In his paper “ON LAPLACE AND THE 3-BODY PROBLEM” Miles gives an argument for why the distance between Saturn’s and Jupiter’s orbit should be shrinking with time if only gravity was present as a force. He writes:

Let us look at four positions of the two planets, in four diagrams, in a straight 3-body problem.

With gravity as a force of attraction, and no other force fields playing a part, we find that we would expect the gap between Jupiter and Saturn to be getting smaller. Because, while Jupiter is sometimes being pulled away from the Sun by Saturn and sometimes toward it, Saturn is always being pulled toward the Sun by Jupiter. I challenge you to find a relative position of the two planets where Saturn is not being pulled into a lower orbit by Jupiter.

(Diagrams created by Miles Mathis.)
It seems to us that this argument does not make any sense. Consider for example the following similar diagram where the big dot represents the Sun and the smaller dot represents the earth:
If Mathis’s arguments were valid, a two-body system could certainly not be stable because the earth could only fall into orbits closer to the sun. The (mathematical) two-body problem however exhibits stable solutions – we are, approximately, living on one!

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30 Responses to A remark on: ON LAPLACE AND THE 3-BODY PROBLEM

  1. shubhash rao says:

    Are you really two graduate students in theoretical physics?
    You’d better forget it. This last “response” is too moronic even for the standard level. Not even stupid.

    • Cee says:

      Dear shubhash rao,

      Would you care to elaborate as why the post is moronic?

      Mathis uses these argument to show that only a repulsive force could be the cause of the observed deviations of the orbit of Saturn and Jupiter from their expected path. He claims that Laplace’s derivation must therefor be false since it only uses the attractive force of gravity in the framework of newtonian mechanics. He goes on to claim that electromagnetic repulsion of the two planets is the cause of the observed perturbations.

      However, only because the force is attractive, that does not mean that things always must come closer together. (See e.g. here.)

      I agree that the post is very short, but it certainly shows that forgetting to take the momenta of the involved bodies into account gives invalid arguments that cannot be used to predict the future motions of the bodies.


    • Dam says:

      You have got remember that these two guys are gradstudents inphysics, and although I have only posted twice I am a grad student in math. People trying to learn physics do in a proper setting. What is being offered here as a service to all those arm chair physicists out there, in a hope that they will not pervert their brain with brackish Internet nonsense.

      Nobody here is shooting for a Nobel prize with what we write, but we have all become somewhat concerned that Mathis is gaining a following and we are doing our tiny bit to help ensure no young mind is corrupted by his nonsense. Any one of us could prove facts prom partial differential equations testing to orbit mechanics that demonstrate he is wrong, but that is first gross overkill and second probably far to involved and sohisticated an argument for a causual conversation.

      And like the othr guy I responded to earlier. Instead of slinging mud, why not use that grey matter between your ears and clearly,concisely, in a scientific method demonstrate how Hecate wrong. You will get much more credibility than by mindlessly mudslinging.

      My two cents

  2. stanly shortner says:

    Your “similar” diagram and the concept behind it are not logically comparable to that of Mathis’ thought experiment. Mathis points out the Jupiter is pulling Saturn into a closer orbit – one that is stable, not unstable as you claim. You’ve twisted this one inside out and have shown your hand.

    • Golden Brown says:

      Jupiter is pulling Saturn into a closer orbit, but somehow, Saturn always escapes, only because its orbiting. The instability is that each time they orbit, Saturn’s orbit would decline. which would have lead to all the planets crashing into the sun billions of years ago, yet in a practical experiment, i.e. observed motions, Even with Jupiter being a giant planet… Saturn is perturbed, but unrelenting. Read this carefully: Saturn is orbiting. orbiting. Mantra: orbiting….orbiting…

      I agree with the authors of this web site, as their arguments are well grounded, and acceptable. make no mistake: the 3 body problem is still a problem. ( there is even a website that shows a lot of what-ifs. for it.


  3. Erto says:

    This post is not to the point. Miles says the gap between planets SHOULD be getting smaller IF gravity was the only force in action. It should state the SAME on the diagram you have presented on a two body “problem”. If gravity was the ONLY force, the earth SHOULD be getting closer to the sun. If there’s ONLY attraction, what would keep the Earth from falling into the Sun? Mathis presents charge repulsion via photon collision as a mechanism to why that doesn’t happen. You haven’t taken down his hypothesis, on the contrary, you’ve just showed the the earth should be falling into the sun according to the standard model, did you not? That’s what the arrows tell us. Then you just state that because the Earth doesn’t fall into the Sun it exhibits a stable solution, even though you don’t explain what that solution is. That’s PRECISELY Mathis point. Did you intend to back him up?

    • Cee says:

      Dear Erto,

      That is precicely the point: Newtonian gravity explains stable orbits of the Earth around the Sun, even with just the purely attractive force of gravity. It is a misunderstanding that an attractive force always implies that systems collapse.

      If you find this counter-intuitive, istead of considering the earth-sun-system, let us consider a satelite orbiting the earth. You wrote: “If there’s ONLY attraction, what would keep the Earth from falling into the Sun?”. Shouldn’t this argument be true for the satelite as well? But it is certainly not using any fuel to stay in orbit, nor is it held up by its charge. (If it were, why do we need to use rockets to put up satelites instead of just setting them free here on earth and waiting for the charge field to make them move up to a stable height?).


      • Erto says:

        Hi Cee! Thanks for the opportunity to debate and possibly learn something!
        First, yes, it should be true for a satellite as well! And it is! Come on, IF the ONLY force is attraction, NOTHING can stop it from being attracted! Imagine this sentence applied to ANYTHING, satellites, pigeons, water bubbles, etc… if there’s ONLY attraction and no other forces between two objects whatsoever, there’s no possible way they wouldn’t attract each other, that’s a logical FACT.
        Furthermore, Newtonian gravity does NOT explain stable orbits that are elliptical. It could explain a stable circular orbit only if gravity were pulling equally strong from all directions, which implies perfect spheres of mass generating that field, which we no is not the case. And in any case, any perturbations would either expel the orbiter or make it fall, since bodies cannot correct their orbits (they’re not fueled!).
        Regarding rockets to put up satellites, that’s really a bad argument, Cee. According to Mathis’ model, our measured gravity is already unified, meaning it is already gravity’s pull minus charge repulsion, so that’s why we would need rockets: at the surface of the earth the pull is stronger than the push. At the moon’s distance, though, push and pull are averaged (to the moon’s weight), so she “floats”. The only REAL problem here is that all our measurements are already unified (according to him), so he should develop a way to test for them separately. He admits that it is still impossible to block either field, but he points to data supporting him all the time, specifically his corrections on eccentricities and some other evidence, like the negative tide on the moon’s near surface and the C shape orbit of a meteor. Truly, is there any other way we can explain that? How can an approaching body suddenly make a turn when gravity obeys the inverse square law? Obviously we NEED a counter force to the pulling of gravity, for the same reason you yourself pointed out: it is certainly not using any fuel. It cannot correct the orbit for itself.
        I visited a physics museum once and there was an apparatus that simulated an orbit only with gravity, and it turned out to be a very slowly decaying spiral down. It presented no explanations for why orbiters wouldn’t fall and I left with the impression someday in a million years we would sink into the sun. Feynman’s visualization of an elliptical orbit has yet another problem: it demands two central bodies to deliver the ellipse, which is obviously not the case.
        I can imagine an ellipse being created by the pull of outer planets, but i cannot imagine how an orbit with such varying perturbations, created only gravity, would become stable.
        Now, how is it a misunderstanding that an attractive force always implies that systems collapse? Please explain to this dumb brain how could only attractive forces NOT end up in a collision! You must use ONLY attractive forces, and please, use a two body problem. And also please, do not just say “Earth and Moon”, I want to know HOW Earth and Moon won’t collide, using ONLY attractive forces between the two bodies, no other forces allowed! And also, if you decide to put them in perfect equilibrium (that’s the only way to solve), then add an outside perturbation and show how can the orbit correct itself and not fall in or spit out.
        TKS, this is fun.

        • Cee says:

          Dear Erto,

          Conservation of momentum nicely explains why things keep moving instead of collapsing. Where do you get all this stuff? Parabola-shaped orbits of asteroid can be explained with newtonian mechanics as well without any counter fources. Concerning the two-body-problem: There are standard derivations of Kepler’s laws and eliptic orbits in every mechanics textbook, so I’m not sure what you want me to do here. If you want, I can write something up and we can go through it together. (This would require basic calculus.)

          Concerning Mathis’ model of orbits: If the moon and satelites were moving on orbits where the gravitionational and that other force cancel each other, would that not imply that there is only one orbit for each satelite of a certain mass? How is it that we can put satelites on orbits of different heights? And most importantly: Why have humans never put up a satelite that is stationary (i.e. does not move). Since in Mathis Model there really is a counter force, there is nothing that would make the satelite fall back on earth. (If we ever find out that Mathis is correct, I suggest putting up stationary solar panels in space to harvest the energy.) Real satelites however are moving (or rather: they are forever falling towards the earth!) – on orbits very much like those of the planets around the sun!


          • erto says:

            Hello Cee.
            Well, first of all, I’m not sure the C-shape orbits I was referring to are parabola-shaped orbits at all, take a look: http://milesmathis.com/aster.pdf
            As for elliptical orbits, all I could find was the same visualization Feynman did, wich has two focal points to create an ellipse, I couldn’t find any way to explain an elliptical orbit of one body orbiting around a central (more massive) body. If you find anything on this, link it to me, please. And yes, if you can write something up I would appreciate it.
            Regarding satellites’ orbits, I don’t know if there is only one orbit possible for a certain mass, but I believe what Mathis points out is just that. That is precisely why satellites we put up are ever falling. We do not know about the unified field so we cannot figure out where exactly we have to put them up in the first place so they can be stationary. Remember that charge repulsion and gravity’s pull are not equivalent: gravity obeys the inverse square law while charge bombardment drops off at 1/Rˆ4. He also points out that surface area (r) of both bodies are as important as mass to solve: http://milesmathis.com/uft.html

            And finally, planets are ever falling towards the sun??? You said: “Real satelites however are moving (or rather: they are forever falling towards the earth!) – on orbits very much like those of the planets around the sun!”- Clarify please.


            • fgd says:

              That is a horseshoe orbit. It only can happen in a rotating coordinate system, so that there is no net force on the “earth” blob and it doesn’t move. This force is not really there, and the graph shows what you would see if you were rotating so the “earth” blob and “sun” blob seemed to be in the same place and you took a long-exposure photo, or if you exposed the plate exactly once a year. Also, you = Mathis, I believe.

              • erto says:

                Hi, fgd.
                Nope, I’m not him, sorry… but if I was him trying to pass as me I don’t think I’d tell you… anyway, returning to the horseshoe orbit, thanks for the clarification, I thought that the asteroid was actually reversing it’s orbit, it makes a lot more sense this way. I did a few searches on the net regarding this orbital shape to have a better visualization of what really happens, so let’s go:
                Mile’s argument is still valid. I believe he already understood this orbit the right way, that was my mistake… But the fact remains that, for some reason, as the asteroid gets close to the Earth, something changes it’s orbital velocity (and it’s path gets closer to the sun)… and then, when the Earth approaches it from behind, its velocity is accelerated (and it orbits farther from the sun). What pushes it back and forth (relative to the Earth) this way? Again, if gravity was the ONLY force (attraction) we would expect the exact opposite, right? The point here is not the horseshoe shape itself, but the varying velocities of the asteroid. What causes these fluctuations? How can you possibly explain an asteroid SLOWING DOWN as gets close to the Earth using ONLY attraction between bodies??? I can’t make any sense of it except a counter force opposing gravity. That is what Miles proposes. Any other explanations?

                Thanks for the response.

              • Gus Mueller says:

                You guys know we have geosynchronous satellites, right?

  4. lkajdglkadj says:

    I find this website hilarious. All I have to say is that kinematic pi = 4. (I don’t actually believe Mathis’s theories because I actually listened in math and physics classes, but they are a great joke when my friends and I have lab parties. There’s a phrase for people like him, “Mathis” not his best subject. LOL!!! 😀

  5. tharkun says:

    If solving the 3-body problem could be accomplished with positing a 2-body problem (as above); there would be no 3-body problem. Your analysis does not address Mathis’ criticism at all.

    • Golden Brown says:

      It actually does. By finding one example, as a special case. Orbiting is Orbiting. Nothing prevents Saturn from falling into the orbit of Jupiter, except one very important thing: Its Orbiting. It moves in, and it moves out. Now… The diagrams are circular, and for the most part, the orbits of Jupiter and Saturn fall far within those circles, but again, because they are orbits, they are elliptical, in Newtonian physics and circumscribing spirals in Eisenstein physics, but again, Einstein did not predict the falling of Mercury, he predicted the precession of mercury, Precession not decline. So consistent with both Newtonian physics and Eisenstein physics, Saturn orbits, and despite the mass of Jupiter, its orbit does not re-orbit into a lower-closer orbit.

      Someone pointed out that they listened in Physics. I did not, I fell asleep, but I recorded some of the most amazing physics lectures. Anyone who has passed the second semester of college physics can laugh at Mathis’s arguments. I get the joke. His error is simplification.

      • Gus Mueller says:

        No, his error is that he says a bunch of stuff that is just flatout wrong. You have to know something to simplify it. Forty thousand Quatloos to the person who can find ONE of his articles on math or physics that is correct.

  6. TYGR says:

    It is interesting that the word belief is used by lkajdglkadj. In my experience faith is the essential requirement for much of science. By faith we believe that our math describes the physical world. By faith we believe that real photons appear from virtual photons as if a computer image of a human can create a real human. By faith we believe that we know the fundamentals of Physics and Chemistry yet both are considered sciences of exceptions because we can’t always explain or predict what we see unless we create a belief and modify the math to support our belief. Cheers to Miles for challenging the beliefs of our religion, Physics.

    • Cee says:

      Dear TYGR,
      Yes, scientists have to believe that what they’re doing somehow corresponds to the real world (although they do so to different degrees). They rely on research done many years, sometimes even generations ago often without being able to always follow all the details there. For people that have not received scientific training, understanding what modern science does in detail, is indeed a formidable task.

      However, please note that the term “virtual photon” is technical lingo and even though we call computer games “virtual”, they are not a good analogy at all to what is meant in the scientific context.

      Science is not something disconnected from all social processes and I must admit that there are some analogies between religion and science (but only insofar as religion and politicts are similar). However, I find it alarming that you equate the two. If you really believe that science is so similar to religion, I feel that science education has a lot to do better in the future.
      Yes, in science one cannot work without believing at least some things, but I feel that the scientific method that is at the heart of science works in a way that is quite different from the way religion works.

      (I don’t really see how Mathis challenges our belief in physics, so I can’t comment on that.)


    • Stefaan says:

      Faith has nothing to do with the relationship between mathematics and reality. Mathematics are nothing more than a formal language that can be used to describe reality. That there is such a thing as knowable reality is a belief, but one that leads to usable results. For example, Maxwell’s equations lead to the development of wireless communications, indicating that the convergence between reality and its mathematical description is pretty good.
      Once you’ve accepted that you can observe and describe reality, mathematics is simply the most suitable language.
      As far as modifying mathematics to support a belief, this is not how things happen in science. It is true that we cannot always explain what we observe, but a scientific theory is not a belief — it’s a testable hypothesis, something that can be proved to be correct, or not. Reality (the experiment) trumps theory anytime.

  7. Rob says:

    This whole Mathis physics is a joke really. Why does he want there to be compound field of Gravity + E/M, while everyone knows that the E/M field necessary cancels itself, since macroscopic bodies on average have equal positive and negative charge, and the forces of attraction and repulsion for the E/M field simply cancel.

  8. We can actually see the the magnetic fields of bodies in the solar system being pushed away from the sun. Calling it a solar wind that does so evades the reality. The solar wind is made up of positive and negative ions, electromagnetically charged particles. In an article in THE NEW YORK TIMES several years ago it was shown the magnets at cryogenically low temperatures can be held in space below an iron bar. So long as that t\low temperature is maintained they just hang in the air. space is also at cryogenically low temperatures so the magnetic fields surrounding the planets are repelled by the magnetosphere of the sun. All this is spelled out in my 1990s book THE ELECTROGRAVITIC THEORY OF CELESTIAL MOTION AND COSMOLOGY. I have come to a similar conclusion to that of Mathis except I maintain EM field is rotating with these bodies and its strength is that of a rotating antenna which fall from infinity at the center of the body to zero over five rotations. To see it google charles ginenthal the electrogravitic theory of celestial motion and cosmology. I am further working on a book that explains Velikovsky’s concept that electromagnetism is a force in celestial mechanics and there I will show that there is plenty of experimental evidence published in peer reviewed journals that shows this force in action

    • Thank you for the references and objective views Charles. I am no physicist or advanced mathematician and only discovered Mathis’ explanation of the Earth’s tilt and Coriolis effect because contemporary explanations puzzled me. To me Mathis makes sense.

  9. Deer says:

    I think Miles would agree that the two-body problem does indeed fail with current theory. You cannot claim the earth is an example of a stable two body system with the sun for many reasons, but even more so you have not considered the entire view of Miles.

  10. Ryan Miller says:

    Satellites are indeed “forever falling towards the earth.” The trick to understanding this is that they are not falling straight down; rather, they are also moving “forward” as they fall. In fact, they are actually moving “forward” so fast that the ground beneath them is bending away as the Earth’s surface curves. A stable orbit, roughly speaking, is nothing more than a fall where this “forward” (or perhaps “outward” or “onward” if you will) motion exactly counterbalances the “downward” pull of gravity, so that the path of the fall ultimately loops back onto itself.

    Take another look at the diagrams in Miles Mathis’ original article. Ask yourself: what exactly are the large circles supposed to represent? Why are they drawn? They are not real–they merely illustrate the paths of *motion* of the planetary bodies being studied. That is the key–these bodies are all in motion. I think eveyone, Miles Mathis included, would agree that if these bodies were stationary, they would indeed gravitate toward one another. (This, by the way, is just another way of casting Cee’s reductio ad absurdum argument that if the repulsive force being described really existed, then we could just place unmoving satellites in space, hovering above a single point on Earth.)

    In conclusion, the key to understanding orbit is realizing that it amounts to nothing more than falling + moving forward very, very fast (usually from a high elevation). And neither of these things is a “repulsive force”.

  11. We are not bothered by these morons who have a keyboard but no brain; it is to be hoped that academia will weed them out so that they never earn degrees in physics (mathematics and philosophy are something else). But will it? We have seen horrible misunderstandings of Newton’s canon-on-mountain thought-experiment in textbooks! Of course, your critical correspondents will not understand how silly it is to have the canon-ball landing at the 7 o’clock position. Nor will they see why the very short-range trajectories still have to have the Earth’s centre as a focus. Keep up the good work … although we favour slapping the likes of Mathis.

  12. Dexter says:

    If there are just 2 bodies it is a simple balance between gravitational pulling and motion away, kinetic energy or whatever you want to call it. Without attraction the body goes further and further. That simple equilibrium, however, doesn´t work for 2 (or more) orbiting bodies. If the orbiting planets are linked by elastic strings, as well as each one to the Sun, they inevitably tend to crush any time Jupiter passes near Saturn. Especially if the attraction is stronger the shorter the distance, contrary to a common string. The kinetic energy mentioned above only prevents Saturn from falling into the Sun (or both planets falling into the Sun), not from falling into Jupiter.

  13. There is no ‘simple balance between gravitational pulling and motion away’ : there is only attraction. For example, the Moon is always falling towards the Earth. However it never gets here, because of its orbital motion. That is obvious to an observer outside of the system. However, an observer on the Earth can choose to invent a fictitious force which opposes the gravitational attraction. This fictitious force is called ‘centrifugal’, and is needed only so that the observer on Earth can continue apply Newton’s laws (even though they do not apply in a rotating frame of reference).

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