Johannes Kepler: Harmonia Mundi

Posted: April 8, 2012 by tallbloke in Astronomy, Astrophysics, Gravity, Philosophy, Politics, Solar physics, solar system dynamics

Johannes Kepler 1571-1630

During his lifetime of investigations into planetary motion, Johannes Kepler discovered simple numerical relationships between the planetary orbits which exhibited harmonic frequencies which matched those of the musical scale. He was intensely interested in Pythagorean number theory and the geometry of the simple solid figures, the tetrahedron, cube, octahedron, icosahedron and dodecahedron. Analysing planetary position data observed and collated by Tycho Brahe, he found that the golden section, phi, and the square roots and cubes of simple whole numbers permeated the relationships of orbital periods, distance and eccentricity ratios. Convinced he had discovered direct evidence of the Creator’s hand in the apparent  perfection of the cosmos, he devoted much of his life to unravelling the interwoven geometrical relationships of the solar system.

DISCLAIMER: This blog does not take any position regarding concepts of ‘Intelligent design’ or ‘creationism’ . Instead it seeks knowledge using reason and data and follows where they lead.

The laws he discovered governing planetary motion hold up very well for the inner planets as measured and calculated by modern sytems such as the JPL ephemeris.

Kepler’s laws are:

  1. The orbit of every planet is an ellipse with the Sun at one of the two foci.
  2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.[1]
  3. The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

Although these three laws are all that mainstream astronomy and modern astrophysics eventually distilled from Keplers work, there is much more to tell, and it reveals the reason only a fraction of his work is acknowledged by the mainstream as belonging to modern science.

Kepler didn’t just find the laws of nature governing individual planetary orbits. He discovered rules governing the relationships between the orbits of the planets of the inner solar system, and the ‘consonances and compensations’ built into their orbital eccentricities and inter-related timings. Rules that now turn out to relate to the recently discovered feedbacks that tie the motion of the planets directly to the variation in the main source of energy at the heart of the system, The Sun.

Kepler intuited this necessity of planetary-solar mutual influence within a holistic paradigm in the epilogue of his meisterwerk ‘Harmonia Mundi’ – The Harmonies of the World. He understood that just as the sun effected the planetary motion,  the sun had to be affected by that motion, so that the whole system could work in harmony.

For as the sun rotating into itself moves all the planets by means of the form emitted from itself … And the movements of the planets around the sun at their centre and the discourses of ratiocinations are so interwoven and bound together that, unless the Earth, our domicile, measured out the annual circle … never would human ratiocination have worked its way to the true intervals of the planets and to see the other things dependent from them, never would it have constituted astronomy.

If as the Earth breathes forth clouds, so the sun black smoke? If as the Earth is moistened and grows under showers, so the sun shines with those combusted spots, while clear flamelets sparkle in all its fiery body.

Still it is not easy for dwellers on the Earth to conjecture what sort of sight is present in the sun, what eyes there are, or what other instinct there is for percieving those [planetary] angles even without eyes, and for evaluating the harmonies of the movements entering into the antechamber of the mind by whatever doorway, and finally what mind there is in the sun.

kepler was drawing an analogy between the effect of planetary conjunctions as seen from Earth on the mind (ratiocinations) and dispositions of the human psyche and their effect on the sun.

In trying to fathom the numerical relationships he observed in the planetary motions, Kepler worked to understand fundamental geometrical relationships, discovering the ‘Kepler triangle’.

This united two of the basic geometrical features of the inner solar system using the golden section – phi and Pythagoras’ theorum.

This leads to the reconciliation of the circle and square – almost. There is an error of 0.1%, about the same quantity as the sun’s decadal variability. More detail at the Wiki page.
On consideration of  his discoveries regarding the planets hidden ratios and harmonies Kepler said;

Geometry has two great treasures: one the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio [ the golden section]. The first we may compare to a measure of gold; the second we may name a precious jewel.

And it’s saying things like this that led to the exclusion of much of his work from the corpus of science. A man of his times, he was part scientist, part mystic, and part-time jobbing astrologer. By the time Isaac Newton became president of the Royal Society 85 years later, the great science institution of its time, there was an effort underway to purge the natural sciences and especially astronomy and celestial mechanics of renaissance concepts of a fusion between science, art and religion. So those parts of Keplers work which related to Pythagorean number theory and the relationship of celestial motions to the harmonies of the musical scale were rejected as mysticism for composers to muse upon, and those parts which used the golden section and the five solid crystal forms were dismissed as ‘mere artifice’, for artists and engravers to design patterns and proportions with.

Geometry was giving way to abstract mathematics. By the time the enlightenment period took full hold, with its emphases on taxonomy and the standardisation of measurement and a more militant stance against the intrusion of religious ideas onto the ground of science, Kepler’s deeper insights into the mysteries of the solar system were lost to view. They were torn asunder by the division of ‘categories’,  harmony and ratio hidden in the linear fixation of metrification: Kepler’s alchemical golden section transmuted to the leaden and dead-handed Astronomical Unit.

In the next part in this series, we will see how the ratios Kepler discovered were found to be the same as those involved in the cyclicity of the occurrence of solar flares and CME’s by Theodor Landscheidt in the 1980’s, confirming the other element of the unifying whole Kepler correctly intuited.

  1. LazyBoy says:

    As a newbie I likes to follows teh rulez. Can I has rulez? Below can’t be for reals.

    Blog rules

    Rule (1) There are no rules.

    Rule (2) See rule (1)

    Rule (3) See rule (2)

    [Reply] Hi LazyBoy. The most important bit is under rule three. Stick to that and we can all get along.

  2. Stephen Wilde says:

    “Convinced he had discovered direct evidence of the Creator’s hand in the apparent perfection of the cosmos,”

    Harry Dale Huffman makes a similar leap of imagination from his perception of the geographical distribution of the continents.

    In his case the thinks there was an alien ‘designer’.

    Still, he remains right about pressure effects on Venus and Earth and of course Kepler was right about some stuff too.

    Good examples of why ad hominem approaches are counterproductive. Lots of intelligent, creative and successful people have idiosyncratic ideas about something so you can’t discount one thing they say on the basis of something else that they say.

  3. Edim says:

    Interesting mathematical coincidence, I’ve forgotten about that.

  4. tallbloke says:

    Stephen: Kepler was a man of his times, and being in the position of developing Copernicus’ theory not too long after Giordani Bruno had been burned at the stake, and Galaileo had been put under house arrest for their views, he goes to great pains in his written work to reassure the ‘representatives of divine authority’ that his work is to the glory of God, not his detriment.

    Kepler’s own mother was accused of witchcraft and narrowly escaped being burned at the stake due to Kepler’s painstaking representation in court.

    In the epilogue ha also analyses the Hymn of Proclus, (which he recasts as though through a christian perspective), but the obvious subtext is the support Proclus gives to a Sun centred cosmos. He also tips the hat to Tycho Brahe, who had some fairly off the wall ideas about life on other planets, and works that into the narrative too.

    When attempting the historiography of scientists from another age, you need to take into account the surrounding social prssures, the demands of the paymaster (Brahe the rich merchant and the royal court fo his astrology in Kepler’s case), and the power of the church.

    So in Kepler’ case it’s not so much idiosyncracy but exigency.

  5. adolfogiurfa says:

    The fact Miles Mathis among others is finding in reality is that the planets perfect orbits should be considered circular (really a projection of the spiral), and eccentricity is due to the EM field: the more charge the more eccentricity.

  6. Ninderthana says:


    It is obvious that you have not read “Darwin’s Black Box”. You can obtain a copy at:

    It’s an interesting read.

  7. Ninderthana says:


    I am sorry but I did not realize that clipping and pasting the url from my browser would
    transfer an image of the front cover of the book. Those Amazon people are tricksey. Please remove the image/link if you can.

    I do not want to distract from your wonderful discussion about Kepler’s search for order in the Solar system and I agree totally with your disclaimer that the discussion should be based on principles that seek knowledge using reason and data and follows where they lead.

    I just wanted to point out that the concept of irreducible complexity is well within the bounds of your disclaimer.

  8. LazyBoy says:

    Michael Behe’s (a personal friend of mine) book Darwin’s Black Box is quite dated. His much more recent one “The Edge of Evolution” isn’t. It’s a great read. I found the discussion of what we know about p.falciparum to be compelling. That’s the malaria parasite and it’s the second most widely studied organism in the world today. Its genome, 26 million base pairs long, has been fully sequenced for quite some and the genomic response (mutations) to intense selection pressure by anti-malarial drugs is revealing. The bug (it’s a single cell eucharyote) multiplies to about a trillion individuals in a single person in a full blown fever. About 100,000 million people get sick with it every year. In the past few decades there have more malaria parasites that have lived and died than all the reptiles, birds, and mammals that ever lived. So Behe compares what evolution was able to accomplish (and more pointedly NOT accomplish) with trillions of trillions of opportunities in the malaria parasite to what evolution did in turning reptiles into mammals with fewer opportunities. It becomes painfully obvious that something is amiss. We are led to believe by Darwinian dogma that countless exceedingly complex random mutations turned lizards into lemurs over a hundred million years (unobserved) but in the same number of opportunities to diversify and solve survival challenges while we’ve actually been observing p.Falciparum it hardly gets anything done.

    To Stephen Wilde: the ideosyncratic view is that the universe is an accident. Only a small percentage of the world’s population has any faith in the accident theory of creation. I don’t know who, what, or how went into the making of this universe but it seems ludicrous to think it just came to be this way by accident. Living things are exquisite machines which carry their own specification within each living cell in an abstract digital code – the genetic code. The only other codes in the universe that we know of are human inventions. Then there’s the physical laws and constants of the universe itself. These are a set interdependent rules and values that make the universe possible and stable over billions of years. Changing any of the these by the tiniest of amounts makes a universe that could not support life. In string theory (the latest theory of everything) there are an estimated 10^500 possible solutions, or outcomes, that each develop some arbitrary set of physical laws by which a universe may operate under. It is postulated that one of these possible solutions defines our universal laws. So far physicists have been unable to find a solution out of this set of possible solutions that makes ANY universe possible to say nothing of a universe which appears finely tuned for life.

    You are of course free to believe whatever you want and barring God deciding to carve what he wants us to know into the face of the moon such that we have to read it every night as we look up at the sky we probably won’t know for sure. But in the meantime when I see an exquisitely complex machine I’m going to assume that at some point there was a machinist involved in its design and construction. That’s the only experience I have to go on. Where there’s a code in every case where I know where it originated there was a coder. Where there’s a machine and I know where it came from there was a machinist. Without exception. So when some code or machine comes to my attention where I can’t determine its origin I’m going with the only known mechanism for producing such things as my working model until such time as I have contrary evidence to make me think otherwise.

    Thanks for taking the time to read my little rant on this subject. I know it’s controversial and blog discussions of the subject never end well and rarely is anyone’s opinion changed. It’s sort of like AGW in that regard.

  9. LazyBoy says:

    Keplar would be a pariah today in the atheistic halls of scientific academia. That’s such a shame. In dark ages it was the Catholic church that funded all science. They built astronomical observatories and universities and all that kind of stuff. To them the study of the universe was the study of God’s creation and science was a celebration of the precious gift of a rational mind that God gave to each of us so we might come to know Him and His creation through the power of reason.

    I’m not saying I buy into all of that but it’s not a bad way to behold the wonder of the universe. I don’t understand how seeing everything as a purposeless, meaningless accident represents an improved outlook. I’m gonna toss my hat in next to Keplar’s. It took me many years, decades in fact, to lose faith in my post-modern scholastic brainwashing that the universe is a just an accident and come around to the respect the beliefs of some of the world’s greatests thinkers such as Keplar, Copernicus, Galileo, and even Einstein. Yes Albert, I can hear the music of the sphere’s now. Thanks for lending me a hand in that, dude. Rest in peace.

  10. adolfogiurfa says:

    Comprehension, understanding it is only reached according to physical laws if the same frequencies/energy level exists in the observer, as to resonance to happen.

  11. tallbloke says:

    Adolfo: Miles reaches for his E/M field too often and to quickly. Important information can be lost by applying one size fits all sticking plasters over anomalies.

    Ian, no problem, I’ll get a copy and then fail to find the time to read it no doubt. 🙂

    LazyBoy: Scientists try to explain this stuff with the ‘Anthropic Principle’

    Very relevant to Kepler is famous Russian astronomer Valery Kotov’s papers
    Solar system, exoplanets, and anthropic principle

    It is shown that the planetary distances of the Solar System are distributed according to the L 0 resonance, where L 0 = cP 0 = 19.24 a.u. is the wavelength of the “cosmological oscillation” of the Universe (whose nature is unknown). Here, c is the speed of light and P 0 = 160 min is the period of pulsations of the Sun and the Universe, which turned out to be equal to 1/9 of the mean terrestrial day. Exoplanets do not exhibit the L 0 resonance; instead, they demonstrate on average a spatial resonance on a scale of 14.8 a.u., pointing to a mechanism of formation of exoplanetary systems which differs from the commonly accepted one (by the capture of “mesoplanets,” rather than from near-star nebulae). This indicates that the L 0 resonance is a specific feature just of the Solar System. The L 0 (P 0) aspect of the anthropic principle, realized only near the Sun, distinguishes our planetary system from a number of observed exoplanetary systems. This fact makes the anthropic principle in its strong formulation more evident, localizing its effectiveness. Probably, it is closely related to the appearance of life on the Earth, which unexpectedly, sadly, and charmingly makes any talks on extraterrestrial civilizations devoid of any prospect.

    I’m trying to obtain a copy of a 1987 paper of his which elucidates all the 160 minute periodicity synchronicitties in the solar system. Kepler would have been thrilled.

    One of the reasons debate on ID rarely goes well is due to the way proponents tend to mischaracterise their opponents positions. Few scientists who have considered the organisation of the solar system think it is random. They just don’t think a designer needs to be invoked to explain it’s non-randomness.

    My own view is that nature itself is a great designer, and produces lots of consonances and myriad synchronistic complexities for us to marvel at. I certainly don’t experience any feeling of purposelessness in my view of the universe. Perhaps because I rejected Big Bang long ago. A story, ironically, made up by a cleric…

  12. adolfogiurfa says:

    The law of the square triangle is found everywhere, wheresoever there is a field, because magnetism and electricity are at right angles. (right hand rule). Hear who may hear…

  13. […] raindrops dampen th…Mushroomgeorge on S.Fred Singer: Climategate Hea…tallbloke on Johannes Kepler: Harmonia…adolfogiurfa on Johannes Kepler: Harmonia…LazyBoy on Johannes Kepler: Harmonia…LazyBoy […]

  14. vukcevic says:

    tallbloke says:
    April 8, 2012 at 4:08 pm
    Very relevant to Kepler is famous Russian astronomer Valery Kotov’s papers
    Kotov:The origin of pulsation of the Sun with period P0 ≈ 160 min is as yet unknown.
    Primary electro-magnetic oscillator’s period 160 min
    Light (electromagnetic wave) travels from Sun to planets with the strong magnetic field (or expressed in harmonics):
    – Earth 1AU -8 min = 20th harmonic
    – Jupiter 5AU -40 min = 4th harmonic
    – Saturn 10AU -80 min = 2nd harmonic
    – Uranus 20AU -160 min = fundamental
    – Neptune 30AU -240 min = 2/3 fundamental
    Idle speculation isn’t good science, but if pursued it may lead to years of fun. One Christmas this started as an idle speculation: and led to and lots more classified as pseudoscience. You’ve been warned.

  15. tallbloke says:

    Vuk: yes indeed, and we could at that the planet with the most circular orbit, Venus, is at around 5 light minutes from the Sun, and 5 minutes is the oscillation period no-one in the mainstream helioseismography area disputes. It is also the 8th harmonic of 160 minutes.

    Kotov also found the 160 minute period in many axial rotation speeds. It is 1/9 of Earth’s.

  16. J Martin says:


    – Earth 1AU -8 min = 20th harmonic
    – Jupiter 5AU -40 min = 4th harmonic
    – Saturn 10AU -80 min = 2nd harmonic
    – Uranus 20AU -160 min = fundamental
    – Neptune 30AU -240 min = 2/3 fundamental

    – – – – – – – – – – – – – – – – – – – –

    Interesting stuff. I can’t help but feel that there’s a breakthrough waiting for someone with all these extraordinary patterns, one of which is the expanding cone of planet diameters as you draw a pair of lines out from the Sun. Diameters, orbital distances, orbital periods, all have interrelating patterns.

    – – –


    A question, speculation;

    Is there a mechanism perhaps for the (electro)magnetic field to directly influence temperature ? or is it (perhaps more likely) a proxy for activity elsewhere, the Sun.

    I did see some time ago one of your fascinating graphs that showed the simultaneous decline in the magnetic field of both the Earth and the Sun. Can you post that again please ?

    – – – – –

    On another note I’d like to see Miles Mathis take a good look at Landscheidt’s work. I think something could come of that.

  17. Doug Proctor says:

    So for a circular orbit, double the distance from the sun and get 2.83 times the orbital period while the circumference of the orbit is 2.00X , while the gravitational force is 0.25X. Hmm. (square root of eight?)

    I’ve long wondered if the differences between various parameters in our universe are due to us perceiving in four dimensions, while “reality” operates in more than four. So that, as another result, photons or electrons can behave both as waves and particles, because what we see is how the multi-dimensional elements are expressed in our 4-dimensional space, not that they are elements of and existing within a space comprised of only 4 dimensions.

    I know that other dimensions are supposed to be tiny, fractions of a proton in size. But I think of Flatland, and how a three dimensional creature would look walking through the two-dimensional space. Sort of like how flying saucers are supposed to behave in the sky, being here and then there, moving with absurd accelerations, merging and dissolving progressively but without apparent cause ….. ( I’m not saying flying saucers exist, but mentioning how an observed phenomena behaves).

    Each time you think of what is known or supposed to be known, oddities appear. Mathematical, electrical, chemical, etc. relationships are easier to discover than they necessarily are to interpret.

  18. tallbloke says:

    J Martin: absolutely. Nicola Scafetta has made a brave start, and managed to get some papers past the gatekeepers. Kotov was still banging the drum in 2003 at Stanford conference, but I think he must have been discouraged by the constant sweeping under the rug of his results. The paper cited on Wiki as having disposed of the 160 minute solar oscillation as an atmospheric effect shows all the hallmarks of a contrived dismissal. However, the helioseismology boys seem to be saying it’s not there as far as they can see from satellites and solar probes, so .who knows.

  19. vukcevic says:

    Hi J. Martin
    ‘Pseudo-science’ as peddled by Vukcevic (according to the old goat) :
    In all text books you will find the Earth’s MF represented by a bar magnet in shape oh ‘I’. However that is not strictly correct, it is more like ‘Y’ shape with each of two prongs under two large land masses (N. America & EuroAsia). South does its thing without much relation to the solar activity, while the north is a bit of a sea-saw. The Arctic field as an average of two and it is changing in inverse proportion to the solar activity.
    Graph you are looking for maybe one half way down here:
    Climate dependence can’t be ever proved conclusively, since none of the important factors can be eliminated, so we are stuck with ‘correlation is(not) causation.
    Scientists take themselves too seriously, I think all this is a great fun 🙂

  20. Tenuk says:

    Great thread, Rog – Kepler developed some marvellous insights into the balance and harmony seen in nature.

    I am a sceptic regarding intelligent design, but do believe that the underlying order we see in nature is not accidental, rather it is an evolving consequence of a few simple rules iterated at different scales along with the driving force of the apparent attraction of gravity and the repulsive charge field.

    I’m currently looking to see if the Constructal Law can provide a route to better understanding. This idea came from Adrian Bejan back in the 1990’s and can be stated as…

    “For a finite-size system to persist in time (to live), it must evolve in such a way that it provides easier access to the imposed currents that flow through it.”

    Bejan starts with three simple rules, which define the parameter space for understanding how periodicity, configuration, pattern, geometry e.t.c are realised in natural design.

    1. Life is flow: all flow systems are live systems, the animate and the inanimate.
    2. Design generation and evolution is a phenomenon of physics.
    3. Designs have the universal tendency to evolve in a certain direction in time.

    Some things are starting to make sense, but not sure if this is really a useful paradigm yet,

  21. tallbloke says:

    We can also add Eris to the list

    It’s the most distant object know to be orbiting the Sun and has a distance of 96.6 au. This is 5.02 x the fundamental of 19.24 au Kotov calculated for the value of L, the 160 minute light speed wave.

    Also, the mean orbital distance of Ceres is almost exactly 1/7th of the fundamental.
    Great page here on Gauss’ calculation of Ceres orbit.

  22. tallbloke says:

    Tenuc: I think you’re going to have to roll your sleevs up and get the calculator hot to verify Mathis’ Bode’s Law paper for the inner planets. Then we’ll talk about it. 🙂

  23. tallbloke says:

    Vuk: “Scientists take themselves too seriously, I think all this is a great fun ”

    Discovery is a joy.

    Gatekeeping is a chore.

  24. Bruckner8 says:

    The fact that we humans are “impressed with order” means that we’ve left the realm of objectivity. As soon as we assign words like “exquisite” and “machine,” and combine them into “exquisite machine,” we’ve left the realm of objectivity.

    The act of “feeling wonderment/awe” is an emotion….it is not pure logic.

    This line of reasoning is emotional, not logical, no matter how good it feels:

    “I see exquisite machines, therefore a [divine] machinist must have built it.”

    That said, here is one single truth we can all agree on: “SOMETHING CREATED US.”

    Everything from there is pure conjecture. It could’ve been aliens (then what created the aliens? not sure, but SOMETHING did). It could’ve been The Big Bang (then what created the BB? Not sure, but SOMETHING did). It’s as equally possible to be some kind of “cosmic accident.” (But what created the cosmos, and what is an accident anyway?) SOMEHOW, we got here…or at least we perceive that we’re here, lol. OK, God created us…umm…sorry to do this, but then what created God?

    The difference between me and most others is that I’m still saying “I’m not sure,” when others have concluded “a God” created us. And that’s fine, as long as the God-loving don’t discount me for remaining skeptical (er, Agnostic). Maybe it’s just semantics at this point, where the SOMETHING = God. I dunno. I just know that when I read the logic behind Intelligent Design (oops, I mean being impressed with patterns of Kepler), the condescension amongst the believers is palpable. “Of course there’s a God! Are you nuts/blind/idiotic?”

  25. tallbloke says:

    Bruckner8: As a wise woman who had spent many years in India living with buddhists told me many years ago:

    “The hands you are in are your very own”

    i.e. Life has the meanings *you* choose to invest in it. Modes of knowledge and the evocation of feeling and emotion have the values *you* choose to assign to them.

    If I get a kick out of enjoying a bit of wonderment and awe at the beauty and complexity I witness, that’s my affair. If I get a bit emotional when I watch an eagle soar along a canyon shining gold against the shadowed cliff, that’s just me.

    When I look at the planets in the night sky I wonder and gaze.
    When I look at someone’s theory about how the cosmos is put together, I suspend disbelief and absorb an impression of the whole first, then I analyse and compute the parts and reintegrate.

    That’s just me.

  26. Joe Lalonde says:


    What is missed is the speed of the forward momentum of the sun. 🙂

  27. Thanks guys, esp LazyBoy, fabulous thread to read on the Easter break.

  28. Bruckner8 says:

    Right on, TB. We are all free to choose. I also feel a sense of awe in Nature. I’ve been known to “feel thankful” for being alive. However, I don’t assign it to a 3rd party; instead I live as if nature and My Self are one entity.

    The subtle parallel I’m trying to draw is this: CAGW believers are similar to God believers in this way. They both make the leap of “C’mon! The evidence is obvious! If you can’t see it, then you’re an ignoramus!” The evangelism is strikingly similar. It’s difficult to argue against faith.

  29. Agile Aspect says:

    Testing to see if this blog supports math equations (the language of science)



    [reply] There is a wordpress page on latex support.

  30. Agile Aspect says:

    Agile Aspect says:
    April 9, 2012 at 9:23 pm

    Testing to see if this blog supports math equations (the language of science)



    [reply] There is a wordpress page on latex support.


    Okay, thanks. My last try – the example from WordPress

    i\hbar\frac{\partial}{\partial t}\left|\Psi(t)\right>=H\left|\Psi(t)\right>

    [Reply] Very nice. 🙂