Sun’s core rotates four times faster than its surface

Posted: August 1, 2017 by oldbrew in research, Solar physics
Tags:


Something new for solar theorists to ponder. Of course the surface itself doesn’t have a uniform rotation speed – at the equator it rotates faster than it does at the poles. ‘The idea that the solar core could be rotating more rapidly than the surface has been considered for more than 20 years, but has never before been measured’.

The sun’s core rotates nearly four times faster than the sun’s surface, according to new findings by an international team of astronomers. Scientists had assumed the core was rotating like a merry-go-round at about the same speed as the surface, says Phys.org.

“The most likely explanation is that this core rotation is left over from the period when the sun formed, some 4.6 billion years ago,” said Roger Ulrich, a UCLA professor emeritus of astronomy, who has studied the sun’s interior for more than 40 years and co-author of the study that was published today in the journal Astronomy and Astrophysics.

“It’s a surprise, and exciting to think we might have uncovered a relic of what the sun was like when it first formed.”


The rotation of the solar core may give a clue to how the sun formed. After the sun formed, the solar wind likely slowed the rotation of the outer part of the sun, he said. The rotation might also impact sunspots, which also rotate, Ulrich said. Sunspots can be enormous; a single sunspot can even be larger than the Earth.

The rotation of the solar core may give a clue to how the sun formed. After the sun formed, the solar wind likely slowed the rotation of the outer part of the sun, he said. The rotation might also impact sunspots, which also rotate, Ulrich said. Sunspots can be enormous; a single sunspot can even be larger than the Earth.

Continued here.

Comments
  1. oldbrew says:

    ‘After the sun formed, the solar wind likely slowed the rotation of the outer part of the sun, he said.’

    So the sun slowed itself?
    – – –
    Abstract: ‘Here, P0 is measured to be 34 min 01 s, with a 1 s uncertainty. The previously unknown g-mode splittings have now been measured from a non-synodic reference with very high accuracy, and they imply a mean weighted rotation of 1277 ± 10 nHz (9-day period) of their kernels, resulting in a rapid rotation frequency of 1644 ± 23 nHz (period of one week) of the solar core itself, which is a factor 3.8 ± 0.1 faster than the rotation of the radiative envelope.’ [bold added]

    http://www.aanda.org/articles/aa/abs/2017/08/aa30460-17/aa30460-17.html

  2. oldbrew says:

    ‘the Earth’s inner core is rotating faster than its surface by about 0.3-0.5 degrees per year’

    Not like the solar result, but interesting.

  3. JB says:

    “The most likely explanation is that this core rotation is left over from the period when the sun formed, some 4.6 billion years ago,” said Roger Ulrich, a UCLA professor emeritus of astronomy.

    I don’t believe him. An inertia driven universe just doesn’t fit.

  4. Curious George says:

    Nothing to do with solar wind. Any movement with a vertical component on a rotating body tends to rotate slower when going up, faster when going down. Same as Coriolis force.

  5. Am I the only one that thinks the sun is driven by something? That the sun has an external source? Everything we observe has a source of energy, why is the conclusion that stars don´t have a source? Because we don´t see it? I don´t like to base my assumptions on what I don´t see.

    Everything else we observe is driven by a source in shape of a force, heat or mass flow, from something with higher energy, right? Is it rational to make an exception for stars? Don´t ask me about black holes and their relationships with stars, I only have fantasies about that;)

    Who is confident in math here? Just hijacking for a moment, considering sources and stuff. Some may have seen my hillbilly-calculations using only TSI as a single driver for earth energy flow. Now I think that my calculations causes infinite number of solutions for g, within the limits of the heat flow. For example: TSI/(4/3)=4/3*8g^2. For anyone interested, 4/3*g^2 is equal to the mean emissive power of the tropopause, and 4g^2 is equal to surface emission, calculated from 1/2*TSI(4/3). There seems to be no end to the solutions when using the volume function and the inverse square law for the flow. The inverse square law can be folded through the surface, a point of irradiation seems to lie next to a point at altitude of emission, if you understand how I mean. Vectors, scalar field, divergence and Maxwell equations seems to arise from geometry inside the sphere. I am learning on the fly.

    What do you think? Anyone? Infinite number of solutions, what should I make of that?

    Sorry, TB, for hijacking. But you run the best comment field on climate science and stuff. Rational and good people here. I guess I am the looney one.

  6. Gaah… 1/2*TSI/(4/3)^2, that is what I should have written. To much numbers in my overheated brain. But that´s natural, Life is thermal.

  7. oldbrew says:

    Even galaxies rotate.
    http://www.universetoday.com/30710/galaxy-rotation/

    Where’s the galactic dynamo – down a black hole perhaps 😉
    – – –
    Wikipedia’s ‘solar dynamo’ page has ‘multiple issues’ – they say.
    http://en.wikipedia.org/wiki/Solar_dynamo

    They say it’s ‘essentially a naturally occurring electric generator in the Sun’s interior’. How many of those did the Big Bang create?

  8. tallbloke says:

    OB: Indeed. Magnetic stuff rotating in a magnetic field generates both a magnetic and an electric field. Wheels within wheels, driven round by,,, the next bigger wheel outside. Galaxies rotate, inside rotating galaxy clusters. Where the mind starts to boggle is when you ask whether the universe as a whole is rotating, and if it is, what’s it rotating relative to? The biggest spinning turtle you could conceive of maybe…

    “It’s spinning turtles all the way down professor…”

  9. tallbloke says:

    But to get back to the topic, If the Sun’s core is spinning 4 times faster than the surface, isn’t that likely to be due to a coupling between the Sun and the more slowly spinning IMF mediated by the solar wind? That would slow the part of the Sun in direct contact with the solar wind, i.e. the surface. Viscous drag would then slow the subsurface layer, and so on down to the core. The planets orbit more slowly than the Sun spins. Their magnetospheres are coupled to the IMF too…

  10. oldbrew says:

    Then there’s the photon-braking effect…

    Escaping Photons Slow Down the Surface Rotation of the Sun
    February 7, 2017

    http://www.insidescience.org/news/escaping-photons-slow-down-surface-rotation-sun
    – – –
    ‘Our universe may exist inside a black hole. This may sound strange, but it could actually be the best explanation of how the universe began, and what we observe today.’

    http://www.insidescience.org/news/every-black-hole-contains-new-universe

    A spinning black hole presumably 😐

  11. oldbrew says:

    This looks interesting…

    New clue to solving the mystery of the Sun’s hot atmosphere
    August 3, 2017

    The elemental composition of the Sun’s hot atmosphere known as the ‘corona’ is strongly linked to the 11-year solar magnetic activity cycle, a team of scientists from UCL, George Mason University and Naval Research Laboratory has revealed for the first time.
    . . .
    Through its 11-year cycle, the Sun moves from relatively quiet periods at solar minimum, to intense magnetic activity at solar maximum, when large numbers of sunspots appear and there is an increase in radiation.

    “Previously, many astronomers thought that elemental composition in a star’s atmosphere depended on the properties of the star that don’t change, such as the rotation rate or surface gravity. Our results suggest that it may also be linked with the magnetic activity and heating processes in the atmosphere itself, and they change with time, at least in the Sun,” said the study’s lead author, Dr David H. Brooks (George Mason University).
    . . .
    “Why the Sun’s corona is so hot is a long-standing puzzle. It’s as if a flame were coming out of an ice cube. It doesn’t make any sense! Solar astronomers think that the key lies in the magnetic field, but there are still arguments about the details,” added Dr Brooks.

    Read more at: http://phys.org/news/2017-08-clue-mystery-sun-hot-atmosphere.html
    – – –
    Where does that leave ‘the solar constant’?

  12. p.g.sharrow says:

    Astro-physicists have a problem with understanding “temperature” of energies. Thermal in degrees are not the same as radiation energies in degrees. Solar mater is heated thru conduction while it also carries energy of radiation. The Sun has a solid core, a “liquid” body, a gaseous atmosphere with a tropospheric “surface” photosphere, and a plasma corona. The last, it’s material; too defuse for conduction, is heated and cooled only thru radiation. Most of the radiation just bangs about and only some of it escapes into space.The wispy plasma material appears to be super heated while the escaping “heat” energy is of much lower temperature. Plasma, a 4th state of mater, is super energized protons and their force field repels all other particles, even electrons.
    The spiraling out of AM ,Angular Momentum, from the sun’s massive core drags the planetary system thru it’s gravity/EMF coupling with them. This transfer of energies tends to keep them in their order. The Inertial drag of the Aether slows while the AM of the Sun speeds the planetary energy exchange…pg

  13. p.g.sharrow says:

    @Tallbloke;
    I look forward to your summation of solar system energy transfers that regulate the motions of the bodies involved.

    From the largest to the smallest or the smallest to the largest, the physics is all the same. GOD is not a mathematician but works in applied science. K.I.S.S. Complex answers mean you haven’t fully grasped the question. 😉 …pg

  14. p.g.sharrow says:

    In the beginning there was only CHAOS. Then there came the word “GOD” and there was order.
    Light and darkness, Mater and void. Complexities built from simplicity.

    Kind of old fashion I know but, it works for me. Energy in chaos, or dark mater/energy in chaos, without organization. Organize some of it and the first true singularity, a proton is born with it’s electron shell, Hydrogen! Mater, Creation, GOD! expanding fields of Electro-Motive-Force as well as Mass/Inertia and gravity. All creatures of organized energy. All follow the same simple principals of physics…pg

  15. tallbloke says:

    The rotation rate of the Sun’s surface has obviously reached a dynamic equilibrium between something trying to slow it down and something trying to speed it up. The core rotates faster, and viscous drag will resist shear between the differential rotation rates, so that’s what is trying to speed the surface up.

    So what’s slowing the surface down? It has to be a coupling between the surface and something in the surrounding space. What’s in the surrounding space? The Sun’s own magnetic field and the planetary magnetospheres it interacts with. The planets all orbit much slower than the Sun spins on its own axis, so that magnetic coupling will create drag. Jupiter has by far the biggest magnetic field of any planet.

    Something I noticed long ago which has no obvious explanation is that measured in Earth years, the inverse of Jupiter’s orbital period is equal to the Sun’s rotation rate, which seen from Earth, is similar to the orbital period of our moon.

    Wheels within wheels. If only we could see all the invisible gears that connect them…

  16. oldbrew says:

    8 Jupiter orbits = 99.9% of 5 Metonic cycles (about one week short per 19-year Metonic)

    http://en.wikipedia.org/wiki/Metonic_cycle

  17. p.g.sharrow says:

    We exist in an ocean of energy in chaos. We only “see” perceive, events or conditions of organization in that ocean. EMF, gravity, mass/inertia, light etc. are all manifestations of organization in that energetic fluid. Aether…pg.

  18. tallbloke says:

    That may well be so p.g.
    Through observation and the testing of hypotheses, we attempt to make that ‘chaos’ intelligible. Going back to what I said about the average rotation rate of the Sun being the inverse of the Jupiter orbital period (in Earth years); I just noticed that the inverse of the Jupiter-Saturn synodic period is the Sun’s polar rotation rate of around 36 days.

  19. oldbrew says:

    TB – re. ‘the inverse of the Jupiter-Saturn synodic period’

    1/19.865y = 18.386~days
    * 2 = 36.77~ days

  20. tallbloke says:

    Sorry, quite right. I meant the half (tidal) period: 9.93 years

  21. Paul Vaughan says:

    V = [5E-√5T(ΦΦ)^e+1/25]/3 = 1 / 0.615196915778351
    V = [5E-Φ√5(J+S)+1/25]/3 = 1 / 0.615197163689601
    V = [5E-φJ+ΦΦS]/3 = 1 / 0.615197069188456

    Tightening up lunisolar-Hale frequency algebra by an order of magnitude yesterday the preceding simplifications turned up.

  22. p.g.sharrow says:

    Examine Archimedes pry-bar. The Barycenter of the solar system is your fulcrum and the mass/inertia of the various bodies along that bar must be in balance because the solar system is a unit. Conservation of energy requires it. Your Fibonacci spiral is the direct result of this balancing of Angular Momentum of mass/inertia over distance…pg

  23. Paul Vaughan says:

    “balanced multi-axial differential” (repeated for many years) = same …(language barrier maybe)

  24. Paul Vaughan says:

    It’s a simple minimization problem. The context is spatiotemporal, not temporal. In the old paradigm, the role of geometry (a boundary condition) in the physical minimization was overlooked.

    I would have thought (based on standard childhood brainwashing that everything simple is already known) that all of this sort of stuff would have been well known, for example to engineers looking to exploit trivial geometry to minimize vibrations in machines or for geographers looking to simply engineer peace and stability …but a vacuous question mark arises trying to fathom why it’s up to us on volunteer hours to rediscover from scratch what’s obvious to sharper minds, as surely so many others have before and will later (wheel reinvention).

    This exploration and learning exercise is underscoring how dependent our sensory apparatus is on linearity. What can we do to increase by several orders of magnitude human ability to perceive nonlinear simplicity? With what general mathematical strategy can we linearize perception of ALL simple patterns, such that we don’t get lost in intersections of nonlinear rings sorting through disordered rafts of transformations and identities?

    Our machines may perfectly solve only within their algorithmic span; they have not the imagination needed to go beyond their logical limits. Teaching machines open-mindedness might be more tractable than teaching intuition. Guess-and-test is a valid learning method, so it can be an AI component even if the search time can’t be minimized by mechanized intuition. Another valid learning method is mutation and recombination — (misunderstandings are often more fun than “the truth”).

    Our exploratory race for stability hinges crucially on rediscovery of methods for exploring and discovering orders of magnitude faster. (Let’s have some really good fun not assuming recorded history is anything more than a laughable model of what really happened.)

    The primary factors limiting artificial stability engineering efforts are sluggish and failed perception and comprehension of simple nonlinear stability in nature. The major western fault is unnecessary dependence on linearity.

    Natural stability’s simpler than the complex imagination of the major western fault. A more naturally principled exploratory race is ripe for orders of magnitude faster fundamental discovery.

    In the immediate context we have a tractable step on a longer evolutionary path.

  25. tallbloke says:

    Paul V: V = (5E-φJ+ΦΦS)/3
    derive 5J ~= QBO.

    OK. we need to rearrange for J and multiply by 5 on both sides of the equation.

    5J = 5((5E+ΦΦS-3V)/φ) ~= 1/2.372 ~= QBO

    Is that right?

  26. Paul Vaughan says:

    I’ve learned to be more principled. Saving time for exploration is vital. Answering questions when the time’s unripe? …not so much!!

    V = [5E-(3J+S-1/25)/2]/3 = 1 / 0.615197116439025

    All of these expressions are derived systematically. Note that they are nearly equal. This is a minimization problem.

    The conventional mainstream hasn’t bothered with comparative exploration and classification of the (geometric) limits of (temporal) polynomial integration. The way they represent this stuff in the computer is a mess. They haven’t bothered with reduction. They just let the machine sort out the convergence numerically (brute force method — i.e. try to walk through a cement wall rather than looking for a door).

  27. tallbloke says:

    Paul V: Saving time for exploration is vital. Answering questions when the time’s unripe? …not so much!!

    Well you could think of it as marking the homework you set then. It’d save more time for exploration to give a simple “correct” or “incorrect because…” than type the above.

    It’d show more simple courtesy too.

    Paul V: It’s a simple minimization problem. The context is spatiotemporal, not temporal.

    Yes. That’s why the abstract of my PRP main paper states:
    “The forces of gravity and magnetism and the principles of energy conservation, entropy, power laws, and the log-normal distribution which are evident are discussed in relation to planetary distribution with respect to time in the solar system.”

  28. Paul Vaughan says:

    Nature sets the path and pace.

    Hale = Φ(T/E)(ΦΦ)^e = 1 / 22.1383572294165
    J+S = φ(T/E)(ΦΦ)^e = 1 / 8.45610000655013
    S = -(1/2)φ(T/E)(ΦΦ)^e+(Φ^5)+(1/2)[φ(φ+Φ)]^(-4) = 1 / 29.4472819261743
    J = +(3/2)φ(T/E)(ΦΦ)^e-(Φ^5)-(1/2)[φ(φ+Φ)]^(-4) = 1 / 11.8625602808965
    J-S = +2φ(T/E)(ΦΦ)^e-2(Φ^5)-[φ(φ+Φ)]^(-4) = 1 / 19.8649807488765
    V = [5E-(φ+Φ)(T/E)(ΦΦ)^e+(φ+Φ)^(-4)]/3 = 1 / 0.615197275210489

    Compare with observations:

    model period
    observed period
    %error
    %error log scale

    22.1383572294165
    22.1384769776823
    -0.000540906%
    -0.000174637%

    8.45610000655013
    8.4561457463176
    -0.000540906%
    -0.000253365%

    29.4472819261743
    29.4474984673838
    -0.000735347%
    -0.000217391%

    11.8625602808965
    11.8626151546089
    -0.000462577%
    -0.000187022%

    19.8649807488765
    19.8650360864628
    -0.000278568%
    -0.000093199%

    0.615197275210489
    0.615197263396975
    +0.000001920%
    -0.000003953%

    r^2
    0.999999999990233 period
    0.999999999999921 frequency
    0.999999999998969 log scale (same for both period and frequency)

  29. Paul Vaughan says:

    Polya problem solving strategy: Use symmetry.

    Ma = J+1/{[2(J+S)]^(1/3)+[2(J+S)]^(-1/3)}

    a simple balance of powers

  30. Paul Vaughan says:

    NOW you know why it’s not quite Ma = J+1/√5 = J+1/(φ+Φ).
    Thanks for your patience while questions were evaded for years.

  31. Paul Vaughan says:

    Recapping:
    Ma = J+1/{[2φ(ΦΦ)^e]^(1/3)+[2φ(ΦΦ)^e]^(-1/3)}

    Any formal summary omitting this would have been premature.

  32. Paul Vaughan says:

    Nothing’s OT.
    “Sun’s core rotates four times faster than its surface”

    Relative frequencies:
    (4/5) / (1/5) = 4

    Axial Frequency
    = Integral of Pareto Principled Division of Unity
    = 4/5 + 1/5 = 5/5 = 1

    5 = (Φ+φ)^2
    √5 = Φ+φ

    φ = 1.61803398874989
    Φ = 0.618033988749895

    [2(J+S)]^(-1/3) = 1.61701248631139
    [2(J+S)]^(1/3) = 0.618424414446623

    [2φ(ΦΦ)^e]^(-1/3) = 1.61703340324967
    [2φ(ΦΦ)^e]^(1/3) = 0.618416414893069

    φ-Φ = φ^(1)-φ^(-1) = Φ^(-1)-Φ^(1) = 1
    φ^3-Φ^3 = Φ^(-3)-Φ^(3) = 4

    φ^3-φ = φ^2
    Φ^3-Φ = -Φ^2

    φ^2-Φ^2 = (φ-Φ)(φ+Φ) = (1)(φ+Φ) = φ+Φ = √5

    Reminder: Me = φ^3-J = Φ^(-3)-J
    Suggestion: Review yesterday’s notes comparatively. Note symmetry of Ma with Me.

    √5 is the arithmetic mean of φ^3 and Φ^3.
    1/√5 is the harmonic mean of φ^3 and Φ^3.
    1 is the geometric mean of φ^3 and Φ^3.

    2(J+S)]^(-1/3) ~= [2φ(ΦΦ)^e]^(-1/3) ~= φ

    V/E is suggestively close to but not quite equal to φ.
    2(J+S) is suggestively close to but not quite equal to Φ^3.
    Exploration removed several orders of magnitude of fog, eliminating these mysteries.

    Me is suggestively close to but not equal to φ^3.
    Ma is suggestively close to but not quite equal to J+1/√5.
    Exploration has defogged these mysteries.
    More than an order of magnitude of fog has been removed thusfar.

  33. Paul Vaughan says:

    Review of JEV (Jupiter-Earth-Venus) derivation:

    (11.8626151546089)*(1.00001743371442) / (11.8626151546089 – 1.00001743371442) = 1.0920796543202
    (11.8626151546089)*(0.615197263396975) / (11.8626151546089 – 0.615197263396975) = 0.648846557532906

    (1.0920796543202)*(0.648846557532906) / (1.0920796543202 – 0.648846557532906) = 1.59868955949705
    (1.0920796543202)*(0.648846557532906) / (1.0920796543202 + 0.648846557532906) = 0.407020193867456

    harmonic nearest 0.407020193867456 is 1.59868955949705 / 4 = 0.399672389874261
    (0.399672389874261)*(0.407020193867456) / (0.399672389874261 – 0.407020193867456) = 22.1392314983839

    Closing in on Mars:

    √5 = 2.23606797749979
    φ = 1.61803398874989

    (11.8626151546089)*(1.88084761346252) / (11.8626151546089 – 1.88084761346252) = 2.23525255532127
    (11.8626151546089)*(1.88084761346252) / (11.8626151546089 + 1.88084761346252) = 1.62344612704193

    Note the similarity with √5 & φ and let your imagination follow parallel paths that focus like a lens.

    JEV harmonic nearest 2.23525255532127 is 22.1392314983839 / 10 = 2.21392314983839
    (2.21392314983839)*(2.23525255532127) / (2.21392314983839 – 2.23525255532127) = 232.011969669376

    JEV harmonic nearest 1.88084761346252 is 22.1392314983839 / 12 = 1.84493595819866
    (1.84493595819866)*(1.88084761346252) / (1.84493595819866 – 1.88084761346252) = 96.6272194493165

    JEV harmonic nearest 1.62344612704193 is 22.1392314983839 / 14 = 1.58137367845599
    (1.58137367845599)*(1.62344612704193) / (1.58137367845599 – 1.62344612704193) = 61.0203365856337

    Notice how they fit together:

    (61.0203365856337)*(232.011969669376) / ( (61.0203365856337 + 232.011969669376) / 2 ) = 96.627219449317 = harmonic mean

    Remember that we’ve seen this framework before:
    https://tallbloke.wordpress.com/2017/04/29/ian-wilson-help-needed-to-solve-an-interesting-lunar-puzzle/#comment-125589

    This is about long JEV cycles and long JS cycles. Somewhere up this hierarchy lies a compact little set of simple expressions for Milankovitch Cycles.

    Some basic review plus a few more steps:

    (11.8626151546089)*(29.4474984673838) / (11.8626151546089 – 29.4474984673838) = 19.8650360864628

    (11.8626151546089)*(29.4474984673838) / (11.8626151546089 + 29.4474984673838) = 8.4561457463176

    φ/Φ = φφ = 1/(ΦΦ) = 2.6180339887499
    8.4561457463176 * 2.6180339887499 = 22.1384769776823
    22.1384769776823 / 2 = 11.0692384888412
    19.8650360864628 / 2 = 9.93251804323141
    29.4474984673838 / 2 = 14.7237492336919

    (11.8626151546089)*(14.7237492336919) / (11.8626151546089 – 14.7237492336919) = 61.0464822565173

    (11.0692384888412)*(9.93251804323141) / (11.0692384888412 – 9.93251804323141) = 96.7215918741308

    harmonic nearest 61.0464822565173 is 96.7215918741308 / 2 = 48.3607959370654
    (48.3607959370654)*(61.0464822565173) / (48.3607959370654 – 61.0464822565173) = 232.723433067725

    Focus derived from parallel insight:

    (1.58137367845599)*(61.0464822565173) / (1.58137367845599 – 61.0464822565173) = 1.62342762859098
    (11.8626151546089)*(1.62342762859098) / (11.8626151546089 – 1.62342762859098) = 1.88082278407335
    100*(1.88082278407335 – 1.88084761346252) / (1.88084761346252) = -0.00132011700412112%

    (1.84493595819866)*(96.7215918741308) / (1.84493595819866 – 96.7215918741308) = 1.88081189266319
    100*(1.88081189266319 – 1.88084761346252) / (1.88084761346252) = -0.00189918625339757%

    (2.21392314983839)*(232.723433067725) / (2.21392314983839 – 232.723433067725) = 2.23518672250026
    (11.8626151546089)*(2.23518672250026) / (11.8626151546089 + 2.23518672250026) = 1.88080100137918
    100*(1.88080100137918 – 1.88084761346252) / (1.88084761346252) = -0.00247824879619476%

    Compare the focused (second-order) estimates with first-order instinct:

    Target:
    (11.8626151546089)*(2.23525255532127) / (11.8626151546089 + 2.23525255532127) = 1.88084761346252

    First shot based on √5:
    (11.8626151546089)*(2.23606797749979) / (11.8626151546089 + 2.23606797749979) = 1.8814249265745
    100*(1.8814249265745 – 1.88084761346252) / (1.88084761346252) = 0.030694305474224%

    Target:
    (11.8626151546089)*(1.62344612704193) / (11.8626151546089 – 1.62344612704193) = 1.88084761346252

    First shot based on φ:
    (11.8626151546089)*(1.61803398874989) / (11.8626151546089 – 1.61803398874989) = 1.87358704127241
    100*(1.87358704127241 – 1.88084761346252) / (1.88084761346252) = -0.386026605140269%

    I introduced the sharper Mars derivation based on 96 before, but this comment underscores that derivation based on longer Jupiter–Saturn (JS) cycles is generalizable.

    Moving beyond first-order instinct we’re developing deeper instinct about the hierarchical geometry of offsets from base level central limits.

    I’ll leave it there for now and spell out some of the frequency algebra in a follow-up comment sometime. Then beyond that there are layers of work to sort concisely insights from trails explored more generally. The structure of my freedom from complementary pursuits guarantees this will take years.

    Summary

    First-order Mars estimates based on:
    φ:
    1.87358704127241 (-0.386026605140269%)
    √5:
    1.8814249265745 (0.030694305474224%)

    Note that they bracket (pointing to a simple inequality) the real thing:
    1.88084761346252 = 1 / Ma (Seidelmann 1992)

    Refined estimates (sharpened by 1-2 orders of magnitude) based on JEV and long JS cycles:

    1.88080100137918 (-0.00247824879619476%)
    1.88081189266319 (-0.00189918625339757%)
    1.88082278407335 (-0.00132011700412112%)

    The sharpest estimate is based on JEV and the “60 year” JS cycle.

  34. Paul Vaughan says:

    The most naive model for Mars’ sidereal orbit:
    • period = harmonic mean of √5 & φ.
    • frequency = arithmetic mean of 1/√5 & Φ.

    Inner Solar System First-Order Model Recap

    1 / 0.240846697327135 = 1 / Me
    1 / 0.23606797749979 = φφφ

    1 / 0.615197263396975 = 1 / V
    1 / 0.618033988749895 = φ

    1 / 1.00001743371442 = 1 / E
    1 / 1.00000000000000 = 1

    1 / 1.88084761346252 = 1 / Ma
    1 / 1.8774978038635 = (Φ+1/√5)/2

    r^2 = 0.999976601526245 (period)
    r^2 = 0.999912913357706 (frequency)

  35. Paul Vaughan says:

    OldBrew will probably be quick to note the Fibonacci pair most nearly approximating Mars:
    frequency = (8/13+1/(13/8+8/13))/2
    period = 2/(8/13+1/(13/8+8/13))

  36. oldbrew says:

    Mars orbit in years can also be expressed as (48/35)². This is accurate to less than an hour, maybe even less than half an hour, but may well just be numerology.

    – or (144/(21*5))² using Fibonacci numbers

  37. tallbloke says:

    Paul V: [2φ(ΦΦ)^e]^(-1/3) = 1.61703340324967

    More beautiful symmetry.

    Apropos nothing but if instead of (-1/3) we raise [2φ(ΦΦ)^e] to the power of -0.3337623775 we get 0.618033988724 vs φ = 1.618033988749…

    Just noting it here in case it turns out to relate to anything.

  38. Paul Vaughan says:

    It’s about second order balance — exploring the geometric balance of departure from first order. Not only does it not equal φ: The way in which it does not equal φ tells something very specific about EV. It’s not just J; it’s J and S and coupled E & V clued us in. Mars was (past tense) the biggest anomaly in v1. Now we have inner clarity as our exploration of outer limits and stability more generally endures.

  39. oldbrew says:

    Synodics: 3 Earth-Mars = 4 Venus-Earth = 7 Mars-Venus works pretty well (> 99.9%).

  40. tallbloke says:

    Sweet. Lucas numbers.

    Symmetrical relationship between Fibonacci and Lucas numbers

    F(n) =
    Phi^n – (–phi)^n
    ___________
    Phi– (–phi)

    L(n) =
    Phi^n + (–phi)^n
    _____________
    Phi + (–phi)

  41. oldbrew says:

    F(n) + F(n+2) = Lucas number
    e.g.
    1 + 3 = 4
    2 + 5 = 7
    3 + 8 = 11
    5 + 13 = 18
    8 + 21 = 29
    etc.

  42. oldbrew says:

    Wikipedia: Mars has an orbit with a semi-major axis of 1.524 astronomical units (228 million kilometers), and an eccentricity of 0.0934. The planet orbits the Sun in 687 days and travels 9.55 AU in doing so, making the average orbital speed 24 km/s.

    The eccentricity is greater than that of every other planet except Mercury, and this causes a large difference between the aphelion and perihelion distances—they are 1.6660 and 1.3814 AU. [bold added]
    http://en.wikipedia.org/wiki/Orbit_of_Mars

    1.666 = 5/3
    1.3814 = 3 – Phi, or (Phi² + 1)/Phi²
    [ratio to Earth at 1 AU]
    – – –
    Venus:Earth semi-major axis ratio = 1(V): ~1.383(E)

  43. Paul Vaughan says:

    It’s also a scaling of √5:
    Φ√5 = 1.38196601125011

    Helliocentric Mars angular momentum with 20/20 first-order frequency hindsight:

    2/√5
    3/√5
    4/√5
    φ/2
    φ/(2√5)

    Challenge: Point to every existing documentation
    that to first order Mars’ sidereal orbital period is 2 / ( Φ + 1/√5 ).

    Is there a search engine that can do that??

    The red planet exposes a red line crossed by conventional mainstream failure (the major western fault) to recognize, appreciate, and respect the roots of natural stability.

    Imagine the limits of human design ensure cycles of lost and found discovery. If civilization’s stability dependently hinges on balance, we may have to lose to gain.

  44. p.g.sharrow says:

    Paul, sometimes stability is in the eye of the beholder. All indications that I see point to very slow change. Perhaps orderly change. I see nothing that indicates the planetary orbital distances from the sun are fixed, but the ratio of distance may well be a fixture of the physics involved…pg

  45. oldbrew says:

    34 Mars orbits = 40 (8 * 5) Venus-Earth conjunctions
    (34 * 686.98 = 23357.32 d, 40 * 583.93 = 23357.2 d)

    5 V-E = one Venus pentagram = ~8 Earth orbits (years) = ~13 Venus orbits
    http://en.wikipedia.org/wiki/Venus#Pentagram_of_Venus

    34 Mars = 8 Venus pentagrams
    5,8,13 and 34 are Fibonacci numbers
    34/8 is a proxy for φ³

  46. Paul Vaughan says:

    pg, “fixed”? No one is saying fixed. This is about centrally limiting geometric boundary conditions, including oscillations and discrete steps. Misrepresentation, misinterpretation, and/or misunderstanding strikes again.

  47. Paul Vaughan says:

    2 / ( Φ + 1/√5 )

    Challenge: Point to everywhere that it has been documented.

  48. tallbloke says:

    Paul V: Helliocentric Mars angular momentum with 20/20 first-order frequency hindsight:

    2/√5
    3/√5
    4/√5
    φ/2
    φ/(2√5)

    I don’t understand. These are 5 different quantities. How are they all “Helliocentric Mars angular momentum”? What am I missing here?

  49. Paul Vaughan says:

    Easily-addressed question TB = a good question.
    You can quickly review Semi’s notes from 8 years ago:
    https://arxiv.org/ftp/arxiv/papers/0903/0903.5009.pdf
    Look just under Figure 69 on pdf p.41.

  50. Paul Vaughan says:

    TB, a thorough search should be undertaken to catalog all recorded instances of the following quantities:

    2/(Φ+1/√5) = 1.8774978038635
    (Φ+1/√5)/2 = 0.532623792124926

    It may be peripherally informative to broaden the search to:

    1/(Φ+1/√5) = 0.938748901931751
    Φ+1/√5 = 1.06524758424985

    I’m not sure if the needed algorithms will be available to searchers.

  51. Paul Vaughan says:

    quickly found this even though I’m only devoting a few minutes to searching today:
    https://pds-imaging.jpl.nasa.gov/data/msl/MSLMST_0002/DATA/RDR/SURFACE/0138/0138ML0008190130104269E01_DRCL.LBL

    The search was for “0.9387489”. It’s a NASA page and “MARS” appears 4 times on the page.

  52. oldbrew says:

    If Mars = (48/35)² years:
    (35/48)² = 0.5316839 = ~ 1/(Mars in years)
    i.e. the amount of a Mars orbit completed during one Earth orbit.

  53. tallbloke says:

    APOD:

    I have a last minute flight out to Mallorca for a hike through the Tramuntana. Back in a fortnight.

  54. oldbrew says:

    Mars:Earth — the radius ratio is the inverse of the orbit ratio.

    Order of data: Mars, Earth, Mars/Earth ratio
    Volumetric mean radius (km) 3389.5 6371.0 0.532
    Sidereal orbit period (days) 686.980 365.256 1.881
    [1/1.881 = 0.532]
    Max. orbital velocity (km/s) 26.50 30.29 0.875 = 7:8
    Min. orbital velocity (km/s) 21.97 29.29 0.750 = 3:4

    http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html

  55. tallbloke says:

    I may be wrong, but I have a vague recollection of doing a calc which resulted in 0.532. It may have been something to do with the falloff in gravity between two planets whose semi-major axes are in a phi ratio. or something.

  56. Paul Vaughan says:

    Semi wrote 8 years ago: “Main frequency of angular momentum of Mars relative to Sun is 1.11 year, 2.75 year, 271.8 days, 11.7 years, 2.12 years, 333 days, 1.23 years, 203.8 days and other.”

    Spelling it out a little more clearly (as always, doing this in incremental slow-walking steps to help any sensible people realize their own previous prejudice and/or inability to recognize simple pattern intuitively and independently):

    1.11
    √5/2

    2.75
    (2√5)/φ

    271.8 / 365.25
    √5/3

    1.23
    2/φ

    203.8 / 365.25
    √5/4

    I’m leaving a few of the quantities as a learning exercise: Explore how quick (or not) you are at deriving the √5 forms.

    The quantities listed above are not from guess-and-test (a logically valid method of exploration); they’re all derived. All the info needed to derive these first-order quantities was presented further above on this page.

    “the ratio of distance may well be a fixture of the physics involved…pg”

    The ratios aren’t fixed. Suggestion: Review Cuk’s video on JEV evection resonance, Milankovtich, and attractors more generally.

    _
    “sometimes stability is in the eye of the beholder.”

    The suggested subjectivity is imagined.
    Bristling at the simplicity is a political exercise.
    Geometric proofs are simple, unambiguous, and strictly objective.
    _
    Now, to have some good fun stirring stability with stability (I’ll accept your “eye of the beholder” comment if you try to put it here)…

    Another fact:
    The major western fault is disinclined towards natural stability …and it’s symbolized by a really clear red line.

    Red lines, red planets, red flags, and red armies — lots of symbolic learning opportunities if we’re ready to understand, appreciate, and respect the roots of stability …the *right* thing to do when we’re *left* with no option …and isn’t it neat that a pentagon and flags with 5-point stars are there to remind (whether polarized east, west, φ, Φ, left or right) of our dependence on √5 stability.

  57. tallbloke says:

    OB: ah yes, 0.526 not 0.532. What’s 0.006 between friends? 🙂
    Maybe the 0.532 would appear if a simple fraction was used instead of phi?

    Paul (quoting pg)
    “the ratio of distance may well be a fixture of the physics involved…pg”

    The ratios aren’t fixed. Suggestion: Review Cuk’s video on JEV evection resonance, Milankovtich, and attractors more generally.

    I think pg might have meant ‘feature’ rather than ‘fixture’. And he’d be right, since resonance (or avoidance of it) is involved.

    Paul: I’m leaving a few of the quantities as a learning exercise: Explore how quick (or not) you are at deriving the √5 forms.

    11.7
    √5*φ(2φ) = 11.7082

    2.12
    √5/2+(φ-(1/φ)) = 2.118
    (√5/2)+1 = 2.118
    (φ^3)/2 = 2.118
    1/(2*φ^-3) = 2.118

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