quoting Livio C.
Stecchini's "The Velikovsky Affair":
"The Venus tablets of Ammizaduga is the most striking document
of early Babylonian astronomy. These tablets, of which we
possess several copies of different origin, report the dates
of the helical rising and setting of the planet Venus during
a period of 21 years...
"Since the first effort at explanation of Archibald Henry
Sayce in 1874, these figures have challenged the wit of a
score of experts of astronomy and cuneiform philology.
(Father Franz Xavier) Kugler (1862 - 1929), a recognized major
authority on Babylonian and biblical astronomy, chronology and
mythology, opposed the contention of those who claim that
these documents must be dismissed as nonsense." [because they
do not conform to present orbital patterns for Venus]
"Let me give some typical passages from the tablet:
"In the month of Sivan, on the twenty fifth day, Ninsianna
[that is, Venus] disappeared in the east; she remained absent
from the sky for two months, six days; in the month Ulul on
the 24'th day, Ninsianna appeared in the West - the heart of
the land is happy. In the month Nisan on the 27'th day,
Ninsianna disappeared in the West; she remained absent from
the sky for seven days; in the month Ayar on the third day,
Ninsianna appeared in the east - hostilities occur in the
land, the harvest of the land is successful.
"The first invisibility mentioned in these lines involves a
disappearance in the east, an invisibility of two months, six
days, and a reappearance in the west. This seems to be a
superior conjunction. The second invisibility involves a
disappearance in the west, an invisibility of seven days, and
a reappearance in the east. This seems to be an inferior
conjunction. Most of the data in groups one and three on the
tablet are of this form. But the lengths and spacings of
these invisibilities have a certain irregularity about them,
and they do not conform to the manner in which Venus moves at
present.
"The data given in the second group on the tablet do have
regularity - even too much regularity to be believable, - but
they do not conform to the present state of affairs
either.....
'How explain these observations of the ancient astronomers, modern astronomers and historians have asked. Were they written in a conditional form ("If Venus disappeared on the 11th of Sivan . . .") ? No, they were expressed categorically.
The observations were "inaccurately" registered, decided some authors. However, inaccuracy may account for a few days' difference but not for a difference of months.
The observations were "inaccurately" registered, decided some authors. However, inaccuracy may account for a few days' difference but not for a difference of months. "The invisibility of Venus at superior conjunction is given as 5 months 16 days instead of the correct difference of 2 months 6 days," noted the translators of the text, wonderingly."
If the tables are true, then both the attractive law of gravity AND Kepler's third law of motion are completely wrong; if they have been falsified, then we have another extraordinary proof of how the "ancient" history has been forged.
"Why did the glaciers of the Ice Age cover the greater part of North America and Europe, while the north of Asia remained free? In America the plateau of ice stretched up to latitude 40° and even passed across this line; in Europe it reached latitude 50°; while northeastern Siberia, above the polar circle, even above latitude 75°, was not covered with this perennial ice.
If we look at the distribution of the ice sheet in the Northern Hemisphere, we see that a circle, with its center somewhere near the east shore of Greenland or in the strait between Greenland and Baffin Land near the present north magnetic pole, and a radius of about 3,600 kilometers, embraces the region of the ice sheet of the last glacial age. Northeastern Siberia is outside the circle; the valley of the Missouri down to 39° north latitude is within the circle. The eastern part of Alaska is included, but not its western part. Northwestern Europe is well within the circle; some distance behind the Ural Mountains, the line curves toward the north and crosses the present polar circle. Now we reflect: Was not the North Pole at some time in the past 20° or more distant from the point it now occupies—and closer to America? In like manner, the old South Pole would have been roughly the same 20° from the present pole.
Billions of tons of ice would have fallen on the polar regions, flash-freezing everything in little more than an instant.
This, at last, would explain the mystery of the mammoths found frozen where they stood. The mammoth, contrary to belief, was not a cold region animal, but one which lived in temperate grasslands."
"The sudden extermination of mammoths was caused by a catastrophe
and probably resulted from asphyxiation or electrocution. The immediately
subsequent movement of the Siberian continent into the polar region is probably
responsible for the preservation of the corpses.
"It appears that the mammoths, along with other animals, were killed by
a tempest of gases accompanied by a spontaneous lack of oxygen caused by fires
raging high in the atmosphere. A few instances later their dying or dead bodies
were moving into the polar circle. In a few hours northeastern America moved
from the frigid zone of the polar circle into a moderate zone; northeastern Siberia
moved in the opposite direction from a moderate zone to the polar circle. The
present cold climate of northern Siberia started when the glacial age in Europe
and America came to a sudden end."
http://asis.com/users/stag/starchiv/transcriptions/ST110Velikovsky.html (exceptionally documented)
The sudden shift in the direction of the axis of Earth would have meant a slowing down of the velocity of the diurnal rotation of the Earth, and there would have no way for the Earth to regain the same velocity of the diurnal rotation as before, after Venus departed to a different orbit.
http://www.world-mysteries.com/sci_2.htm (superb documentation)
Let us now get back to the initial conditions paradox.
Basically what Poincare discovered was that the orbits of the planets (within the heliocentrical solar system) CANNOT BE DESCRIBED by a set of nonlinear ordinary differential equations.
As I have abundantly demonstrated, present day mathematicians HAVE NO IDEA what the initial conditions were in the beginning in order to correctly and precisely predict not only the calculation of Lyapunov exponents, but also to indicate the regions of chaotical orbits/motions.
The minutest of changes in the initial conditions of a set of nonlinear ordinary differential equations which describes the three body problem will lead to homoclinic tangles.
Jack Wisdom (MIT): It is not possible to exclude the possibility that the orbit of the Earth will suddenly exhibit similar wild excursions in eccentricity.
The exponential divergence of chaotic trajectories precludes long-term prediction given the limited knowledge of the state of our solar system.
Let me show you what sensitive dependence on initial conditions means, using one of the most famous examples: the Lorenz attractor butterfly effect.
In 1961, Lorenz was running a numerical computer model to redo a weather prediction from the middle of the previous run as a shortcut. He entered the initial condition 0.506 from the printout instead of entering the full precision 0.506127 value. The result was a completely different weather scenario.
Here is the set of Lorentz equations:
Now, the set of differential equations which describe the planetary orbits is much more complicated than this.
Again, to put it bluntly: there is no way to predict anything pertaining to the heliocentrical solar system based on Newton's description of the orbit of the planets using a set of nonlinear differential equations.
(from the classic work by Charles Ginenthal, Newton, Einstein, Velikovsky):
https://books.google.ro/books?id=M8RACwAAQBAJ&pg=PT243&lpg=PT243&dq=solar+system+chaos+initial+conditions+are+not+known+velikovsky+stability&source=bl&ots=UyzFGZdBy0&sig=4Mnw8Vcgaw_qIuq7wR1vThLGIf8&hl=ro&sa=X&ved=0ahUKEwjpyvDGu5_KAhUHaxQKHa_wAi4Q6AEIKTAA#v=onepage&q=solar%20system%20chaos%20initial%20conditions%20are%20not%20known%20velikovsky%20stability&f=false