About the notion of barycenter

The TYCHOS book says the following:

In the TYCHOS, Earth is positioned near (or at) the center of mass of the Sun-Mars binary system.

However, it seems earth is not positioned at the barycenter of Sun and Mars.
The barycenter must be located at a point somewhere on the line connecting Sun and Mars. Earth does not meet this requirement, it is very far from the line connecting Sun and Mars in most cases, as shown in the following screenshots of the Tychosium simulator:


Dear misuzato, this statement of yours simply doesn’t stand up to what is actually observed in any known binary system. It is a common (mis)conception that the two main components of binary systems must always ‘face each other’ in relation to their common barycenter. This is simply not the case: binary systems come in an infinite variety of orbital sizes and orbital speeds - and will thus hardly ever behave as you suggest. And yes, this means that we need to revise the very notion of ‘barycenter’ (as commonly conceived and envisioned) and its true meaning in the cosmic context of two bodies revolving ‘around each other’. As I point out in Chapter 3 of my book:

“A possible reason for why the Sun and Mars have never been considered to be a binary pair may be due to the fact that Mars returns “in opposition” (i.e. on the other side of Earth with respect to the Sun) every TWO solar years - instead of every SINGLE solar year (as we might expect a ‘classic’ binary system to behave). This 2:1 ratio is however not so evident over shorter periods of time (it is estimated to be around 2.13:1) - due to the eccentricity of Mars’s orbit. As we shall see further on, this ratio will - in the long run - “average out” to an exact 2:1 ratio: the Sun will return in the exact same place in our skies in 25344 years - whereas Mars will do so in 50688 years (i.e. 25344 X 2).”

In other words, whenever we try to determine the ‘true barycenter’ of a given binary system, we need to set aside our preconceptions of what represents a given binary system’s barycenter - and instead seek for the secular, long-term period needed for the determination of the entire system’s true ‘middle point’. Now, what the TYCHOS research has determined is that Mars appears to act as what we may call the ‘pivotal point’ of our Solar System - over a period of 25344 years:

You may now ask: "does this prove that the Earth is located ‘at or near the barycenter of our system’ - as stated in the TYCHOS book?" Perhaps not - further study is needed - but the fact that Mars’s closest Earth transits (“in opposition” to the Sun) keep occurring at about 56.6 Mkm - i.e. smack in the middle of Earth’s 113.2 Mkm PVP orbit! - over a 25344-year cycle should help us determine, once and for all, the true meaning of ‘barycenter’ in the cosmic context of binary systems.


Thanks for your explanation. You are basically saying that the mainstream theory of binary star is totally wrong. That is, in a binary system, two stars may revolve around a point other than their (commomly defined) barycenter and can have different orbit period. Could you provide some concrete data/examples as observational evidence for this?

Well, dear mizusato - before we get on with our interesting discussion, we should probably first determine what the mainstream theory of (the motions of) a binary system actually is.

Is it this? (1)

Or is it this? (2)

Or is it this? (3)

Next - and before you submit me other questions - I would be happy to see you actually contributing to the TYCHOS research. Are you game? If so, your first task will be to find any official data of any known binary system that has been proven (beyond doubt) to behave in any of the three manners depicted above.

I’ll be waiting. Good luck! :slight_smile:

p.s. : Your next task will be to find any official data of a star system that features a central, single and “static” star being circled by a bunch of planets in concentric orbits - just like our Solar System is officially meant to be according to heliocentrists (see below graphic). Again, good luck with THAT!

Besides, even heliocentrists are starting to realize that we live “in the weirdest Solar System”:smiley:


your first task will be to find any official data of any known binary system that has been proven (beyond doubt) to behave in any of the three manners depicted above.

The following GIF is an observation of the Luhman16 system, which clearly matches (1). Note that the two stars always ‘face each other’.

Luhman 16 A and B orbit each other at a distance of about 3.5 astronomical units with an orbital period of approximately 27 years. --Wikipedia

‘Clearly’ you say? Here is what I see:

  • Between 2015 and 2016, one of the two appears to ‘catch up’ with the other. I can’t see how that would ‘clearly match’ the above example (1)…

  • Most interestingly though, the two Luhman companions move across the sky in a trochoidal trajectory, similarly to Proxima Centauri - and just as predicted by the TYCHOS model (see Chapter 21)


:joy: I saw that too Simon!


What then determines that two space objects are a binary system? And above all, what would determine that the Sun and Mars are such a system? Their barycenter lies deep below the surface of the Sun. Simple calculations show that this barycenter is approximately 75 km away from the center of mass of the Sun!
I read in Tychos: “Would the (alleged) huge mass of the Sun versus the (alleged ) tiny mass of Mars rule out the idea that the two of them are binary companions?”
And I ask: Can we say that the mass of Mars is SUPPOSEDLY small?
Since Mars has been explored by many devices for several decades, and landers designed for mass-related accelerations land on its surface, can its mass be significantly greater? Can it at least approximately reach a mass several hundred thousand times greater to approach the mass that would enable the creation of a system that deserves the term binary?
Can we doubt the mass of the Sun if we know the orbital parameters of the system’s planets? Even if we assume doubts about the orbits of the inner planets, there are others - Jupiter, Saturn, etc., whose orbits clearly indicate the mass of our star?
And further - I look at the Tychosium simulation and see that the line connecting Mars and the Sun matches the position of the Earth FOR A MOMENT once every more than 2 years. Would this be proof that it is a binary system?
Something else - Is the Earth located 75 km from the center of mass of the Sun - this is clear from the entire theory of this binary system - the Earth would be located at the barycenter of this alleged binary system.

Hello Matik, I will try and address your many questions (I can count at least 8 of them) as time permits. However, allow me to first submit you a question of my own. You wrote:

"Simple calculations show that this barycenter is approximately 75 km away from the center of mass of the Sun!

My question would be: what sort of simple calculations are you talking about - and exactly on what existing theories are they based upon?

Thanks for a kind clarification. :slight_smile:

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I don’t really understand what theory would be needed to determine the barycetnrum of a two-body system. This is the center of gravity of the system and the distances of this center from the centers of mass of both bodies are inversely proportional to their masses. The ratio of the masses of Mars and the Sun is approximately 1:3,000,000 (3 million). Half the diameter of Mars’ orbit is 1.14E11 m. So the distance between the barycenter of the system of these two bodies and the center of mass of the heavier body (the Sun) is 1.14E11/3E6 = 38,000 m = 38 km. I had previously counted in my head and I was wrong - in reality it is even less than 75 km.

That’s great, Matik - you seem to have a good grasp of what is officially claimed.

Now, please help me understand what follows:

As you rightly say, the officially-claimed “mass” of the Sun is 3 112 832 x the “mass” of Mars.

But hey, do you know what? Get this:

The officially-claimed “mass” of the tiny Sirius B is 3 169 014 x the “mass” of Mars.

Yet, Sirius B is reckoned to be less than twice as large as Mars (11688km versus 6792km in diameter)!

So if Isaac Newton were alive today, you would have to ask HIM (not ME) just what he meant by the notion of “mass” - and how two bodies as similar in size as Mars and Sirius B could possibly have a 1:300 000 000 “mass” ratio. To be sure, Newton stated that physics work the same everywhere in the universe (“what was true on earth was claimed to be true in the heavens”), yet he died long before Sirius B was discovered. As it is, when Alvan Clark discovered (in 1862) the tiny Sirius B to be the binary companion of Sirius A (the brightest star in our skies), it was a devastating shock for the world’s scientific community, since it completely contradicted Newton’s theories. I would warmly recommend you to read the below-linked fairly recent (2017) paper by Gopi Krishna Vijaya, a most brilliant physicist - and a very good friend of mine:

> Furthermore, based on which body was rotating around which and at what speed, heavenly bodies were assigned masses. This needed a new concept of “gravitational mass”, once more simply created. All of these elements were combined into the “Theory of Universal Gravitation,” and what was true on earth was claimed to be true in the heavens. The numerical backing for the entirety of this theory was the numerical relationship of one particular motion of the moon with the value of gravity on earth – almost like building an entire castle on a single reed. And yet he claimed: “I feign no hypotheses.” https://www.gopivijaya.com/_files/ugd/01c972_812eeded7fc74eabb568cb49b09e7165.pdf

Welcome to the forum, dear Matik - I think I’ll enjoy answering any further questions you may have. :slight_smile:

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I see that we are separated not only by space but also by centuries of scientific progress :flushed:.
I agree that these progresses did not always go as expected by some groups, but they usually managed to come close to the observed results.
Since my previous questions could not be answered, perhaps due to lack of time (as you mentioned), I will ask one by one and I will manage to bring my views closer to the new science presented on the Tychos pages.
So the first problem that anyone who accepts the “official” science results sees is the location of the barycenter of this underlying binary system. According to what you claim and what can be seen in the Tychosium simulation, this barycenter agrees with the “official” position of the Earth’s orbit in relation to Mars and the Sun - the average Sun-Mars distance is divided in the ratio of approximately 15:8
So please show me what calculations result in this compliance and why the simple lever relationship used to calculate the center of gravity does not apply in space?

This is such a good question and at this forum it is broadcast to the world. But I, for one, am happy that Simon’s book is not filled with such calculations. This can be left to the many ‘young guns’ of astronomers out there wishing to make their reputations by bringing down the ‘giants’ of the science world.
I am reminded of Sun Tzu here, at least what I gleaned from my reading of it years ago: that the difficulty is bringing your opponent out onto the battlefield… this is indeed the difficultly you will will face, Matik, in getting an answer to your question, to get the ‘experts’ to even enter the fray.

No, dear Matik, I would rather say that we are separated by our different interpretations of scientific progress - and our propension and willingness to question or review the same. As you surely must be aware of, the science of astronomy is currently in dire disarray - since modern technological advancements have enhanced the observational accuracy of distant star systems or “galaxies” - and the orbital motions (and sizes) of bodies revolving within these systems have falsified pretty much every ‘established axiom’ of astronomy. In short (and to put it very simply / for the layman), what has been discovered in later decades is basically that:

  • The vast majority (more than 90% and counting) of stars are ‘locked’ in binary systems, meaning that they have a local orbit of their own and that they revolve around a smaller ‘star’ (more often than not invisible by our best telescopes). To think that our star - the Sun - has no local orbit of its own and no binary companion is thus ‘statistically improbable’, as dictated by plain common sense.

  • The orbital velocities of bodies revolving around very distant stars are estimated (according to the heliocentric stellar distance paradigm) to be so formidably fast as to be totally incompatible with either Newton’s or Einstein’s theories. This is the reason why the existence of some invisible “dark matter” is being assumed / conjectured - in order to “explain” these formidable velocities. Under the TYCHOS model (which holds that the stars are far closer than currently believed) these orbital speeds would turn out to be far slower than currently estimated - and thus the need for this ghostly and invisible “dark matter” would simply vanish. And no, this is not my fantasy - it was stated by none other than Jacobus Kapteyn (probably the world’s foremost expert of stellar statistics):

“If all stars were binaries there would be no need to invoke ‘dark matter’ in the Universe”. (Jacobus Kapteyn) Chapter 26: Probing Kapteyn, Hubble and Esclangon – Nextra

  • Astronomers are baffled by the discoveries of binary stars with highly unequal masses - since this would be in stark contradiction with Einstein’s general relativity theory:

If the general relativity method is correct, it ought to apply everywhere, not just in the solar system. But Van Flandern points to a conflict outside it: binary stars with highly unequal masses. Their orbits behave in ways that the Einstein formula did not predict. “Physicists know about it and shrug their shoulders,” Van Flandern says. They say there must be “something peculiar about these stars, such as an oblateness, or tidal effects.” Another possibility is that Einstein saw to it that he got the result needed to “explain” Mercury’s orbit, but that it doesn’t apply elsewhere.Tom Van Flandern Articles (ldolphin.org) ← The entire paper is well worth the read!

Eclipsing binaries can have irregular intervals. There is an infinite variety of binary star configurations in the universe, so the fact that Mars and the Sun don’t return ‘in line’ on either side of Earth every solar year (but only every 2.13 solar years or so - in our epoch) is not an argument against them being a binary pair.

In any event, the TYCHOS model (the physics of which certainly needs further study) wins hands down when it comes to geometry vs empirical observation - and this is amply demonstrated in my book which I hope you will set aside some of your time to read from start to finish. Yes, the heliocentric model is geometrically impossible - and this fact alone invalidates any physical theories constructed around it.

Okay, Simon. You are missing the point of the topic, but I will take it at face value and for now I will not return to the problem of calculating the position of the barycenter of the Mars-Sun system.
I’m starting to read Tychos again from the beginning - Preface here, and I’m having trouble finding some case of retrograde that is inexplicable on the basis of the Copernican system. This phenomenon is, as we know, an optical illusion that depends on the reference system (place of observation). A good explanation can be found e.g. here Apparent retrograde motion - Wikipedia
Another questionable issue:
“The current Copernican theory (which claims that the Sun needs circa 240 Million years to complete only an orbit) clashes with the observable fact that the overwhelming majority of our visible stars appear to revolve around relatively small ‘local orbits’ of their own - with relatively short periods. For instance, Sirius A and B revolve around each other in only about 50 (solar) years, the Alpha Centauri A and B binary pair do so in only 79 years, while the Polaris A and B binary pair do so in just 29.6 years. Other recently-discovered binary systems exhibit even shorter ‘mutual orbital periods’ of only a few months, weeks, days, or hours! None of our visible stars are observed to be moving around orbits in the range of hundreds of millions of years. Moreover, no star system has ever been observed to resemble the “Copernican carousel” (as illustrated above) what with a central, ‘fixed’ star surrounded by bodies revolving in neat, concentric circles.”
Well, the periods of revolution of the own barycenter by the stars of binary systems have nothing to do with the period of revolution of the Solar System around the center of the Milky Way. You are comparing two different parameters. The same binary systems you quote, travel around the center of the galaxy in a similar time, depending of course on the distance from this center, but counted in millions of years.
What arrangements did you have in mind? Maybe from another galaxy?

Dear Matik, the problem with the heliocentric explanation of Mars’ retrograde motions is expounded here:

You wrote:

"The same binary systems you quote, travel around the center of the galaxy in a similar time, depending of course on the distance from this center, but counted in millions of years."

That is indeed what we are told, Matik - i,e that all our surrounding stars are revolving in unison around the center of the galaxy (while. at the same time, revolving around each other at wholly different speeds and periods). If this were true, however, we should expect to observe some common / collective motion of them all in a given direction. This is not what is observed, though: all star systems appear to have proper motions of their own - in every imaginable “x-y-z” directions, some of them approaching us at high speeds (e.g. the Barnard’s star) and others receding from us - all in seemingly random and peculiar fashion.

As you reach Chapter 26 of my book, you will see how the TYCHOS model provides a plain and logical explanation for Jacobus Kapteyn’s discovery of “star-streaming” - which was another instance that shook the very foundations of Copernican / Keplerian astronomy. Read on - and enjoy the read! :slight_smile:

Matik, I’m sorry if you don’t think that my replies are on topic - or that I’m somehow ‘dodging’ your questions - but I’m sincerely doing the best I can. Besides, I should point out that you seem to have ignored or ‘skipped’ what I wrote above about Sirius B, namely that its “mass” is officially claimed to be more than 3 million times that of Mars (whose physical diameter is more than half that of Sirius B). Would you kindly address this topic? Please explain in simple words why that would be - and how anyone could possibly accept this extraordinary claim at face value.

I, for one, would encourage Matik to stay in the fight… I enjoyed the link to ESA Gaia Mission posted above and I can thank Matik for that.
Take my case… I have received my copy of the Second Edition. I sit outside in good light and read and my simple goal is to complete the book. I didn’t say ‘to understand it all’, but to have a top-down view of the whole.
I did the same with the first edition and it took three successive readings to reach a certain comfort level with the model and I felt extremely grateful for that understanding.

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I avoided this problem because you reject everything that science has been stating for several centuries. If you don’t recognize the laws of gravity, how can we talk about mass compression due to the gravity of the star’s masses?
The structure of matter is precisely determined by the equation of state resulting from the laws of nuclear physics.
In order not to complicate matters for readers who avoid mathematical equations, a simple comparison can be made - the diameter of the nucleus of an atom is approximately one hundred thousandth of the diameter of the atom. Translating this into volume, we have the volume of the nucleus of an atom as one trillionth of the volume of the atom - 1/1,000,000,000,000,000. Matter is a great void. There is nothing between the nucleus and electrons.
What does the “unacceptable” ratio of the mass of Sirius B, which, as we know, is a white dwarf - a star that, after exceeding a critical mass, collapsed - mean to the mass of Mars, which is simply a rocky planet?
The density of white dwarfs, estimated at approximately 2E9 (two billion), is still small compared to neutron stars, whose density is hundreds of thousands of times greater.
You will probably write that this is just theory, unconfirmed by facts.
The atomic and hydrogen bombs were not believed in either, but the equations of nuclear physics proved true.
Sirius B is simply a very dense star and comparing it to Mars makes no sense.

Hello Peaker!
You are right that there is no point in inserting complicated equations in a popular science publication, as it discourages readers who do not have extensive mathematical knowledge.
In this case, however, it is not about any complicated calculations. The center of mass is simply the weighted center. Let’s put one mass on one end of the stick and the other on the other, and let’s support the stick so that it’s balanced. It’s a simple principle of leverage. The equation of masses is their static moment. The mass of the Sun multiplied by its distance to the barycentum must equal the mass of Mars also multiplied by its distance to the barycente. Knowing the distance from the Sun to Mars, finding the barycente is a task for primary school children.
Aaah, I forgot! After all, Simon questions the masses of these bodies. This changes things😳
The whole Sun-Mars binary system invented by Simon cannot withstand the simplest criticism.
For now, I won’t go any further, e.g. into the PVP orbit, because it’s completely weird. The Earth revolves around a center where there is nothing. It curves its course even though there is no source of gravity in the center?