Spin Orbit Coupling – The Missing Angular Momentum Found?

Spin Orbit coupling is the transfer of orbital angular momentum to spin momentum between orbiting bodies. Total angular momentum (AM) is made up of orbital & spin momentum and both must balance. If there is an imbalance between solar AM and Planet AM we might have the missing AM to fuel a rotation change at the Sun. In a recent paper by Ian Wilson et al  “Does Spin Orbit Coupling Between the Sun and Jovian Planets Govern the Solar Cycle?” Ian discusses a viable theory of spin orbit coupling but also states there is no mechanical link. Perhaps now there is a new line of inquiry that may provide this mechanical link.

AM must always be conserved and this basic principle of the universe is seen all around us, one example is the Earth/Moon system where the reducing rotation speed of the Earth caused by tidal friction sees a conservation where the Earth/Moon distance increases by about 5cm a year.

Spin orbit coupling could be one area that may provide a link between the Planetary motions and a changing rotation speed of the Sun, basically if there is a mismatch in orbital AM it can be transferred to spin momentum (rotation speed). The Sun has it own angular momentum as it orbits around the centre of the solar system. 99% of this comes from the gravitational affects from the combined positions of the Jovian planets, this is clearly seen in Carl’s famous graph. Each planet also has its own AM which is  mass x distance x velocity, and as I have shown previously AM can be calculated using the SSB (solar system barycenter) or the Sun as the orbit axis point. If we measure the planet AM it can be compared against the solar AM and if done correctly any variation or missing AM can be determined. In the past this has been done by wiggle matching which is comparing 2 graphs, rescaling one to fit the other and comparing. This method does not provide mathematical results and the detail can be hidden in the scale of the graph.

I have always wanted to do my own comparison and in particular use the Sun as the orbit axis point when calculating planet AM. Gerry and I have collaborated on this project and combined our skill sets to produce an outcome.

To compare planet AM with Solar AM the inertial frame should be the same. The planet inertial frame calculated from JPL was another surprising result which looks to suggest it is in the barycentric frame rather that heliocentric. For our project we needed to make allowances. The project calculates planet AM using the Sun as the orbit axis point and the solar AM is calculated using the SSB as the axis point, then the solar AM is subtracted from the planet AM and the results recorded, Gerry explains ” By subtracting the solar orbital AM, we are making a simple Galilean transformation from the barycentric inertial frame for the freefall motion of the Sun about the solar system barycenter to the inertial frame of the Sun itself.  The reason we have to do this is that your planet position and velocity vectors are heliocentric.  Coordinates, and properties like AM derived from them, have to be in the same inertial frame as the inertial body (or alternatively a barycenter) to which they are referred.  That’s why I was surprised to see that the heliocentric Horizons data was referred to the barycentric frame used by the JPL DE ephemerides.”

The planet AM values were carefully calculated specifying the planet barycenter coordinates where applicable, and using planet mass measurements (13 decimal places) and velocity/distance coordinates xzy from the JPL Horizons database. The asteroids Ceres, Juno, Vesta and Pallas have been included. The initial planet AM values when summed showed a moving variation (not a constant as some have suggested) of each daily measure and when wiggle matched, lined up precisely with the solar AM curve, BUT there is detail missing that must be uncovered.

The next step was to subtract the solar AM from the planet AM to achieve the same inertial frame. The finished data showed a remarkable result that is still a work in progress value but at this stage looks promising. We have calculated an underlying fluctuating AM value that nearly follows the same curve as previously calculated by Carl. It makes up roughly .0000035% of Jupiter’s AM and could represent .2% of the average solar AM. These calculations are still in progress.



Here we have a comparison of Solar AM and the Planet AM variance…there is no way we can wiggle match these two data sets, the divergence points are of particular interest. The spreadsheet will be available in full detail shortly.

UPDATE: Some food for thought, below is the solar AM vs solar velocity graph (another wiggle match attempt). I have mentioned before that the two curves go out of sync which is strange for 2 data sets that are reliant on one another. It may be just a result of the mix between distance and velocity. The bigger variances look to line up with the bigger variances on the Sun vs missing AM graph.

If there proves to be an imbalance between solar and planet AM it could be traded off in velocity or spin or distance. Distance is unlikely and as seen the velocity does not follow a consistent pattern (although it is still a pattern). The first disturbance of the set (green arrows) sees a decrease in velocity, the second disturbance shows an increase…its not uniform. The blue dots also showing a divergence in the same places as the previous graph.










5 comments on “Spin Orbit Coupling – The Missing Angular Momentum Found?

  1. Now that you have lined up the curves so beautifully, Geoff, I see that the ‘missing AM’ curve values are just 0.048% of the solar AM curve values. The 0.2% figure cited was based on an erroneous estimate that I had made and passed on to you. My apologies for any confusion this may have caused to readers.

    I feel the analysis, as you have presented it, is a very significant quantitative result that appears to numerically confirm the general conclusions of Ian Wilson and Jose.

  2. You have calculated the AM of the Sun around the SSB, Sun_AM_SSB. Then the Planets_AM_Sun.
    I assume the first graph is (Planets_AM_Sun)-(Sun_AM_SSB) which is meaningless because they
    have different axis points. Then you have put (Planets_AM_Sun)-(Sun_AM_SSB) and Sun_AM_SSB
    together (with totally different scale of course) but what is that supposed to show? Please clarify

    REPLY: The first graph and method is up for testing and comment, this is an attempt to rectify the two different data sets to the same inertial frame, my thoughts have always been that true AM needs to be calculated from the true axis point to be accurate. The second graph displays the solar AM curve against the inertial frame adjusted planet AM, the divergence showing an imbalance (at the wiggle matching level) between the 2 sets. If this imbalance is correct we will have a situation where AM will need to be conserved.

  3. Could you comment on the 1900-1920 part where the smooth slopes dont match up ?

    REPLY: If our conclusions are right it may be a sign that when the 2 lines diverge the Sun is less active, this is purely speculation at this stage, but I have seen similar patterns in the solar AM vs velocity graph as well as in Hung’s work on the 11 yr cycle.

  4. Geoff,

    This is really interesting, since if orbital angular momentum is not completely conserved then it must go somewhere else, presumably into the spin of the planets or Sun, and the latter is most plausible.

    I want to clarify for you something about “axis point”. Angular momentum is conserved about *any* fixed point in an inertial frame of reference, and the barycentre (SSB) is the logical point to use, and will be more reliable in avoiding errors. So, if it were me, I would calculate relatve to SSB first, and then if at any time I wanted it relative to the instantaneous position of the Sun, I would do the linear translation.

    Now, the planets don’t revolve around the SSB, in fact they don’t revolve around anything! They are mainly attracted by the Sun and so follow roughly elliptical paths around it, but only “roughly” because of the perturbations of other planets.

    I hope this helps,

    REPLY: Hi Rich, calculations comparing the solar AM and planet AM using the SSB for both have been done but perhaps this method does not show the whole picture. AM can be calculated from any point but I am interested in the actual AM so proper comparisons can be done. My research and thinking suggests that gravity rules ie the revolving planets must orbit around the central gravitational body (Sun) and other planets in the vicinity via their gravity slightly push and pull on the intended orbit line that is controlled by the major body. This changes the velocity of the orbiting planet with in turn changes distance to the orbit axis point. My research and others shows a very different outcome when comparing planet AM using the 2 axis points, with only the Sun centered graphs showing the perturbations.

  5. Geoff,

    Thanks for the reply, on which I have no further comment at present.

    However, I want to say a couple of things further. First, having read Wilson’s paper further, but not yet in total detail, I am more convinced of the empirical evidence in favour of planetary influences driving grand minima. But I see a disconnect in evidence here. Carsten Arnholm, in his replies to the 2009/04/11 blog, stated that he had done simulations/calculations which showed that orbital angular momentum of Sun and planets was constant, leaving no room for modulation of the rotational AM of the Sun. But you seem to be saying different. Of course, one might need high precision in these calculations, because changes of velocity on the surface of the Sun might require relatively little angular momentum transfer to drive them.

    The second thing is that I want to consider again the possibility of a tidal influence. If you look at my table in my Comment 16 to 2009/04/11, you will see that VEJ are the biggest tidal players. Now, the phase locking which explains why Cycles 23 and 24 should be long is entirely in terms of VEJ syzygies, so this favours a tidal effect. In the future I may want to propose some sort of tidal graph to compare with the S v SSB AM graph.

    Previously, Leif Svalgaard has discounted tidal effects on account of the calcualted height of J’s tide on the Sun being tiny. But I think this does not properly account for the dynamics of the Sun. It is not a thin layer of liquid lying on a solid. The plasma at the surface is “floating” there, in equilibrium between strong gravity pulling it down and strong radiation and atomic collisions pushing it up. Therefore I think that Jupiter could raise larger tides than one might at first think. But I don’t know how to do the mathematics to support this idea.

    Anyway, if Jupiter could raise reasonable tides, then Saturn, in certain positions (notably 45 degrees from conjunction or opposition), could grab those tidal bulges and apply a torque to them from its own tidal effect. Since Jupiter and Saturn revolve slowly, a small effect can build up over time into a significant one (there’s far less friction compared with terrestrial tides).

    To summarize: is there proof of a small transfer between orbital and rotational AM, and irrespective of that answer can the tidal effects amount to something greater than might at first sight seem plausible?

    (Await Arnholm and Svalgaard devastating demolition at this point.)


    REPLY: We are talking about 2 separate factors that could affect Solar modulation and timing. My research points towards AM being responsible for solar cycle modulation as well as grand minima. The tidal research tends to line up with solar cycle lengths and could be responsible for the 11 year average cycle…SC24 max will be a good test for the theory.

    I have looked hard at the evidence Arnholm has released and I have several doubts. For one he uses the SSB as axis point for the calculation of planet AM, he also does not use JPL data but calculates the AM using his own methods. Also his spreadsheet numbers on the total planet AM variation shows no variance throughout the years but shows a modulation on his graph…something wrong here. Just for the sake of the argument I would like to see the exercise done properly using JPL data. What must be remembered is that both projects are just a wiggle matching exercise, we can only compare the trends which involves scaling one set of data to fit over the other.

    The AM project performed by myself and Gerry is accurate and quite different from Arnholm’s project, but I would like to get some confirmation on the method used. The inertial frame logic in particular.

    On the tidal values Saturn is considered too far away to have any affect with Jupiter and Venus having the greatest power (vertical). Semi has done some work on possible sideways effects of tides instead of vertical, there is some discussion here on tallbloke’s blog. http://tallbloke.wordpress.com/2009/12/30/meet-the-new-kepler-p-a-semi/

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