Introducing the TYCHOS

Simon Shack's (Tycho Brahe-inspired) geoaxial binary system. Discuss the book and website for the most accurate configuration of our solar system ever devised - which soundly puts to rest the geometrically impossible Copernican-Keplerian model.

Re: Introducing the TYCHOS

Unread postby PianoRacer on Tue Jul 10, 2018 8:19 am

In the rare case that anyone is interested, I put the graphs that I've been referencing out on the interwebs:

Feedback welcome.
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Re: Introducing the TYCHOS

Unread postby Skinnylegsandall on Sat Jul 14, 2018 9:47 pm

How do you explain this phenomena?
Happening in 5 days claiming revolving around sun.
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Re: Introducing the TYCHOS

Unread postby hoi.polloi on Mon Jul 16, 2018 1:15 am

Please elaborate the claim you are talking about, in text. Do you mean "all planets on one side of the Sun"?
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Re: Introducing the TYCHOS

Unread postby simonshack on Mon Jul 30, 2018 6:26 am

A delicious humble pie ^_^

I'm quite happy to eat some (tasty) humble pie regarding this latest realization of mine: Earth's PVP orbit is not, after all, tilted at about 23 degrees in relation to the Sun's orbit (as of my original Tychos configuration). Instead, Earth itself is.

The reason why I'm happy will soon be clear. For a long while, I had tried to find some reliable historical information regarding the observed secular precession of our Southern polar stars. Astronomy literature offered plentiful material concerning the precession of our Northern pole stars - but precious little about the Southern ones (specifically, the rotational direction in which they were observed to precess). As I finally found what I was looking for, it dawned upon me that Earth had to be tilted at 23 degrees - yet not in the "fixed" manner proposed by the heliocentric / Copernican model. I must admit it took me many days (as Hoi and Kham can testify, as we discussed it vividly over brunches & dinners) to wrap my head around the issue and to figure out exactly how to solve it! Ultimately though, not only was the solution disarmingly simple but, to my immense delight, it also simplifies the entire Tychos model's geometry - since it does away with the only awkward or, if you will, 'inelegant' feature of my original model : the PVP orbit's obliquity.

And yes, this also means that our member Seneca (who rightly argued with me last month, via several personal e-mails, the equivalence of the 23-degree tilt) was right all along. So, many respectful hat tips to you, dear Seneca! This has led me to revise the relevant sections in my book (see the revamped chapter 12) and to make a couple of new graphics (see below) to illustrate this wonderful development of the Tychos' geometry.



As 'luck' has it, this development has no disruptive bearings on the TYCHOS' core principles - but simply makes the model even simpler! :)
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Re: Introducing the TYCHOS

Unread postby simonshack on Fri Nov 02, 2018 2:07 am

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"!



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?

Image ... lassic=YES

What 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 :

"In 1773, Lambert used advanced perturbation techniques to produce new tables of Jupiter and Saturn.The result was surprising. From the mid-17th century the Great Anomaly appeared to go backwards: Saturn was accelerating and Jupiter was slowing down! Of course, such behavior was not compatible with a genuinely secular inequality."

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." ... 20&f=false

So, 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”. ... rs/sns.pdf

On 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:
Image ... 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. " ... 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.
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Re: Introducing the TYCHOS

Unread postby simonshack on Fri Nov 02, 2018 3:47 am

Here follow the (boring yet necessary) mathematical demonstrations of the TYCHOS paradigm, in relation to the observed motions of Jupiter & Saturn. I'm just posting them here for the record - you don't need to read them if you are short of time! -_-

GENERAL JUPITER AND SATURN DATA (as of the TYCHOS, the two complete their orbits in exactly 12 and 30 years)
Jupiter Orbit circumference > 4,891,899,584.6 km (5 Jupiter orbits = 24,459,497,923 km)
Saturn Orbit circumference > 8,964,009,501 km (2 Saturn orbits = 17,928,019,002 km)

Jupiter's orbital speed: 46,504.48 kmh (Jupiter completes 1 orbit in 105,192 hours - or  exactly 12 y)
Saturn's orbital speed:  34,086.27 kmh (Saturn completes 1 orbit in 262,980 hours - or exactly 30 y)

Every 12 y, Jupiter advances by 15min of RA, i.e. by 1.25min EACH YEAR.
Since our celestial sphere is made of 1440 minutes of RA, we can easily compute how long it will take for Jupiter to "lap" our Sun's orbit:
1440 / 1.25 = 1152

Ergo, Jupiter will "lap" the Sun's orbit once every 1152 years.

Hence, in one TYCHOS Great Year, Jupiter will "lap" the Sun 22 times : 25344 / 1152 = 22

Every 30 y, Saturn advances by 28.3 min of RA, i.e. by 0.9433(periodic)min EACH YEAR.
Since our celestial sphere is made of 1440 minutes of RA, we can easily compute how long it will take for Saturn to "lap" our Sun's orbit:
1440 / 0.9433 = 1526.5

Ergo, Saturn will "lap" the Sun's orbit once every 1526.5 years.

Hence, in one TYCHOS Great Year, Saturn "laps" the Sun 16.6 times : 25344 / 1526.5 = 16.6)

At intervals of (slightly less than) 60 years, Jupiter and Saturn are observed to regularly conjunct almost at the same place in our skies (yet each time slightly more East vis-à-vis the starry background).

That is, 5 orbits of 12y for Jupiter -  and 2 orbits of 30y for Saturn. Thus, in one TYCHOS Great Year (of 25344y), there will be a total of 422.4 Jupiter-Saturn "60-year conjunctions": 25344 / 60 = 422.4

If we now divide 1440min of RA (i.e. our 360° celestial sphere) by 422.4, we obtain :
1440 min of RA / 422.4 = 3.409(periodic)min of RA (Right Ascension)

Hence, this RA value of 3.409 (periodic) represents the mean distance between ALL of the Jupiter-Saturn conjunctions, if we were to plot (around our 1440-min celestial sphere) each one of those 422.4 Jupiter-Saturn "60-year conjunctions" over one Great Year (of 25344 solar orbits). 

Note for now that 3.409(periodic)min is 0.23674242 % of 1440min (i.e. our 360° celestial sphere).

Let us now use a typical pair of such circa-60-year conjunctions of Jupiter & Saturn to verify whether the TYCHOS model (and its proposed snail-paced orbital speed of Earth, i.e. 1.601169kmh / or circa 1mph) can provide an explanation for their peculiar periodicity. 
Typical example of a pair of Jupiter-Saturn "60-year" Great Conjunctions:

2000(May31) >to> 2060(Apr10) = 21,864 days, or 524,736 hours apart (i.e. only 51 days short of 60 full years).
(NOTE : 21,864 days is 0.23326% short of 60 full years)

In this time, Jupiter will cover 46,504.48 kmh X 524,736 h = 24,402,574,817.28 km  - completing 4.9883638 orbits,
(or just 0.23326 % short of 5 full 12-year Jupiter orbits)

In this time, Saturn will cover 34,086.27 kmh X 524,736 h = 17,886,292,974.72 km - completing 1.99534516 orbits,
(or just 0.23328 % short of 2 full 30-year Saturn orbits)

So, the question is: WHY would Jupiter and Saturn conjunct in 524,736 hours, i.e. just a whisker less than 60 full years?

Well, simply because during that time (524,736 h), Earth, moving along at 1.601169 km/h, will have covered the distance of :

1.601169 kmh X 524,736 h =840,191km which, as it "happens", amounts to 0.23619 % of Earth's PVP orbit circumference of 355,724,597 km !

And as we saw earlier, the MEAN distance between each Jupiter-Saturn conjunction is:
3.409(periodic)min , which amounts to 0.23674242 % of 1440min (i.e.360°).

Now, 3.409(periodic)min = 204.54(periodic) seconds of time.

We see that 204.54(periodic) seconds of time equals 3068.18 arcseconds... ... arcseconds 

...and 3068.18" /51.13636" i.e. the Tychos' all-important ACP (Annual Constant of Precession)= 60 !

In other words, the OBSERVED Jupiter & Saturn conjunctions provide yet another qualitative AND quantitative confirmation of the TYCHOS model's proposed precession rate (51.13636"/year) caused by Earth's 1-mph motion. It is hard to wish for better / more conclusive proof of the correctness of the TYCHOS model.
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Re: Introducing the TYCHOS

Unread postby pov603 on Fri Nov 02, 2018 6:42 am

Good stuff, Simon.
I haven’t been able to “keep up” with some of the observations but that one made sense to me (that’s my problem not yours!).
Are there any Astronomy publications that would be willing to publish your data?

Edit: typo
Last edited by pov603 on Fri Nov 02, 2018 11:15 am, edited 1 time in total.
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Re: Introducing the TYCHOS

Unread postby patrix on Fri Nov 02, 2018 10:27 am

Excellent article Simon. This puts an end to the hundreds of years and thousands of hours poured into this dilemma by some of the brightest minds.

Simon's astronomical research needs to become more widely known and I hope we all help out in achieving this and study his work. I’m currently working on a new version of Tychosium 3d. It’s going well, but no need to wait for that. All that's needed to understand the significance and importance of this is laid out in Simon's book and illustrated by his drawings and the existing Tychosium 2d

Please study this material. You do not have to know anything about astronomy beforehand. Just read up on astronomical terms like declination and right ascension (nothing more than the astronomical coordinate system used to describe where a planet/star is located at a certain point in time).
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Re: Introducing the TYCHOS

Unread postby simonshack on Tue Nov 20, 2018 5:41 pm




In my Tychos book I have already expounded and illustrated why all the stars are observed to move (annually) around a trochoidal loop. The reason for this being (quite simply) that any earthly observer will, in fact, be "carried around" a trochoidal path, as Earth moves by 14036km every year - while rotating around its axis once a day. Hence, Earth (moving at circa 1.6 km/h) covers annually a distance slightly larger than its own diameter (12756km) - and therefore, any astronomer monitoring a given star during a full year will see this star performing a peculiar loop, similar to his own yearly path :


My book features this graphic (from the Rochester Institute of Technology) showing the path of star Vega over a three-year timespan :


However, I was still hoping to find further official confirmation of the fact that stars are truly observed to "behave" in such manner. You may therefore imagine my delight as I recently found this animation - by none other than... the European Space Agency (ESA) ! :

Please watch this brief, 30-second animation by ESA:

(You may also wish to watch this other ESA animation, which shows ALL the stars in our skies "wobbling" in similar manner)

Naturally, I was curious to verify whether the peculiar trochoidal stellar path illustrated by ESA was comparable (proportionally) to the curve that I had calculated (a couple of years ago) for what I call "A man's yearly path". Well, here's the result, ladies and gentlemen :

Note: I have of course rigorously respected the relative proportions of these graphics - and not indulged in any sort of proportional fudging of their relative dimensions!

As you can see, the "X" to "Y" ratio of my calculated trochoid ("A man's yearly path") turns out to be a PERFECT MATCH with that trochoid shown in the ESA animation! That is, a trochoidal curve with a 2.05 : 1 ratio.

To be sure, the Copernican model cannot account for this peculiar trochoidal motion of the stars:

If Earth is moving around the Sun at 107,226 km/h (as claimed) and our entire solar system is moving around our galaxy at 800,000 km/h (as claimed), that trochoid should have a 7.46 : 1 ratio (800,000 / 107,226 = 7.46). Now, are we perhaps to believe that ALL the stars in our Milky Way - whose observed proper motions proceed in all kinds of directions - are also / simultaneously ALL moving at the same speed of 800,000 km/h along with our solar system?.. In any case, here's the caption we can read under that ESA animation linked above:

"Simulated motion of a star in the sky caused by the combination of parallax, an apparent shift caused by Earth’s yearly motion around the Sun, and proper motion, which results from the star’s true motion through the Galaxy."

At this point, dear reader, you are left with two options:

Option 1: The trochoid of "A man's yearly path" (at a 2.05 : 1 ratio) is just coincidentally equal to that exhibited by the above ESA animation.
Option 2: The TYCHOS is the only existing model of our solar system that agrees with the empirical observation of stellar motions.

It's all up to you.

If you choose Option 1, you can keep hurtling at 107,226 km/h (i.e 90X the speed of sound) around the Sun - and at 800,000 km/h (i.e. 648X the speed of sound) around our galaxy to your heart's content. -_-
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Re: Introducing the TYCHOS

Unread postby pov603 on Wed Nov 21, 2018 10:39 am

Hey Simon, without wishing to add to your Tychos "workload" is it possible for you to list/tabulate [even in a locked/separate post] all of the many issues/observations/anomalies that have been noticed, accumulated, postulated over the centuries?
If so, would it be too much to ask if you could then indicate in a column alongside [if tabulated] whether Tychos has answered/explained these observations/anomalies?
This would, in effect, be a "tick list" so that we know which ones are still to be accomplished and/or which ones, anomalous as they are, have been answered fully by Tychos.
It is, in part, to "dumb it down" for people such as myself so that we may look into issues that we may already be aware of [though not understand] or even become aware of for the first time [analema for one in my experience...].
It could even then have an additional column with "link" to an explanation from you [or others] either in the Tychos forum or this forum itself.
A lot of what has been developed by you in this regard is somewhat above my understandings [at present] so I would hope that having a "compendium" of issues that can be or are being or even will be explained by Tychos would be of great me...and hopefully others!
Keep up the great work, it is a fascinating journey.
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Re: Introducing the TYCHOS

Unread postby simonshack on Wed Nov 21, 2018 8:38 pm

pov603 » November 21st, 2018, 10:39 am wrote:Hey Simon, without wishing to add to your Tychos "workload" is it possible for you to list/tabulate [even in a locked/separate post] all of the many issues/observations/anomalies that have been noticed, accumulated, postulated over the centuries?

If so, would it be too much to ask if you could then indicate in a column alongside [if tabulated] whether Tychos has answered/explained these observations/anomalies?

Dear pov603,

This is indeed on my "to do" list - and I'm currently working on it : that is, a summary / compilation of the most notorious, longstanding and controversial "mysteries, conundrums, dilemmas" and unresolved questions of astronomy - which the TYCHOS (however pretentious this may sound for me to assert), systematically resolves - in the simplest imaginable manners (most of which thanks to Earth's propounded 1-mph-motion).

In fact, the most captivating - and oftentimes exhilarating - part of my last few years of study has been reading (untold volumes of) all sorts of astronomy literature dealing with the most recalcitrant problems which this world's scientific community has had to struggle with for the last 400 years or so - i.e. ever since the "universal acceptance & establishment" of the Copernican / Keplerian / Newtonian heliocentric model. What ensued was an endless string of heated & bitter debates (between our world's most eminent scientists) - since, at every turn, one seemingly inexplicable "anomaly" after the other kept popping up, each one of which "alarmingly" threatened to burst the (by then already "sacrosanct") heliocentric theory.

At every step, formidably abstruse ad hoc "solutions" were offered (mostly by our "mathemagical priests") to rescue the heliocentric theory from catastrophical collapse. Over time - and although no general consensus was ever reached (e.g. NO evidence whatsoever of Earth's supposed revolution around the Sun was ever produced), these vexing matters were ultimately deemed to be resolved & settled - that is, within the confines of Academia. Of course, we - the general public - were told that those who didn't understand the contorted "Proofs & Laws" (proclaimed by Newton, Kepler, Laplace, Einstein et al) were simply too damn stoopid. Someday, someone ought to write a book about it all...

As it is, I can see myself (in my older days) stitching together a non-fiction novel about this Kafkaesque, four-centuries-long comedy of errors which has seen our world's most eminent scientists occupied in endless "circular" feuds - which have kept our civilization's astronomical knowledge virtually stagnant since the days of Tycho Brahe. It should make for a fun read. ^_^
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Re: Introducing the TYCHOS

Unread postby simonshack on Sat Nov 24, 2018 8:35 pm


"MARS, THE SUN'S BINARY COMPANION? Preposterous, my dear Simon - you must be mad!!!"

The very first, "standard" objection that opponents of my TYCHOS model regularly submit to me is that Mars is far-too-small-a-celestial-body to be our Sun's "dance partner". They argue that it would gravely contradict Newton's Laws of Gravitation - and that if this were the case, Mars would immediately crash into the Sun. Besides, they say, "Mars is a planet - not a star! And hey, binary double stars are composed of two stars - not a star and a planet!"

A screenshot from the Tychosium 3D Planetarium - a work in progress by Patrik Holmqvist and Simon Shack

Well, it is a matter of historical record that when the first binary star systems were discovered (not so long ago), our world's astronomers were totally stumped: the extremely small size of these newly-detected companion stars (which they kept finding thanks to powerful modern telescopes) made no sense at all - that is, within the framework of Sir Isaac Newton's Gravitational "Laws". For instance, here's what Astronomer Royal Sir Arthur Eddington had to say - following the discovery of Sirius B (the tiny binary companion of Sirius A):

"We learn about the stars by receiving and interpreting the messages which their light brings to us. The message of the Companion of Sirius when it was decoded ran: 'I am composed of material 3,000 times denser than anything you have ever come across; a ton of my material would be a little nugget that you could put in a matchbox.' What reply can one make to such a message? The reply which most of us made in 1914 was—"Shut up. Don't talk nonsense." (Sir Arthur Eddington)

In fact, as these small binary companions were discovered, Newton's "Laws" were, once more, in grave danger of catastrophic collapse. Eventually though - and to make a long story short - the whole question was "settled" by what must be the most egregious case (in science history) of "backwards reasoning" or, if you will, of "confirmation bias". The ad hoc 'resolution of the mystery' went as follows: if Sirius B is so very small [its diameter is almost equal to Earth's diameter] then it must be made of extraordinarily dense matter! Today - and to be sure -astronomy students are actually taught that a sugar cube on Sirius B would weigh some 1000 kg - because the forces of gravity on Sirius B are 400,000X stronger than on planet Earth! Hence, Sirius B would be "heavier" than our Sun! That's right, we are told that the atoms composing Sirius B are "packed four-hundred-thousand times tighter" than our earthly atoms... I trust that anyone (graced with earnest brain matter) can see what they (our world's most revered scientists) did there - in the name of their sacrosanct and untouchable "Science God", Sir Isaac Newton.

Now, let's take a look at a picture that we can find on Wikipedia. The caption for this image says :
"Image of Sirius A and Sirius B taken by the Hubble Space Telescope.
Sirius B, which is a white dwarf, can be seen as a faint point of light to the lower left of the much brighter Sirius A."

Image < An image to be found on Wikipedia

Note for now: these extremely small - yet "formidably dense" - celestial objects ( such as Sirius B ) are now officially named "white dwarfs".

Before proceeding, let me just remind my readers that some years ago - as mentioned in my TYCHOS book - I decided to compare the relative sizes (diameters) of Sirius A versus Sirius B with those of our Sun versus Mars. It turned out that Sirius B is 0.4888% of the size of Sirius A - and that Mars is 0.4881% of the size of the Sun. Ergo, the four of them are proportionally alike. One could therefore reasonably imagine that, as viewed from Sirius, our solar system may well look a bit like this:
Image < My own "adaption" of the above image from Wikipedia
Note: in my TYCHOS book, I also show that the ratios of the relative distances (closest and furthest) between Sirius A and B - and between the Sun and Mars - are practically identical : 1:3.88 for Sirius A/B - versus 1:3.763 for Sun/Mars. You may agree that, if all of this is entirely coincidental, it is a heck of a string of coincidences!... Could Sirius - the brightest star system in our skies - perhaps be some sort of "twin sister" of our solar system? Please know that I don't pretend to answer / nor to explain these questions. However, isn't all of this worth a major scientific debate? WHY is it that the Sun and Mars exhibit virtually IDENTICAL relative sizes as Sirius A and B - as well as virtually IDENTICAL relative maximum & minimum distances to each other?

Let us now talk about "white dwarfs" (remember, Sirius B is deemed to be a "white dwarf" star).

So, according to "official astronomy" (for lack of a better term), Sirius B is a "white dwarf". This would be the sort of super-duper-dense star type that can be the binary companion of a FAR, FAR larger star (the two dancing around each other in mutually intersecting orbits). Could Mars - which we currently define as a "planet" - possibly be (or have been) a white dwarf? Can such a contention be dismissed offhand? Well, let's look at what "officialdom" has to say about the secular evolution of white dwarfs. Wikipedia provides us with a short animation depicting what sort of transformations white dwarfs are believed to go through - over long periods of time:

Please watch this short animation (to be found on Wikipedia's "White Dwarf" page) : ... p.vp9.webm

That's right: "white dwarfs" are believed to become gradually yellow - and then orange/reddish, over time:

Here's a photograph of what we all know as our "red planet" Mars - snapped in 2016 by an amateur astrophotographer:

Hmm. Could Mars perhaps be a very old "white dwarf"? Has it become what is now known as a "black dwarf"? Let's consult Wikipedia again...

"A black dwarf is a theoretical stellar remnant, specifically a white dwarf that has cooled sufficiently that it no longer emits significant heat or light."

As it happens, this is precisely what two independent researchers (the authors of "Stellar Metamorphosis", Wolynski and Taylor) have concluded:

"Mars is a much older black dwarf star that resembled Earth earlier in its history as is also evidenced by presence of water-like erosion on its surface and past volcanic activity, and a magnetic field would compliment those features."

The basic gist of Wolynski's & Taylor's research is that most or all the celestial bodies in our cosmos (known as "stars, planets and moons") are stars in various stages of their evolution (or ejected debris thereof - such as asteroids, comets, etc.). I have to say this makes sound sense to me - and hope to hear from Wolynski and Taylor in the near future. They are both very much welcome to discuss their work on this forum.

Meanwhile, Iet us stop calling Mars "a planet". I'd say that the TYCHOS provides enough evidence that it can very well be the Sun's binary companion: Mars is just an older star orbiting around a younger one - namely, the Sun. To quote Wolynski & Taylor once more:

"It is suggested that the rule of thumb of stellar age delineation is that old stars orbit younger ones, the younger ones being the more massive, hotter ones."

One thing seems clear to me: we cannot trust our "official / academic" scientists any longer. The time has come for free and independent researchers to start collaborating with each other - although this appears to be a tough challenge due to the egoes of each one of us (alas, we're all human ^_^ ). In all honesty, I'm jolly proud of my TYCHOS model - as it has resolved (for me, at least!) most of the "mysteries" of astronomy - which were bugging my mind. This said, I hereby pledge to do my very best not to let my ego blind my brain in any future interaction with fellow independent researchers - in the quest for a better understanding of our universe which, in my humble opinion, will benefit humankind as a whole.
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Re: Introducing the TYCHOS

Unread postby aa5 on Sun Nov 25, 2018 12:29 am

Basically to any open minded person, aka to the handful of us lol, its a supremely unlikely 'coincidence' that Sirius A and Sirius B.. and the Sun and Mars 'coincidentally' happen to be the same relative sizes and the same distances apart.

Now maybe if out of 1 million stars, we found one star out there that had this coincidence, I would say it is a funny coincidence. But when it is also the brightest star in our sky, (and hence the one we are most able to see the second star and its distance).. it has to be more than coincidence. There has to be a logical reason for why it is so.

I read a lot of pharmaceutical studies, and they use p value. And say in the drug group 30 out of 100 people get better. And in the placebo group 10 out of 100 people get better. And you can calculate out the odds of this being by random chance. Because even if its literally a '1 in a million' chance, it still could be that it is by chance. Just a reasonable person at some point comes to believe that its 'unlikely' to be by a chance, and a more likely explanation is that the drug is having some beneficial effect.
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Re: Introducing the TYCHOS

Unread postby patrix on Sun Nov 25, 2018 6:55 am

Basically to any logic minded person

Fixed that for you :) But seriously, this so true what you write aa5. This ratio that Simon has discovered simply can't be a coincidence and it makes the hypothesis that the Sun and Mars are binary companions very likely. And this is supported by the rest of the massive amounts of astronomical data Simon has looked at, and it has not been falsified by any of it as opposed to the Copernican model.

So what we have here is the only Solar system model that is in accordance with observations and experiments.
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Re: Introducing the TYCHOS

Unread postby simonshack on Wed Dec 12, 2018 2:19 am




Dear friends, it is most ironic that the greatest (and still ongoing) astronomical controversy of all times revolved around our own Moon's motions. After all, the Moon is our largest, nearmost and thus most intensely studied celestial body: shouldn't our world's scientific community have fully settled the matter by now, after all these years / centuries? How can the Moon's motions still be such a hotly debated question? Here's what we can read today at Wikipedia (my bolds) :

"Lunar theory attempts to account for the motions of the Moon. There are many small variations (or perturbations) in the Moon's motion, and many attempts have been made to account for them."

Attempts. Just attempts....The "Lunar theory" Wikipedia page goes on saying that "after centuries of being problematic, lunar motion is now modeled to a very high degree of accuracy." Well, that is simply untrue - since modern scientists are still looking to solve the Moon's seemingly inexplicable orbital motions - as this abstract (from a scientific study dated 2011) concludes:

"Thus, the issue of finding a satisfactorily explanation for the anomalous behavior of the Moon's eccentricity remains open."

As for what concerns Newton's stance on the matter, the Moon's motions were notoriously problematic to him :

"The motion of the Moon is very complicated. Sir Isaac Newton is supposed to have told his friend Halley that lunar theory "made his head ache and kept him awake so often that he would think of it no more." ... /0006-0024

No wonder that the Moon's motions caused pain in Sir Isaac's brain : they stubbornly refused to comply with his gravitational theories!
Let's have a quick look at what the Moon Controversy was all about - as documented in astronomy literature:


To be sure, the Moon's motions were (and still are) in serious conflict with Newton's gravitational "Laws". It is a matter of historical record that Newton's "Laws" were contradicted by the Moon's "inexplicable, renegade behavior" - and that this plain fact ignited a humongous, endless controversy among our world's scientific community which, incredibly enough, remains unresolved to this day. Now, don't let any smartass astronomer tell you otherwise (i.e. that "the Moon controversy was eventually resolved") - for it would be a bare-faced lie which flies in the face of what has been repeatedly admitted in (earnest) astronomy literature - as I am partially documenting here.

What astronomy students are taught today is that the Moon's utterly bewildering motions were successively "resolved" by some of the most revered scientists of our times (e.g. Euler, Horrocks, Lagrange, Laplace, Clairaut, Dunthorne, Mayer, Einstein - to name a few), all of whom contributed in constructing a vast number of "terms" and "perturbations" that would supposedly account for the Moon's puzzling motions. Eventually, a veritable hodgepodge of theories were formulated in order to "rescue" Newton's sacrosanct Gravitational Laws. Here's what we can read today at the "Lunar Theory" Wikipedia page:

"The analysts of the mid-18th century expressed the perturbations of the Moon's position in longitude using about 25-30 trigonometrical terms. However, work in the nineteenth and twentieth century led to very different formulations of the theory so these terms are no longer current. The number of terms needed to express the Moon's position with the accuracy sought at the beginning of the twentieth century was over 1400; and the number of terms needed to emulate the accuracy of modern numerical integrations based on laser-ranging observations is in the tens of thousands: there is no limit to the increase in number of terms needed as requirements of accuracy increase."

As you can see, dear friends, there is apparently "no limit" to the increase of terms needed to explain the Moon's motion! The numbers of these terms keep growing - year by year. And most assuredly, our modern-day astronomy students are strongly discouraged from questioning the validity of the same. To be sure, it is "scientific heresy" to question the "established science" of our world's most acclaimed scientists. But let me submit a few more excerpts of astronomy literature to back up and document my previous assertion (that most astronomers, back in the days, agreed at least upon ONE thing, i.e. that the Moon's motions gravely contradicted Netwon's Gravitational Laws):

Here's an extract from the book "Pierre-Simon Laplace, 1749-1827: A Life in Exact Science" - by Charles Coulston Gillispie (1997) :

Source: ... an&f=false

And here's an extract from the "Edinburgh Review or Critical Journal", again highlighting the fact that the Moon's observed motions (with its so-called "anomalies and inequalities") were in stark contradiction with Newton's gravitational theories :

Source: ... on&f=false

The problems with the Moon's motions ranged from its observed periodic (short-term) motions - and all the way to its secular (long-term) motions over the centuries. The latter triggered a gigantic (and still unsettled) debate - as studies of the ancient solar / lunar eclipses suggested that the Moon, over time, was thought to be continually "accelerating" although, paradoxically enough, its orbital speed was thought to be decreasing! Other theories proposed that Earth's rotation was actually decelerating. In short - and to put it bluntly and frankly - it was all a big mess.

“Astronomers who studied the timing of eclipses over many centuries found that the Moon seemed to be accelerating in its orbit, but what was actually happening was that the Earth’s rotation was slowing down. The effect was first noticed by Edmund Halley in 1695, and first measured by Richard Dunthorne in 1748 — though neither one really understood what they were seeing. ... g-Away.htm

I shall start with these supposed secular "accelerations" of the Moon - and demonstrate how the TYCHOS can account for them in the simplest imaginable manner. My two below graphics should suffice to illustrate the matter in easily comprehensible fashion.

The TYCHOS - and the Moon's apparent secular acceleration

My below diagram illustrates how and why the Moon will APPEAR to accelerate over the centuries (yet, it is only an illusion caused by what I believe must be the true geometry / configuration of our solar system - as expounded in my TYCHOS model) :


My next graphic shows how the Moon (in the TYCHOS model) will naturally appear to accelerate in relation to an earthly observer - yet, at the same time, will appear to decelerate in relation to the Sun (due to the Gregorian calendar's faulty year count - as thoroughly expounded in my TYCHOS book ( :


This, dear friends, concludes the TYCHOS model's explanations for the observed SECULAR (long-term) motions of the Moon. In short, the apparent "accelerations" (of the Moon) and "decelerations" (of Earth's rotation) are illusory. They are all due to Earth's tranquil yet steady 1.6-km/h motion around its PVP orbit (covering 14,036km every year), a motion that the TYCHOS model has now proven beyond reasonable doubt.

Let us now take a close look at the PERIODIC (short-term) motions of the Moon - an issue which has baffled astronomers and mathematicians alike for many centuries :

The TYCHOS - and the Moon's major longitudinal variation (a.k.a. the "evection")

The Moon is observed to oscillate (it apparently "accelerates and decelerates" Eastwards and Westwards against the 'fixed' stars) by +/- 1.274° (or 4586.45" seconds of arc) with a period of 31.8 days. This is what astronomers call the Moon's "EVECTION" - which they believe to be caused "by the action of the Sun" - or / and by a host of other proposed effects, such as "tidal forces", "core-mantle coupling" - assorted turbulences and "planetary perturbations".

All these various "gravitational / or non-gravitational disturbances" had to be imagined / invented by our most eminent astronomers, physicists and mathema[g]icians - since the Moon's observed motions obstinately refused to obey Newtons' Laws. The theories kept piling up, yet none of them succeeded to attain any sort of plausible, let alone precise answers to the puzzling motions of the Moon.

Perhaps the most cringeworthy attempt ever made to "save Newton's face" was that of Paul Dirac, considered as "one of the most significant physicists of the 20th century." Here's what we may read in a paper by F.R Stephenson published in the Journal of the British Astronomical Association :

"The most plausible cause of a non-tidal acceleration is a possible time rate of change of G, as was first proposed by Dirac. Such a change would affect the planets as well as the Moon, producing accelerations (or decelerations) in the exact ratio of the mean motions."

Huh? A "time rate of change of G", the so-called "gravitational constant"? Oh well... So hey, gentlemen, let's just tweak that "constant" and make it a "non-constant," et voilà - Newton wins again!.. It is almost comical to see how many ad hoc "solutions" have been unashamedly put forth - by the brightest (or most acclaimed) minds of science - so as to try and "accomodate" the Newtonian principles.

We shall now examine (under the TYCHOS "lens") the largest observed "inequality" (or "anomaly") of the lunar motion - i.e. what is known as the Moon's "EVECTION" :


"In astronomy, evection (Latin for "carrying away") is the largest inequality produced by the action of the Sun in the monthly revolution of the Moon around the Earth. The evection, formerly called the Moon's second anomaly, was approximately known in ancient times, and its discovery is attributed to Ptolemy.

Evection causes the Moon's ecliptic longitude to vary by approximately ± 1.274° [or ± 4586.45" seconds of arc], with a period of about 31.8 days. The evection in longitude is given by the expression +4586.45''\ sin(2D-L), where D is the mean angular distance of the Moon from the Sun (its elongation), and L is the mean angular distance of the moon from its perigee (mean anomaly). It arises from an approximately six-monthly periodic variation of the eccentricity of the Moon's orbit and a libration of similar period in the position of the Moon's perigee, caused by the action of the Sun."

In simpler words, this means that the Moon's longitude in the sky is observed to vary by as much as ± twice its diameter (Eastwards or Westwards of the so-called "mean moon"*) for a total of somewhat more than four lunar diameters (3474km X 4) - or approximately 14,000km. Here follows a simple diagram to visualize this fact:


* [The "mean moon"] is an imaginary body which orbits the Earth, in the ecliptic plane, at a steady angular velocity that is equal to the Moon's mean orbital angular velocity ... de133.html

The Moon is observed to move every minute of time (as seen from Earth) by 32.9" seconds of arc. We can therefore express the amplitude of the Moon's observed oscillation (4586.45") in minutes of time:

4586.45 / 32.9 = 139.4 min
Hence, the Moon is observed to oscillate back and forth (i.e. appears to speed up and slow down) by +/- 139.4 minutes of (solar) time every 31.8 days.

31.8 days is 16.6% more than 27.2848 days - which is the mean value of the Moon's 360° annual revolutions within the time frame of a tropical year, i.e. 365.24219 / 13.386266. The latter little-known value is from a rigorously researched paper by the Binary Research Institute:

"Lunar calculations, comparing the delta of the moon’s revolutions around the earth in a tropical year, 13.386266, to the number of new moons in a tropical year, 12.368266, apply the same principle and confirm the same thing; the delta of “one” (lunar orbits in this case) occurs in the time frame of the tropical year." ... pg-web.pdf

Now, in 31.8 days the Moon will have moved considerably more than 360°. However, since we wish to know the mean / average amplitude of the Moon's evection over just 360° of its motion , we need to reduce our 139.4-min figure by 16.6% - which gives us a figure of 116.4 minutes of time. In other words, the Moon "accelerates" by 116.4 min of time during one half of its orbit around Earth - and "decelerates" by 116.4 min of time in the other half of its orbit (the two halves corresponding "spatially" to the Sun's two six-month periods).

Our celestial sphere's time scale (around which our clocks are calibrated) is of course determined by the Sun's annual 360° revolution around Earth: there are 525,948min in a 360° solar (or "tropical") year.

Hence, we will need to quantify the amplitude of Moon's evection against our 360° "solar minute-scale", since the observed longitudinal (East-West) oscillations that this evection induces (over a 360° lunar journey around our celestial sphere) corresponds to ±116.4 minutes of solar / clock time.

Now, 116.4 min amounts to 0.0221% of 525,948 min (i.e. one solar year)

As of the TYCHOS, the Moon's "mean" (or actually constant) orbital speed is ca. 3656 km/h.

We see that 0.0221% of 3656 equals 0.8079 or approximately 0.8. This 0.8 "coefficient" would thus represent the six-monthly* speed variation - i.e. the apparent yet illusory acceleration (and / or) deceleration of the Moon.

(*Remember the above-quoted Wikipedia statement: "It [the Moon's evection] arises from an approximately six-monthly periodic variation of the eccentricity of the Moon's orbit.")

In the TYCHOS, we may illustrate this apparent variation of the Moon's speed like so :


Hence, this 0.8 factor would appear to nicely confirm Earth's orbital speed of 1.6 km/h - as proposed by the TYCHOS - as this tranquil speed of Earth would account for the Moon's largest longitudinal inequality known as the "evection". As it is, my proposed 1.6km/h speed of Earth has already solved many other 'mysteries' of astronomy, so this is just yet another confirmation of its qualitative and quantitative exactness.

Let us now perform a last cross-verification of this result (for math geeks and assorted critics) to verify our above figure of 116.4 minutes representing the Moon's observed, six-monthly EAST-WEST "acceleration/deceleration :

1.601169km/h (Earth's orbital speed) is 0.043795% of 3656km/h (the Moon's orbital speed).

0.043795% of 39,290min (the minutes contained in 27.2848 days, i.e. the Moon's mean "tropical" period) is 17.2min.

Now, the full amplitude of the Moon's evection is gauged over a six-month period. In six months, there are 182.625 days, which is 6.6933 X 27.2848 days. In order to verify our above-determined 116.4min-value for the Moon's evection, we should therefore multiply 17.2 minutes by 6.6933:

17.2 X 6.6933 = 115.12 minutes.

Ok, so 115.12 is not exactly 116.4 (a 1.1% discrepancy) - but you may agree that it is a reasonably close match - within the margins of probable error. Perhaps further study will clarify this 1.1% discord, conceivably due to periodic variations of the eccentricity (not ellipticity) of the Moon's circular orbit. To be sure, the Moon's motions are quite complicated - and the TYCHOS does not pretend to resolve all of their subtle irregularities. However, I have just demonstrated that the Moon's LARGEST longitudinal "anomaly" (the so-called evection) can be shown to be accounted for by Earth's 1.6km/h-motion - as proposed by the TYCHOS model.

The TYCHOS accounts for the Moon's perigee oscillation

Here is a classic diagram depicting the minimal and maximal Earth-Moon distances (perigee versus apogee):


In simple words, the Moon's orbit is off-center of Earth's barycenter. Now, does using the "barycenter" word necessarily mean that we are still talking Newtonian gravitational physics? No. Magnetic forces (as experimentally demonstrable here on Earth) may be at play. The TYCHOS model is, in any case, primarily focused on determining the correct geometry of our solar system. As long as we Earthlings haven't correctly determined this geometry (so as to make it agree with empirical observation), we surely cannot pretend to formulate any valid theories as to the physics regulating the same.

NOTE: The above diagram showing the Moon's orbit strangely talks about "overemphasised eccentricity" - whereas what is depicted is a very flat, highly-exaggerated ellipse (a senseless yet all-too-common feature in astronomy illustrations). The circular orbits of our solar system's bodies can be eccentric (i.e. offset from the centre of the body they revolve around) - but need not be ellipitical to be eccentric. As we shall see, in the TYCHOS the perceived ellipticity of our Moon's orbit (as viewed from Earth) is caused by our 1.6km/h motion around the PVP orbit ( see blue orbit in the Tychosium simulator: )

As I came upon this database which features annual charts of all the Moon-Earth distances for the lunar perigee (and apogee) passages, I was curious to see if those distances might be of interest to the TYCHOS model. Before we get on, I should remind the reader of one of the most 'crucial' distance-values established by the TYCHOS model:

This is the distance that Earth covers every year (in the TYCHOS) - as it moves along its PVP orbit at 1.6km/h. I will henceforth refer to this key value as the "EAM" (Earth's Annual Motion).

As I consulted that detailed chart of the Moon's perigee transits, my attention was naturally drawn to these long-term (i.e. secular) average minimal and maximal lunar perigee distances:

"Over the 5000-year period from -1999 to 3000 (2000 BCE to 3000 CE), the distance of the Moon's perigee varies from 356,355 to 370,399 km." ... p2001.html

So let's see: the difference between 356,355km and 370,399km is:

370,399km - 356,355km= 14,044 km

How interesting: this value is only 8km "off" of the "EAM". As it is, by carefully consulting these lunar perigee charts, it can be easily verified that the Moon's perigee regularly oscillates back and forth every solar year by an average distance of approximately 14,000 km !

As we saw earlier, the Moon's longitudinal variations are also in the 14,000-km range. We may therefore intuitively sense the plain logic of it all - and conceptually illustrate it with the following diagram :


Thus far we have determined that Earth's annual 14,036-km motion (as of the TYCHOS paradigm) can nicely account for both of the major lunar variations (i.e. the Moon's so-called "anomalous inequalities"): the ca. 14,000-km oscillation of its perigee - and its ca.14,000-km longitudinal oscillation (a.k.a. the lunar "evection").

And now comes the "cherry on the cake" - so to speak: the above diagram only conceptually illustrates the fluctuating behavior of the Moon's perigee. So what about the Moon's apogee? Can we also find a 14,000-km "component" in connection to its apogee (the Moon's furthest distance from Earth)? Indeed we can! Here's what we can read about the AVERAGE values of the lunar perigee and apogee:

"The Moon’s distance from Earth (center-to-center) varies with mean values of 363,396 km at perigee (closest) to 405,504 km at apogee (most distant)." ... p2001.html

So let's see, we have a difference of: 405,504km - 363,396km = 42,108km

We see that 42,108 equals 3X 14,036 (14,036 + 14,036 + 14,036)!

Since (as we have just seen) the Moon's perigee oscillates by about (1X)14,036km, the other two (2X14,036km) would seem to be logically accounted for by its apogee.

As astounding as this may be, this allows me to reasonably conclude that the eccentricity of the Moon's orbit (i.e. the relation between its perigee and apogee) exhibits an exact 2:1 ratio based on the TYCHOS' all-important EAM value of 14,036km - the distance covered by Earth each year.

Now, to keep our feet firmly anchored on Earth, let me state what follows, dear friends: I am fully aware that all of this may seem almost too good to be true (for the TYCHOS) - but I am certainly not making it up: I have only 'bumped into' this discovery (through patient & persistent efforts, mind you!) - whilst perusing available observational data. Of course, this same data (e.g. the 14,036-km-value) would have meant next to nothing to a Copernican / Keplerian researcher.

To the inevitable naysayers who will argue that this may all just be a case of (multiple) coincidences - I wish them the best of luck computing the odds / probabilities of this being the case. More likely - and in my honest opinion - the Moon's orbital perigee / apogee variations unequivocally "reflect" Earth's annual motion and decidedly concur to corroborate the TYCHOS model's principal contention: namely, that Earth travels at 1,6km/h - covering 14,036km every year.

As ever, more study is needed to finally figure out the exact periodic & secular dynamics of the Moon's motions, yet I am confident that this is well within reach given modern computing power - and given that we now know "what to look for", geometrically speaking.

And thus, my dear friends, the TYCHOS elegantly "conquers the Moon" (and cures Newton's headache)... :)
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