Dear Cluesforum readers, it's been a while since I posted any updates of my TYCHOS model - but this is just because I am currently looking ever deeper into the vast volumes of astronomy text books available, in order to find further indications which may go to support / confirm the TYCHOS paradigm. I must say it is a most rewarding experience - which "never stops giving"!

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About "THE GREAT INEQUALITY" Back in the 18th century, the spiny question of the observed behavior of Jupiter & Saturn ignited a humongous & long-lasting debate among our world's most celebrated astronomers and mathematicians (Halley, Flamsteed, Euler, Lagrange, Laplace and Poincaré - to name just a few). What every astronomy historian will know as the

"Great Inequality" is a 'scientific saga' of epic proportions. In short, the problem was that the motions of Jupiter and Saturn didn't seem to obey either the Newtonian (gravitational) nor the Keplerian (elliptical) theories ... not a trivial problem, you may say. Surely, both Newton and Kepler couldn't possibly be wrong, could they?

http://adsbit.harvard.edu/cgi-bin/nph-i ... lassic=YESWhat had been observed, first by Kepler himself and later by Halley, was that Jupiter appeared to

accelerate - and Saturn appeared to

decelerate. This was terrible news for mankind: it meant that (according to Newtonian theories) Jupiter would end up crashing into the Sun - while Saturn would be driven away into the depths of space !... In any case this is what, by all accounts, was ominously predicted at the time (on the basis of Newton's gravitational theories) : a truly apocaliptic scenario! Make no mistake, this was no petty matter: it was all about the very stability of our solar system - so the stakes were "sky high". In fact, the Paris and Berlin Academies set up special prizes to encourage scientists to resolve the pesky (and embarrassing) matter. Euler (the most acclaimed Swiss mathematician of all times) was the first recipient of such a prize, although his calculations showed BOTH Jupiter and Saturn accelerating - contrary to ANY astronomical observation ever made!...

The magnificent Isaac Newton himself had recognized the problem of the apparent "instability" of our Solar System (on the grounds of the observed behavior of Jupiter & Saturn) - but he never tackled the troublesome matter - while basically saying (freely paraphrasing his words) that

"God should take care of this problem in due time - and restore the apparent, chaotic nature of our planetary motions". Kepler, on his side, also "gave up" and admitted that only future generations may eventually unveil the mystery of our Solar System's apparent instability (suggested by Jupiter and Saturn's odd behaviors). Kepler, for once, was right about that...

Enter Lagrange and Laplace, perhaps the two most acclaimed French mathema(g)icians of all times. The two French science icons engaged in a long struggle to try and "justify" the so-called Great Inequality (so as to "rescue" the sacrosanct Newtonian Gravitational Laws). Depending on what old text books one may bump into, it was either Lagrange or Laplace who "solved the problem", basically concluding that, according to their (formidably abstruse) calculations, the so-called Great Inequality (the growing gap between Jupiter's and Saturn's celestial longitudes) was only periodic - i.e. only temporary - and would eventually reverse. In other words, the gap would gradually (in the course of ca. nine hundred years) diminish - and cancel out itself. Our Solar System was, after all, a stable one (*phew!*).

However, it is unclear just how Lagrange & Laplace reached their "mathemagical" conclusions. In academic text books, we may only find some dreadfully complex equations and computational wizardry based on mere assumptions (about how "planetary / gravitational perturbations" and "tidal friction effects" might cause these puzzling "inequalities"...). To be sure, there is no plausible explanation as to why Jupiter's & Saturn's celestial longitudes would (under the Copernican model's configuration) oscillate back and forth, as observed. In time though - and here's where it gets funny - Lagrange and Laplace were "proven right" : the apparent, relative accelerations/decelerations of Jupiter and Saturn were then observed, several decades later, as being

reversed :

One of the greatest observational astronomers of the times, William Herschel, had also noticed the "back and forth" oscillations of Jupiter & Saturn :

"He [Herschel] describes Saturn's period as increasing [i.e. Saturn seemed to be slowing down] during the seventeenth century, Jupiter's period as diminishing [i.e. Jupiter seemed to be speeding up]: and he adds - "In the eighteenth century a process precisely the reverse seemed to be going on."https://books.google.com/books?id=S68RA ... 20&f=falseSo, after all, there was no apocalyptic scenario for humanity to fear - whatsoever... Nonetheless (as pointed out by a number of independent, contemporary researchers), the "Great Inequality" and its corollary, the very "Stability of our Solar System", both remain - to this day - unsolved riddles. For instance, here's what Antonio Giorgilli (a veteran Italian expert in this peculiar area of astronomical studies), and the author of "LA STABILITA' DEL SISTEMA SOLARE: TRE SECOLI DI MATEMATICA" ("The Stability of the Solar System: Three Centuries of Mathematics") warns the reader with:

Su queste basi cercherò di illustrare che significato si possa dare alla domanda: “il sistema solare è stabile?”(...) Quanto alla risposta, non vorrei deludere nessuno, ma sarà: “non lo sappiamo”. http://www.mat.unimi.it/users/antonio/r ... rs/sns.pdfOn these grounds I will attempt to illustrate what significance we can give to this question: "is the solar system stable?" (...) As for the answer, I don't wish to disappoint anyone, but it will be: "we don't know".

"We don't know..." Well, we obviously cannot attain any firm knowledge of our solar system's behavior - if we haven't even envisioned its correct geometric layout, can we? As I will presently illustrate, the TYCHOS model's geometric layout provides the simplest imaginable explanation for the "Great Inequality". Now, what you need to know is that, as seen from Earth, Jupiter & Saturn appear to conjuct about every 60 years (or actually a whisker less than 60 years - due to Earth's 1-mph-motion).

Since Jupiter employs 12 years to circle around us - while Saturn employs 30 years to do so, the two will regularly "meet up" every 60 years, i.e. respectively 5 X 12 (=60) and 2 X 30 (=60).

These "60-year conjunctions" move around our celestial sphere in anti-clockwise manner - as illustrated here:

http://adsbit.harvard.edu/cgi-bin/nph-i ... lassic=YES Let's now see how the TYCHOS model accounts - in the simplest possible way - for the Great Inequality "mystery" :

1: Whenever (in a certain epoch) Jupiter & Saturn are observed - over a 60-year interval - to conjunct in the "upper quadrant" of our celestial sphere, it will seem as if Jupiter is accelerating.

2: Whenever (in a certain epoch) Jupiter & Saturn are observed - over a 60-year interval - to conjunct in the "lower quadrant" of our celestial sphere, it will seem as if Saturn is accelerating.This, because as Earth moves slowly (at 1 mph) around its PVP orbit, Jupiter & Saturn will alternately conjunct as they proceed in the opposite / or in the same direction as Earth. My below graphic should clarify conceptually what causes the so-called "Great Inequality" (one of astronomy's still-unsolved mysteries):

Antonio Giorgilli then points out something of paramount interest (to the TYCHOS model's paradigm). Here's a paragraph from his afore-mentioned paper

("The Stability of the Solar System: Three Centuries of Mathematics") that I have translated into English, to the best of my capacities:

"The first long-term simulations have been carried out since the end of the 1980s by some researchers, including A. Milani, M. Carpino, A. Nobili, GJ Sussman, J. Wisdom, J. Laskar. Their conclusions can be summarized as follows:

the four major planets (Jupiter, Saturn, Uranus and Neptune) seem to move quite regularly even over a period of a few billion years, which is the estimated age of our Solar System. On the other hand,

the internal planets (Mercury, Venus, Earth and Mars) present small random orbital variations, in particular of their eccentricity, which cannot be interpreted as periodic movements: we must admit that there is a chaotic component. Not that the orbits change much, at least not in the short term, but there may be, for example, small variations in the eccentricity of the Earth's orbit that have very significant effects on the climate: the glaciations appear to be correlated to these variations. "

http://www.mat.unimi.it/users/antonio/r ... a_2016.pdf

In other words, this nicely goes to confirm that there are TWO distinct groups of celestial bodies in our Solar System (as proposed by the TYCHOS):

1: The Binary group (a.k.a. "the inner planets") composed of the Sun, Mars, Mercury and Venus (and of course, Earth and our Moon)

2: The P-type group (a.k.a. "the outer planets") composed of Jupiter, Saturn, Uranus and Neptune (and Pluto, small as it may be)

And thus, the TYCHOS once more resolves another major / historical, astronomical debate ("The Great Inequality") - in simple fashion.