This blog post is inspired by the conversation in The biggest blunder in physics? where Berry was grilling TOEBI like no tomorrow. Calculations made inside my head are not necessarily the most accurate ones so here I do the math in format of a blog post.

Basic facts are here:

  • \(G_{Mercury}\approx 1.96*10^{-14}\frac{m^3}{kg*s^2}\) if whole Mercury is spinning at the same rate.
  • \(G_{Sun}\approx 3.2*10^{-13}\frac{m^3}{kg*s^2}\) based on estimated total spinning frequency [1]
  • \(M_{Sun}\approx1.98*10^{30}\) kg (TOEBI agrees with this value)
  • \(M_{Mercury}\approx3.3022*10^{23}\) kg (current value)

Everything should match with the next equation (Newton vs. TOEBI’s II Law \[G\frac{M_{Sun}M_{Mercury}}{R^2}= (G_{Sun}+G_{Mercury})\frac{M_{Sun}X}{R^2}\tag{1}\]hence \(X\approx6.5*10^{25}\) kg. Obviously such a value is pretty suspicious. Let’s keep that in mind…

Berry also pointed out that \(g_{Mercury}\approx 3.7\) m/s² and that value would give Mercury even higher mass in case of \(G_{Mercury}\approx 1.96*10^{-14}\frac{m^3}{kg*s^2}\). What’s happening? There is two possible explanation, either TOEBI can’t calculate Mercury’s mass or Mercury’s crust and core have a very different spinning frequencies.

Due to Mercury’s size it’s obvious that there is much smaller pressure inside Mercury caused by gravitational interaction. Smaller pressure makes these potentially very different spinning frequencies between the core and the crust plausible.  I wonder if this same explanation works with my Moon mass calculation…? The idea of very large spin frequency differences between a stellar object’s core and crust didn’t occurred to my mind earlier, shame on me.

At this point, I shall release Berry. I might continue with this post later on.

Ok then, what is the real \(G_{Mercury}\)? We can calculate it from equation (1) by substituting \(X\) with Mercury’s mass, so we  get \(G_{Mercury}\approx6.64*10^{-11}\frac{m^3}{kg*s^2} \). Total spinning frequency is hence \(1.15*10^{-5}\) 1/s which means sidereal rotation period \(\approx 1.007\) d.

Now gravitational acceleration on the surface is \[G_{Mercury}\frac{M_{Mercury}}{R_{Mercury}}\approx3.68\text{ } \frac{m}{s^2} \tag{2}\]


40 thoughts on “Mercury

  1. In equation (1), M_Sun and R are obviously irrelevant as they cancel out and were are left with
    where we have ToEbi-quantities on the left hand side and mainstream ones on the right. Obviously, it’s not a first-principle equation but a “conversion”, i.e. which mass X_planet ToEbi has to assume for a planet in order to agree with experimental observations. But which observations? I had brought up surface gravity, i.e. the acceleration of a test mass at a planets surface due to the planet’s own gravitational field. So, my question remain: Why does G_Sun appear in the equation? What the heck has the Sun to do with Mercury’s very own gravitational field? Would we have to use the same fomula also for X_Pluto?

    Another question: If indeed we have to deal with a non-rigid rotation, what does ToEbi tell us about calculating the final f from that? Same context: What is a “total spinning frequency”? I can’t find [1] to mention such a thing.

    And finally: What about the cannon balls? Surley they are no stellar objects, so ToEbi doesn’t even need its second law being expanded for that. What does ToEbi predict for their mutual atraction?

  2. Ok, to answer my question “Buty which observations?” myself: Equation (1) considers the attraction between Mercury and Sun and yields X_Mercury = 6.5E25kg. But, as you repeated above, if we don’t consider the Mercury-Sun attraction, but Mercury’s surface gravity, we get a different value for X_Mercury (much higher).

    Thus, even if Mercury suffers from non-rigid rotation and you would be able to derive some effective (higher) f_Mercury from that, you can only fix X_Mercury to one of the needed values.

    In other words: Equation (1) and your g-formula (fourth equation in “The Biggest blunder in physics?”, if applicable not only to Earth but to Mercury as well) contradict each other. That’s bad!

  3. Erratum: With g-formula, I was referring to the sixth equation in “The Biggest blunder in physics?”, not the fourth.

    BTW: In said blog, you still state “In order to overcome the mismatch both in units and magnitude they decided …”. To which mismatches are you referring to? Whoever may be denoted by “they”, that took place long before the advent of your private theory. What exactly had to be overcome in that situation in the past?

  4. @Berry:

    A minor issue: It is spelled “TOEBI” not “ToEbi”

    Please respect the correct spelling in the future.

    Thank you.

  5. I took the spelling from the blog title: “ToEbi 2 Years Old”

    But sure, I’ll spell it TOEBI from now on, no probs.

  6. ???

    Ok, “total” usually denotes “summed up”. In your case it rather seems to be something like a “representative” or “mean” frequency. Difficult to tell without a formula. But never mind, it’s not that important.

  7. Actually it is great that Berry has pointed out few problems with my calculations. That has made me think. I have spent also too much time on atomic scale lately, hence neglected gravitational phenomena, which, btw, was the original playground of TOEBI.

  8. >> Shouldn’t that be a 😉 ?

    > Totally not! If I made a “;-)” instead of a “:-)”,
    > one might confuse that I am ironically about that issue.

    I couldn’t interprete your comment “Sounds reasonable.” on a mass of Moon, which would imply a density over 100 times larger than any natural element, in any other way than being ironical. If that was indeed not the case, it makes evident that you’re incapable of any indedpendent scientific thought and are blindly following Kimmo whatever he’s saying. Also your “four rational reasons” are just repetitions of what he’s saying. In other words: You’re his disciple. That may be emotionally supporting for him, but scientifically it’s worthless.

    I comment only on “rational reason 4)”: I cannot see humbleness in someone spouting out posts with titles like “Lorentz Factor is Bull’s Shit”, “Quantum computers are BS”, “Participate the scientific revolution!”, “The Biggest blunder in physics?”, … (while at the same time thinking that kg/(s²m²) was a valid unit for acceleration).

    And I still can’t get rid of the feeling that you’re actually pulling our legs with statements like “Your [Kimmo’s] brain is probably currently the most precious object on this planet.” or when describing my criticism (to which Kimmo refers as “grilling TOEBI like no tomorrow”) as “having some small doubts”. Heck, even “So I never use irony or sarcasm, when posting comments.” reeks quite of sarcasm.

    One last point: … Oops? Can’t find it anymore, all your comments have obviously been pulled by Kimmo. Apparently it became too much sarcasm for him.

  9. If gravitational phenomena are the original playground of TOEBI, how come you never checked it beyond Earth and Moon? How come its “Second law” only very recently needed to be “expanded” for stellar objects?

    If gravitational phenomena are the original playground of TOEBI and if my feedback is most welcome and if you take it very seriously, how come you don’t answer my simple questions:

    Q1: Which attraction predicts TOEBI between two cannon balls (or any two massive bodies of mass M_1 and M_2, that is)?

    With Newton’s gravitation, it’s just the same formula with the same G all the time. What’s wrong with TOEBI there? From this latest post of yours, I would have concluded that this attractive force just reads
    F_12 = (G_1+G_2)*M_1*M_2/r_12²
    but somehow you seem to be reluctant to speak that out.

    Q2: Which “mismatch both in units and magnitude” precisely did “the fathers of classical mechanics” have to overcome?

    Hint: It cannot possibly have been the mismatch with your very own private theory, because they weren’t aware of that. Hence, which mismatch did “they” face at their time, that did lead to the introduction of G?

    If gravitational phenomena are the original playground of your very own TOEBI, why are you not bothered that your g-formula either works only for Earth or (worse) contradicts equation (1) above?

    If you take my feedback very seriously, why do you think shifting around discrepancies (like you did in the last update of this Mercury-post) would help? You shifted your problem from an absurdly high M_Mercury to an absurdly high f_Mercury. One revolution per day (the agreement with f_Earth is no coincidence, of course), in striking contrast to observation, seriously? Probably you will now postulate that only the visible crust of Mercury rotates slowly while the inner part rotates about 60 times faster, right? If yes, any idea about the viscosity of magma? No equilibration within four billion years? Forget it. But don’t forget: Newton’s gravitation, which you regard as inferior to your TOEBI, doesn’t need such weird claims.

    And what are you going to do with the absurdly high M_Moon? Postulating f_Moon=1/d as well? For your information: Mercury and Moon have a very good reason to spin so slowly.

  10. Obviously I need to make some corrections (or new derivations) here… I’ll try to figure this out in near future.

    If we have two stationary objects side-by-side, then we have to calculate attractive force between particles of those objects and then use third law of TOEBI (dampening factor caused by Earth’s gravitational effect).

    Update: Actually without external rotation or uniform electron spin pattern my theory predicts 0 force…

  11. > If we have two stationary objects side-by-side,
    > then we have to calculate attractive force between
    > particles of those objects

    That’s true for Newton’s gravitation as well. (Fortunately, for spherical mass distributions the result is extremely simple.) But why only for stationary objects in TOEBI and not for spinning ones?

    > and then use third law of
    > TOEBI (dampening factor caused by Earth’s gravitational effect).

    According to TOEBI the gravitational force between two mass elements depends on the presence of the Earth? That sounds “totally Earth-centric” to me!

    > Actually without external rotation or uniform
    > electron spin pattern my theory predicts 0 force…

    What’s a “uniform electron spin pattern”? Do I guess correctly, that (only) a ferromagnet has one?

  12. >

    Yuck, too much a pain to read in order to check it. But we’re discussing now TOEBI, anyway.

    Meanwhile I had a look into “Second law of TOEBI”. I don’t get the vector x_2 yet, it is defined via the vector f_x, which itself is not explained.

    Considering this an effort to answer my question Q1 myself, I remind you that you still didn’t answer my question Q2.

    > Ferromagnet has it, but also electric current
    > generates one (a.k.a magnetic field).

    But a stone or a (current free) block of lead does not?

  13. I have to face the fact that rotation induced force generation doesn’t apply with stellar objects directly or I have missed something crucial along a way. If I remember correctly I had some difficulties with my early gravitational calculations and that’s why I dropped those from my paper. Currently II law applies only to interactions between two particles or between particle and a system of particles, but now that later case seems to be in jeopardy.

    However. I can calculate rotation induced force between rotating ball and stationary ball ( with II & III laws, which is strange because those two are both systems of particles.

  14. I got that, but which one?

    If \(\vec{F}_1\) is the attractive force acting on particle 1 due to particle 2, then \(\vec{x}_1\) in its formula must clearly point towards particle 2. But which one of \(\vec{f}_1\) and \(\vec{f}_2\) has to be used to construct \(\vec{x}_2\)?

    BTW: The usage of the symbols \(\vec{x}_1\) and \(\vec{x}_2\) is very unfortunate, because their indices 1 and 2 do not refer to the particle labels 1 and 2.

  15. \(\vec{x}_2\) is constructed on \(\vec{f}_{x}\) basis. In case of \(\vec{F}_{1}\), \(\vec{x}_{1}\) (from point of view of particle 1) and \(\vec{f}_{1}\) are used.

  16. Thanks for correcting the LaTeX. Unfortunately, we have no preview function.

    Well, “\(\vec f_x\) basis” isn’t clear to the reader, especially since \(x\) doesn’t take on the values 1 and 2 anywhere. Ok, is the following correct (according to TOEBI, that is)?

    \(\vec F_{1\leftarrow 2}=(G_1+G_2) \frac{M_1 M_2}{r^2_{12}}\left(\vec e_{12}\cos\alpha+\vec e_{12}\times\vec f_1/f_1\sin\alpha\right)\)

    as the force acting on particle 1 due to particle 2, where \(\vec e_{12}=\vec r_{12}/r_{12}\) is the unit vector pointing from particle 1 to particle 2.

  17. (Correct up to the the missing ² in den denominator, that is.)

    Consequently, the force acting on particle 2 due to particle 1 is

    \(\vec F_{2\leftarrow 1}=(G_1+G_2)\frac{M_1 M_2}{r_{12}^2}\left(\vec e_{21}\cos\alpha+\vec e_{21}\times\vec f_2/f_2\sin\alpha\right)\)


  18. (Thanks for fixing the typo!)

    Ok, and it doesn’t bother you that \(\vec F_{1\to2}\neq-\vec F_{2\to1}\) (unless \(\vec f_1\) and \(\vec f_2\) are parallel), i.e. that your force law flatly violates Newton’s third axiom?

  19. Oops, I meant \(\vec F_{1\leftarrow 2}\) and \(\vec F_{2\leftarrow 1}\), but that was probably clear.

  20. Well, “Second Law of TOEBI” is quite flexible, isn’t it? Just fix it on the fly. And despite this fundamental change, no conclusions from it are affected?

    But what about its status now, anyway? It cannot describe stellar objects anymore? Despite gravitational phenomenta being TOEBI’s original playground?

    BTW: I’m still waiting for your answer to Q2.

  21. Why haven’t you? If \(\vec f_1\cdot\vec f_2\approx 0\), it’s the only contribution to the force. And a quite peculiar one, I must say.

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