Heliocentrist Propaganda

Heliocentrism and Geocentrism

Here’s another problematic image I came across on Facebook. It was accompanied by the statement, “Heliocentrism is not necessarily the only perspective, but it is certainly the simpler one. When explanatory power is equivalent, simplicity is a powerful deciding factor.”

Can you see what is wrong with the picture?

Here’s what I wrote in a comment: “Not with circular orbits on both. That was a major reason why heliocentrism was not persuasive when first proposed. If you do not shift to elliptical orbits, then you still need epicycles to get the proposed system to fit what is observed.”

The page on Facebook then kindly responded with this: “Profile says professor of religion, but dude comes and lays down some astrophysics like a boss. Thank you for clarifying that.”

And so I concluded the conversation by saying the following: “No problem – I have a big interest in science, even though it isn’t my area of expertise. If the left had Kepler’s proposal rather than Copernicus’ then your point would have been sound – although ellipses rather than circles seemed less “simple” a solution to many in a time before Isaac Newton provided gravitational explanations for these phenomena.”

I was considering keeping this for some other time, but it fits so nicely as a complement to the previous post. It is an example of someone wanting to make a point about heliocentrism over against geocentrism, and simplicity vs. complexity, and yet not getting the facts right and thus undermining their own point by going beyond oversimplification into factual error. As Einstein is purported to have said, “Make everything as simple as possible, but not simpler.”

And so, in the interest of following the axiom as well as my own advice, I will point out that simply saying “Einstein said” would have been too simple. The saying is attributed to him, but we have no evidence that he actually said it.

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  • Brad Feaker

    I’ll just leave this here :)

  • Brian Westley

    Here’s a diagram showing some ellipses with various eccentricities:


    The planet with the largest eccentricity is Mercury at 0.205

    Notice how an ellipse with an eccentricity worse than that, at .3 in the diagram, still looks like a circle.

    An orbital diagram drawn with correct ellipses would look identical to the animated gif.

    • arcseconds

      Well, no, it wouldn’t look identical.

      I mean, yes, the point needs to be made that the orbits are close to circular for most planets (and I would have made this point if you hadn’t), the diagram shown is still quite misleading.

      This shows circular orbits with the sun at the centre, evenly spaced. But the real orbits are not like this.

      The actual orbits are sometimes noticeably off-centre (due to the fact the Sun is at a focus, not the center of the ellipse) and enough non-circular to look ‘odd’:



      This looks significantly ‘messier’.


      And once you start looking at more bodies it looks even more like a mess:


      ( source )

      Picking the neatest-looking orbits makes the solar system look neater and less complex than it actually is. Sure, a ptolemaic-style geocentric orbital diagram would be even worse, but rather than having the gut reaction of ‘simple!’ and ‘complicated mess!’ to the situations as pictued in these gifs, presented diagrams that expose more of the complexity, the reader is more likely to go ‘well, they’re both complicated messes, i don’t know what to make of this.’, which is a more appropriate response to someone naive about astronomy!

      • Brian Westley

        Well, no, it wouldn’t look identical.

        Yes, if the circles as used in the gif were replaced by ellipses with the correct eccentricities, it would look identical, as the difference is less than a pixel.

        Now, it’s obvious that the orbit sizes are also completely different, but that wasn’t the original objection. Drawing the orbits as ellipses would look the same as the original.

        • arcseconds

          How do you know it is less than a pixel?

          The radius of Mercury on the diagram is about 10 pixels.

          With an eccentricity of 0.205, an ellipse of the same average distance, the perihelion is 8 and the aphelion is 10, so two pixels difference.

          For Mars, the radius is 45 pixels.

          With an eccentricity of 0.0934, an ellipse of the same average distance the perihelion is 41 and the aphelion 49, so 4 and 5 pixels different respectively.

          The orbits are only about 10 pixels apart, so I’m pretty sure the fact that they aren’t concentric circles would be noticeable.

          But you seem very confident, so maybe I’ve made a mistake. How did you determine the <1 pixel difference?

          I used this ellipse calculator and measured the pixels using a drawing program.

          • Paperboy_73

            The previous poster is in error when they say that every planet would have a difference of less than a single pixel. But they are correct when they say that the orbits are generally so close to being circular that the naked eye would have trouble distinguishing the appropriate ellipse from a circle.


            Mercury: 0.2056
            Venus: 0.0068
            Earth: 0.0167
            Mars: 0.0934
            Jupiter: 0.0484
            Saturn: 0.0542
            Uranus: 0.0472
            Neptune: 0.0086

            Mercury is a strong exception, as its orbit experiences odd behaviour due to the influence of general relativistic effects, and is not totally explained by Newtonian mechanics. But in general, representing these orbits as circles would rarely be in error by more than a few percentage points.

            Certainly, the qualitative behaviour of the figures on the left and right is reasonable.

          • arcseconds

            Pop quiz: what form does the deviation of the orbit of Mercury from that expected from Newtonian physics, and what is the magnitude of the deviation?

            Hint: it can’t possibly be seen on a diagram like this.

            Here is a diagram consisting of the inner planets, with the original gif on the left, and the orbits from the picture I posted earlier, shrunk so that the orbit of mercury is the same size.

            (hopefully this works, first time I’ve uploaded an image to disqus).

            Even at this size, while it might not be obvious they are not circles, it’s clear that they’re not concentric circles, and they’re not all centered on the Sun.

            So, no, it doesn’t look like the actual solar system. By drawing them as concentric circles, whoever drew this simplified it.

            And as far as ‘qualitative’ goes, that’s entirely my point. You can’t just look at diagrams like this and make a subjective decision as to which one looks simpler. A Keplerian model is not really any simpler than a Ptolemaic system, regardless of how it might look. The complexity of a system is in its mathematical description, not in the qualitative effect of a diagram on a naive viewer.

            Especially not a grossly oversimplified diagram.


          • Paperboy_73

            My point is that if you centered an actual diagram of the soluar system on the Earth, you’d see very similar orbital effects to the ones shown by the diagram. It exhibits the appropriate qualitative effects, even though it’s quantitatively incorrect.

            Scientists make use of qualitative schematics to illustrate behaviour or concepts in research papers all the time.

          • arcseconds

            Also: please don’t just guess at stuff like what effect relativity has on the orbit of Mercury.

            Look it up.

            It is not hard.


          • Paperboy_73

            There’s no need to be aggressive. I know physics, and lecture mathematics. I didn’t calculate out the pixels, this is true. But Mercury is just a weird orbit, because it’s sitting on the edge of a deep gravity well, and does some things that seem a bit odd. It has some other funny features going on as well, with its inclination, etc. My point there was simply that it’s not really representative of “typical” orbital behaviour. 😀

          • arcseconds

            But the “atypical” eccentricity is not atypical by Newtonian lights, and the deviation from Newtonian behaviour is extremely small.

            You said that “Mercury is a strong exception” in the context of explaining that the naked eye would have trouble distinguishing the ellipses from circles.

            The most plausible interpretation of your actual words is that you think Mercury having the most elliptical orbit is to be explained by reference to relativity. After all, that’s the way it is exceptional with the numbers you have given.

            But this is not correct. The elliptical orbit is explicable on entirely Newtonian grounds (there are plenty of other far more elliptical orbits, comets, for example, and they present no real problem to Newtonian mechanics).

            it’s hard for me to believe that you actually know, or knew, what the deviation of Mercury from Newtonian behaviour actually is, and nevertheless made this statement. Especially as you still seem to show no sign of knowing what it is. So it seems to me that you guessed that the more elliptical orbit was due to general relativistic effects.

            But in the event you know perfectly well that GR effects have nothing to do with the eccentricity, you really need to work on your clarity of expression. “Mercury is a strong exception… due to… general relativistic effects” when the only thing that’s being discussed is eccentricities (and it does in fact has the most eccentric orbit) really does not suggest you’re talking about some other completely unmentioned exceptional behaviour.

            Someone could easily read your comment and, not knowing any better, come away with the understanding that the eccentricity is due to GR effects. No doubt as a lecturer you will see the importance of not giving a false impression to your readers.

            I’m sorry if I come across as being snide, but you and Brian seem keen on defending the circular diagram, and the defence seems to rest on looking at a list of eccentricities and assuming that they’ll be indistinguishable from circles. OK, so rookie mistake, fine, but the insistence that there’d be less than a pixel difference and that it wouldn’t be noticeable came after I had already posted an orbital diagram correctly drawn, and also drawn attention to the fact the ellipses are not centred.

            And then you go bringing GR into it in a completely misleading manner!

          • Paperboy_73

            Mercury is a bit weird because it’s so deep in the gravity well. If you want to latch on to my comments on the relativistic aspect, I do know perfectly well that GR affects the precession of the orbit. It has other effects, but they are comparatively very minimal. I was just driving at the idea that weird things happen with Mercury’s orbit because of the substantially higher gravitational influence – it generally shouldn’t be taken as a representative example of planetary orbital behaviour within our solar system, because it’s much deeper in the gravity well than the other planets. And this is true, but it is an unimportant side-issue.

            So we can remove GR from the discussion entirely, and I’m happy to agree that the picture is still definitely wrong if taken to be a an accurate depiction of the solar system. The orbits are not elliptic, even if the eccentricity would largely be negligible in the visual representation. The distance scales are obviously wildly inaccurate, which is by far the most significant inaccuracy on a qualitative scale.

            But the thing is, if you rectified all of that, and made the equivalent picture, it would have exactly the same qualitative features. In a situation like this, scientists writing papers have no problems producing representative schematics that illustrates the behaviour in question. It still conveys the information you want to see, which this picture clearly does.

          • arcseconds

            Why are you talking in theoretical terms about what you think would be observable, when I’ve already made a diagram and shown that it is observably different from the original gif?

          • Paperboy_73

            But your diagram doesn’t show the key aspect of the image, which is what would happen if you centered the reference frame on Earth.

            The diagram in the original post shows the same thing you’d see if you centered your diagram on Earth:

            If you have any planetary system, then the average size of the orbital subcycles increases as you move the reference frame away from the center of mass.

            That’s the million-dollar observation. It’s true in our universe, and it’s true in the diagrammatic universe. That’s what the picture is trying to show.

          • arcseconds

            I think you have entirely misunderstood the point of the original diagram.

            Perhaps you understand ‘geocentric’ in terms of a change of reference frame.

            I think it’s vastly more likely that this is comparing Ptolemy with… I’m not really sure, actually, maybe the original author thinks its Copernicus, but at any rate, the author’s conception of a heliocentric system.

            In other words, these are supposed to be ‘objective’ diagrams where on the left the Sun is really the stationary centre, and on the right the Earth is really the stationary centre, as viewed from an observer a long way to the north of the centre of the system.

            It’s pretty clear the expectation is that we should prefer the diagram on the left as describing the real situation because of its simplicity.

            So while it may inadvertently show us subcycles increase as the frame moves away from the center of mass, there’s absolutely no indication that the author had this in mind, and every indication the point of the exercise is to demonstrate something about Occam’s razor and historical accounts of the solar system.

          • Paperboy_73

            In fairness, the Sun holds 99.8% of the mass in the solar system. The variance in the center of mass would absolutely be far less than one single pixel, in either the accurate figure or the qualitatively-representative schematic. The Sun is, on this scale, a stationary center.

          • arcseconds

            I cannot see the relevance of this point.

            The difference between a heliocentric model and a Newtonian model is of course smaller than the difference between either and a Ptolemaic model. That is not in dispute.

            If you think this is relevant, it suggests to me that you have completely failed to understand what I am saying, and as I am trying to explain to you the point of the original diagrams, that you also still do not understand what they are trying to show.

            Or are you just engaging in some kind of word association game? If ‘centre’ is mentioned you reel off a fact or two about centres, without worrying yourself as to whether those facts are at issue in the discussion?

          • Paperboy_73

            I was just facetiously (perhaps a touch cheekily) pointing out that picking a purely heliocentric reference frame does accurately depict revolution around the center of mass. Not trying to pick a fight or anything.

  • arcseconds

    Well, my first reaction is, as always, why is simplicity a powerful deciding factor?

    I’ve never heard a really satisfactory answer to this. People who actually try to give a robust account of this can make some sense of it, but it gets very complicated very quickly, suddenly you start talking about information entropy and all sorts.

    Now, there is a strong reason for not assuming more than you need to, so Occam’s original statement ‘plurality should not be posited without necessity’ is certainly apt, but Ptolemy didn’t propose plurality without necessity: the deferents and equants are necessary to recover the observed motions.

    The drive to simplicity seems to be largely an aesthetic one, although one can also detect a strong rationalist (in the philosophical sense) influence, even today. I can’t deny that this impulse hasn’t been pragmatically useful, but I wonder whether there’s any real justification for it. We haven’t, after all, ended up with theories that seem very simple at all.

    While I mention aesthetics, as I indicated with my reply to Brian, this particular display seems rather slanted. We’re just supposed to look at it and go “oh yes simpler better on the left”, but the display conceals rather a lot about the complexity. And it suggests we can make this judgement just by eyeballing the diagrams.

    To see how eyeball judgements can be completely off, consider putting two diagrams up, one like the diagram on the left, except with the actual eccentricities (but still evenly spaced). This gives visual information that it’s elliptical, but it’ll still look fairly neat. Then on the right put up highly eccentric ellipses, like the orbits of the comets. Then ask “which is simpler?”

    I think most people will say “the one on the left”, but actually (from a parameter-counting perspective, at least) both are equally as complex.

    Parameter counting is one way to assess the complexity of the systems, but if we do this honestly which one is simpler is not so obvious. A Ptolemaic model has a deferent and an equant for each planet. They are both circular, so can be defined just by their radii, so that’s two parameters. With ellipses, we need an orbital distance measure (distance at aphelion will do) and an eccentricity. That’s two parameters!

    I’m being a bit pat here, as there are other parameters in both systems, but that is something you could note from the two simplified gif diagrams, had the first been honest and had ellipses. While the second would still look complex, actually they’re both defined by two parameters per planet, so by one possible quantification they are just as complicated as one another. They don’t look like that, but we really ought to be pretty suspicious of our initial aesthetic reaction, particularly if we’re totally untrained in the area.

    Also, it needs to be mentioned that heliocentricity needs to make a big assumption that geocentricity does not need to make: to account for the lack of observed stellar parallax, it has to assume the universe is very much bigger than the orbit of the Earth.

    • arcseconds

      The other thing i wanted to say on this topic is that the Newtonian model is much more complex than either Kepler or Ptolemy.

      In both Kepler and Ptolemy the planets move endlessly around in paths described by relatively simple equations, each with only a handful of parameters. They do this independently of one another.

      With Newton, there are the laws of motion, the law of universal gravitation, and a point-in-time state where each body (especially the Sun) has a mass, a position, and a velocity. That’s already rivalling both the other two theories in terms of the complexity of the set-up. Then to compute a later (or earlier) state, you can’t just trace the trajectory of the planets independently of one another, you have to take into account that every body attracts every other!

      That’s insanely complex and is computationally intractable, so a useful model has to be a simplification. Even the simplified models are mathematically vastly more complex than either Kepler or Ptolemy.

      So much for the expectation of simplicity!

      • David Evans

        The models of Kepler and Ptolemy are not in competition with Newton’s, because they lack its explanatory power. Newton can explain Kepler’s laws, which for Kepler are unexplained facts and which Ptolemy, with his geocentric perspective, didn’t even notice.

        • arcseconds

          Yes, Ptolemy is almost curve-fitting, and Kepler is not a lot more than that. That’s fine: while it’s a simple system in some sense (the interactions are dominated by the influence of the Sun), the observed paths of the planets are not actually all that simple, and getting any kind of traction beyond the obvious is actually quite impressive.

          My point is that the ‘powerful deciding factor’ of simplicity does no work here, and the really explanatory theory is not simple. So why do we keep appealing to simplicity?

      • Paperboy_73

        It is a common undergraduate exercise to use Newtonian mechanics to derive all three of Kepler’s laws. Newton isn’t more complicated than Kepler. Newton explains Kepler.

        • arcseconds

          This is clearly just plain false. Kepler’s laws are basically single-bodied problems. A relatively simple calculation can be performed to calculate where a planet will be as a function of time.

          And a lot goes unexplained: the precession of the perihelion of the elipses, for example, has no explanation nor even recognition in Kepler’s laws. Also the planets don’t actually exactly obey the angular velocity indicated by Kepler’s laws, due to the attraction of the other planets.

          Newton’s system, on the other hand, give a highly complicated multi-bodied problem. An analytic solution is impossible, so approximations must be used. Those approximations were refined over centuries and continue to be a complex area of investigation even in contemporary times.

          A mathematical model that can be refined endlessly with the help of powerful computers is obviously more complicated than one that can be solved with a pen and paper.

          Plus, you say it explains Kepler as though we’d expect the explanatory theory to be simpler than the explained theory. But this is not generally the case: the ideal gas laws are simpler than statistical mechanics, Newtonian physics is simpler than relativistic physics, etc.

          • Paperboy_73

            It’s not plain false. It’s basic ODEs and approximation theory. Starting with Newtonian mechanics, you can derive Kepler’s laws by making some basic asymptotic approximations:

            – The distances between planets are large compared to their radii
            – The mass of the sun is large compared to the mass of the other planets
            – The gravitational influence of the sun is large compared to the other planets

            Each of these can easily be shown in the universe to be true by orders of magnitude, and therefore very valid leading-order approximations. You then just turn the handle on Newtonian mechanics, and Kepler’s laws fall right out. You can do it yourself, if you’re comfortable with undergraduate calculus:


            Again, I’ve set these derivations as tasks in undergraduate differential equations classes, and I’m not the only one.

            Why would I expect the explanatory theory to be simpler than the explained theory? I wouldn’t. In fact, they rarely are, because “what do things do?” is almost always a less complicated question than “why do they do it?”

          • arcseconds

            Newton isn’t more complicated than Kepler.

            This is what is plain false, and this latest post of yours is a good argument of why it is false. If you can derive one theory from another by making approximations, then the first theory is very likely to be the simpler one.

          • Paperboy_73

            I would argue that Kepler’s Laws are a subset of Newtonian Gravitation subject to certain empirical simplifications, rather than a distinctly different alternative. Even though Kepler arrived at them by observation rather than theoretical derivation.

            I’d also argue that Newton explains planetary motion with one law (the inverse square law), while Kepler requires three laws (which it turns out can be derived from the inverse square law, although he had no idea this was true). So it could be argued at its basis that one law is simpler than three.

            At some point we’re quibbling over the definition of “simple”, which is imprecise at best, and a semantic argument rather than one of substance. And semantic arguments are nobody’s idea of a good time.

          • arcseconds

            You need the laws of motion as well as the inverse square law, so that’s four laws.

            Yes, simplicity is hard to assess: I have made this point already in my previous comments. But I think it’s very hard to argue that a Newtonian model is simpler than a Keplarian one. It is more complicated in terms of the mathematics, the underlying laws, the number of interactions, the number of parameters (you need a mass, position and velocity for each planet), etc.

          • Paperboy_73

            I agree that simplicity is not a simple concept. :)

            It depends on whether you consider the simplicity of the reasoning, the simplicity of the equations, the simplicity of the trajectories, the simplicity of the required information, etc. Although my contentions regarding simplicity isn’t to do with an evaluation of the laws themselves so much as a claim that they’re two consistent ways of representing the same underlying process, so on some basic level, they’re precisely as simple as each other. Either way, it’s either philosophical or semantic quibbling at best.

            On a technical level, the important information the image is trying to show is that the subcycles increase in size when the center of mass is not chosen as the reference frame. Our brains process this as “simplicity”, so we use “simplicity” as a glib description of what is going on visually. It’s just a semantically imprecise phrase to describe what we’re seeing, and it turns out that what we’re seeing is an important clue as to what’s going on scientifically.

          • http://timebottle.weebly.com/ Beau Quilter

            You have a curious notion of Newton’s simplicity:

            “You can do it yourself, if you’re comfortable with undergraduate calculus”

            Not if you’re Newton. He had to invent calculus first.

        • arcseconds

          (*deleted to reply to the appropriate comment *)

    • Tony Prost

      Well, gravity explains the simpler diagram. Nothing but necessity explains the Ptolemaic diagram.

      • arcseconds

        But it doesn’t explain the simpler diagram, because the simpler diagram doesn’t display a Newtonian model. Nor, for that matter, does it display a Keplerian model, nor a Copernican one (as Coperincus also had epicycles, as circular orbits don’t work).

        ( it is easy to appeal to the simplicity of a model which is a massively more simple than any model ever actually produced!)

        Also, I am addressing the point the person McGrath quotes is making. They argue that simplicity is why we should prefer the left-hand diagram. Not that Newton explains it.

        As it is heliocentricism that’s being talked about here, not the Newtonian model, and you’re appealing to Newton to explain it, it’s probably also worth pointing out another big difference: the Newtonian model is not heliocentric. The Sun orbits the centre of mass of the solar system, like everything else.

        (I’m sure someone will argue again that this couldn’t appear on this diagram, but why couldn’t it? The sun is drawn immensely bigger on this diagram than it is in real life. If you’re going to draw a simplistic, not-to-scale diagram, you may as well exaggerate the important motions so they are visible.

        And if your diagram isn’t going to display the important motions, then it’s just a silly trick to appeal to its simplicity.

        But they’ve got a reasonable excuse for not showing the orbit of the Sun, actually, as they’re not claiming to display a Newtonian model)

  • Uncle Dave

    “Heliocentrism is not necessarily the only perspective, but it is certainly the simpler one. When explanatory power is equivalent, simplicity is a powerful deciding factor.”

    Simplicity is desirable but there are more important factors to prefer the Heliocentric model. The Geocentric model, although with enough math and computing power you could use it to plot a trip to the moon and back, has a bigger problem than complexity. The Geocentric model would require different laws of physics and gravitation for the Earth than for the Sun and planets. In the Heliocentric model there is one consistent universal set of physical laws governing orbital mechanics.

  • http://historyforatheists.blogspot.com Tim O’Neill

    There’s a good discussion of what is wrong with this diagram and with the over-simplistic article that it is taken from here:


    As usual, scientists tend to get the history of science wildly wrong.