Solar Gravity Gradient Torque

It is often said (often by Leif, especially) that the only mechanism of interest in changing solar spin due to barycentric motion would be tidal forces and that those are just way too small to matter. Yet there ARE other forces. Electromagnetic, for one. (As Adolfo is fond of pointing out, and occasionally posts interesting movies of homopolar motors – we know the sun dumps a lot of charged particles into space and it must do something. The question is how much…)

I had a tiny “Ah Hah!” moment when I realized that the guys managing satellites must have already dealt with the miscellaneous forces and might well have a language and an understanding that would be helpful. That lead to mention of electromagnetic forces in some of their literature, along with solar wind and light forces; but the one that caught my eye was gravity gradient torque. This is strong enough that it is regularly used in satellite attitude control (or must be overcome with heavy reaction mass / attitude control wheels).

Unfortunately, looking into it, the math is mind numbing and most all of it is centered around a very small thing orbiting a very large thing, not a very large thing orbiting a common center of mass. Furthermore, the math is specifically described as being not possible to solve in a closed way. There must be simplifying assumptions made, and those assumptions are orthogonal to the solar case. That means I can’t say “Eureka!”, only “Hmmmmm…..”

I’d started on this from the point of view that a simplified model of solar angular motion could be made (no, I didn’t finish it). The idea was just to say that the sun had most of its mass in the middle, so you could model point masses of 1, 2, 4, 2, 1 rotating about that central point with mass 4 when the barycenter was at the center, then look at the case where it moves to the edge. With L = r x mV
So at one point, the angular momentum would be a series of 1 x 2, 2 x 1, 4 x 0, 2 x 1, 1 x 2 when rotation was central and then 1 x 4, 2 x 3, 4 x 2, 2 x 1, 0 x 0 when the barycenter was at the edge. As those two cross product sums would be different, the question was “Where did the angular momentum come from / go to?” as it is a conserved quantity.

I figured that one could compute the AM of the whole sun vs the barycenter that way, then of the solar rotation compared to it’s center of mass, figure the change in one to allow for the change in the other, and look for any ‘order of magnitude’ similarity to what is actually seen in changed solar motion. (That ignores the change in the planetary motion, but if it’s at all close and of the proper sign, would support the notion of “Dig Here!” more precisely to find more evidence).

Before I even got to that point, I ran into The Falling Cat problem…

Basically, if you look at ALL the angular momentum problems / physics I was exposed to in school (and most of what folks talk about when discussing planetary / solar interaction) it is treated to the usual rules from that Angular Momentum wiki. Sliding past, hardly noticed, is “For a rigid body rotating around an axis of symmetry”. Right out the gate, we’ve violated those things. The physics we know and love does not apply. (Well, it sort of applies, but in a very messy way we can’t really solve well). Thus the falling cat problem.

How does a falling cat turn itself feet down while not violating conservation of angular momentum?

It depends on the fact that the cat is not a ‘rigid body’ and may not be rotating about its ‘axis of symmetry’. As the sun is not rigid, it will follow ‘different rules’ from what folks say when they trot out their high school physics and conservation of angular momentum rigid body solution mindset. Just like the cat. That is why so few folks can answer the falling cat question.

The cat, you see, bends in the middle. It acts like two different cylinders, with a pivot at the waist. That lets it combine two different spin actions into one overall rotation of the feet downward.

Falling Cat Dynamics

Falling Cat Dynamics

The falling cat problem consists of explaining the underlying physics behind the common observation of the cat righting reflex: how a free-falling cat can turn itself right-side-up as it falls, no matter which way up it was initially, without violating the law of conservation of angular momentum.

Although somewhat amusing, and trivial to pose, the solution of the problem is not as straightforward as its statement would suggest. The apparent contradiction with the law of conservation of angular momentum is resolved because the cat is not a rigid body, but instead is permitted to change its shape during the fall. The behavior of the cat is thus typical of the mechanics of deformable bodies.

The solution of the problem, originally due to (Kane & Scher 1969), models the cat as a pair of cylinders (the front and back halves of the cat) capable of changing their relative orientations. Montgomery (1993) later described the Kane–Scher model in terms of a connection in the configuration space that encapsulates the relative motions of the two parts of the cat permitted by the physics. Framed in this way, the dynamics of the falling cat problem is a prototypical example of a nonholonomic system (Batterman 2003), the study of which is among the central preoccupations of control theory. A solution of the falling cat problem is a curve in the configuration space that is horizontal with respect to the connection (that is, it is admissible by the physics) with prescribed initial and final configurations. Finding an optimal solution is an example of optimal motion planning (Arbyan & Tsai 1998; Xin-sheng & Li-qun 2007).

In the language of physics, Montgomery’s connection is a certain Yang-Mills field on the configuration space, and is a special case of a more general approach to the dynamics of deformable bodies as represented by gauge fields (Montgomery 1993; Batterman 2003), following the work of Shapere and Wilczek (Shapere and Wilczek 1987).


At that point, I realized I was not going to find a nice formula for momentum, apply it to the sun, and be done.

So that’s ONE body, solid but flexible. Without massive electrical and magnetic fluxes and without the occasional mass ejection. (Mine, at least, waits until on the ground and in the litter box before undergoing ‘mass ejection’ ;-)

It was just about there that I figure I’d not be able to solve this, given that the cat problem was only solved in 1969 and was still being expounded in 2003.

That led to the notion of satellite mechanics instead. Where I found that the “axis of symmetry” matters. Satellites are sometimes spin stabilized via the long axis, but can sometimes be spin stabilized on a minor axis (but only under specific conditions). What happens if the spin moment gets a bit off from the axis of symmetry? Well, the thing starts to ‘have issues’. There’s a lot of effort put into avoiding that case. From reaction mass, to control wheels, to using magnetic devices against the earth’s magnetic field.

“Right Quick” it sunk in that things in orbit are subject to a whole lot of forces that act in a variety of poorly understood ways to perturb them into various undesired spins, tumbles, and problem states. As these are often very rigid bodies, it is NOT just “tidal forces”…

Has an interesting discussion of some of the issues.

First things first: Suppose that a specific (constant) angular velocity will keep a satellite in the desired attitude indefinitely. If that angular velocity vector is aligned with one of the principal axes of the satellite and if the satellite has that exact angular velocity, then some external torque will be needed to make the satellite veer from the desired attitude. That second if is a mighty big if; it is impossible to make a satellite’s rotation rate be exactly as desired. The reason attitude control is needed is to counter internal errors in pointing and to counteract those external torques.

Most satellites do not use thrusters for attitude control, at least not as the primary means of attitude control. Many satellites do not even have attitude control thrusters. Many do not have any thrusters at all. The Hubble, for example, does not have any thrusters.

Many techniques are used to keep a satellite pointed in the right direction. Early satellites were spin stabilized. The whole satellite was set spinning either about its minor or major rotational axis. For a rigid body, rotation about either the major principal axis or minor principal axis (the principal axes with the largest and smallest moments of inertia) are stable. (This is not true for non-rigid bodies such as spacecraft with solar arrays. The only stable axis is the major axis.)

OK, first off we’re talking about a constant angular momentum. What happens when it changes? Then it has to be on a specific axis of rotation. What happens when it’s off axis? What happens when the thing is a ball of fluids? And we have the point that an orbiting body has external torques. And, once again, are reminded that bendy things have even more trouble being stabilized.

One approach is purely passive: Put the vehicle in an attitude where the perturbing environmental torques will put the vehicle back in that attitude should the vehicle drift from the desired attitude. The desired attitude for many satellites is nadir pointing. The satellite needs to be pointing toward the Earth and it needs to rotate at one revolution per orbit to maintain that pointing. The principal perturbing torques on a satellite in low Earth orbit are gravity gradient torque and torque from atmospheric drag. One way to take advantage of these environmental torques is to make the vehicle have a longish cylindrical shape with the cylinder axis pointing radially. Aero torque will be fairly small, and gravity gradient torque will naturally keep the vehicle in this vertical orientation.

OK, the sun is not a cylindrical shape and is not pointing toward the barycenter, I think this will matter. It implies to me that various angular momentum perturbations can cause various bits to wander around a ways from the expected places and this is likely to show up as various kinds of fluid flow, being as the sun is not a solid body. Those, then, are likely to stir the pot on magnetic and electrical forces that will even further perturb things. This is not looking like a ‘nothing happens’ scenario to me. But at least we don’t have any ‘aero’ forces (other than the solar wind).

But the ‘gravity gradient torque’ was what got my attention. Leading to:

Analytic signals of the gravity gradient tensor and
their application to Euler deconvolution
M. Beiki
Department of Earth sciences, Uppsala University, Uppsala, Sweden

The analytic signal concept can be applied to the gravity gradient tensor data in three dimensions. For
the gravity gradient tensor, the horizontal and vertical derivatives of gravity vector components are
Hilbert transform pairs. Three analytic signal functions then are introduced for the x , y and z
components. The amplitude of the first vertical derivative of the analytic signals of x and y
components enhances edges of the causative bodies. It’s also shown that the directional analytic
signals are homogenous and they satisfy the Euler’s homogeneity equation. The application of the
directional analytic signals to the Euler deconvolution is demonstrated on some generic models to
locate causative bodies. The advantage of this method is that it allows the automatic identification of
the structural index from solving three Euler equations derived from the gravity gradient tensor for a
collection of data points in a window.

Oh dear. Tensors. My brain said “no”…

It is also shown that the
directional analytic signals are homogenous and satisfy the Euler’s homogeneity equation. The
advantage of this method is that the constant base level is removed from the Euler’s equation. Then the
structural index and source location can be estimated from Euler deconvolution of the directional
analytic signals directly. This improves the conventional Euler deconvolution using three gradients of
the vertical component of the gravity vector.

The key takaway for me, here, was just that this is NOT a tide force (or perhaps a tide force but without a tide), and it is not easy to calculate, even for a small rigid body.

6.1 Environmental Torques
Important environmental torques affecting satellite attitude dynamics include gravity
gradient, magnetic, aerodynamic, and solar radiation pressure torques. We develop
expressions for these torques in this section, and in subsequent sections we study the
effects of the torques on attitude motion.
Currently this section only includes the development of the gravity gradient torque.
6.1.1 Gravity Gradient Torque
We assume a rigid spacecraft in orbit about a spherical primary, and every differential
mass element of the body is subject to Newton’s Universal Gravitational Law:

Again, that rigidity issue…

In the integrand, the vector c~r is the only variable that depends on the differential
mass element. However, in general, this integral cannot be computed in closed form.
The usual approach is to assume that the radius of the orbit is much greater than
the size of the body, i.e., (formula didn’t copy well. Orbit >> body radius),
and expanding the integrand as follows:

BUT, what happens when the radius of the object is about the same as the radius of the orbit, as with the sun vs the barycenter motion? It would seem that you get to invent a new solution to the problem if you want to answer that question.

Again, my takeaway is just that there is something called “Gravity Gradient Torque”, it has an effect on orbiting things and changes their rotations, and it is very hard to ‘do the math’ other than in particular cases that have already been solved (small bodies orbiting big ones, and rigid).

Now, one other minor point: The gravity gradient comes out of the fact that some parts of both the earth and the satellite are nearer and further from each other. Yet for Jupiter vs the Sun, they are always a long ways away. I’m not able to say to what degree gravity gradient torque will act as though it were from the barycenter vs as though it were the J-Sun Distance. As Jupiter moves a very long ways in an orbit, it might well be that ‘one side of the sun vs the other’ is a large impact; or it might be that the sun spins so fast it all ‘averages out’. Need to “do the math” to know, and I’m not up to ‘doing that math’ as I have other things I care about more and it would take me a lot of time. Just realize, though, that you can’t just dismiss it with a “tides only” argument.

The rest of the paper gets a bit more hairy from there and folks with a masochistic streak are invited to read it…

Is somewhat more readable. It confirms the notion that this is a hard problem to solve, and will be worse for a magnetic ball of fluids with convection.

The interaction of three point masses under an inverse square law and
the rotation of a heavy asymmetric top about a fixed point are the two most
outstanding unsolved problems in Classical Mechanics. The solutions for
these problems are unknown in what is loosely called ‘closed form’, which
usually means the solution is specified or described by means of familiar
functions and/or afinite set of integrations of known expressions (quadratures).

Functional dependence of gravity gradient torque. -At a given point in a
gravitational field, a small body experiences a torque if the vector gradient
is not zero . For a spherical Earth field , the torque is given by the

which relates torque to ‘the unit vector from the Earth’s center’ and “The inertial dyadic of the satellite” whatever that is…

Completely unanswerable for me is how that same physics would apply to the sun wobbling about in space. I note in passing that the sun has a lot of inertia. The “I” term shows up as both a dot product and a cross product vs the radius and is not a divisor…

For amusement, you can listen in on a couple of folks trying to make a math simulation of the simple case of a small satellite orbiting earth:

I found this bit of ‘correction advice’ particularly interesting as it point toward an exchange of orbital angular momentum for rotational angular momentum, which is exactly what I’ve been trying to show happens on a macro scale (so SIM could ‘stir’ the sun).

If you do not take the orbital motion into account, then your spacecraft will just behave like a pendulum
– the angular rate will vary periodically, which looks like what you are getting. The reason that the angular motion dampens out in orbit is because, as the orbiting body moves around the parent, the direction of the gravity gradient changes in the inertial frame. For your current model, the direction of the gravity gradient in the inertial frame is constant and, in a frame of reference rotating with the rigid body axes, the direction of the gravity gradient does not change any faster or slower than the angular rate of the orbiting body. This means that there is no mechanism for exchanging the angular momentum of the orbiting body with its orbital angular momentum, and therefore no damping mechanism.

The guy forgot to let the gravity come from a different direction as the thing rotated, so lost the mechanism to turn spin into orbital momentum. If I’ve read it right.

So it looks to me like he’s saying that as long as a satellite (the sun) is feeling gravity from changing directions (via the barycenter math construct or the real forces from the planets proper) it can convert between spin angular momentum vs orbital angular momentum. I think this matters. As it is a very real effect, causing all sorts of equipment to be put on satellites to control / use it; I think it would be very unwise to dismiss it with a wave of the Tidal Wand.

Now, what I’ve been singularly unable to find, is a simple explanation of just what mechanism causes it…

So this posting is more a ‘marking how far into the woods I got’ and not so much a map to the General Store. Perhaps someone else can move the map making a bit further than I was able to do.

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About E.M.Smith

A technical managerial sort interested in things from Stonehenge to computer science. My present "hot buttons' are the mythology of Climate Change and ancient metrology; but things change...
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29 Responses to Solar Gravity Gradient Torque

  1. u.k.(us) says:

    Trying to comprehend the reflexes of a cat is folly, they can pin a fly to a window with their little paw, and make it look easy.

  2. adolfogiurfa says:

    @E.M.: marking how far into the woods I got’… into the woods?…Your were so close to a tree trunk that you were able to see its individual cells!
    The following, from “Malaga view” it´s a beauty, it returns the Earth to the center of our universe!:
    I don´t know if we need a “machete” to clear up the jungle or a Guillotine….

  3. omanuel says:

    Thanks for the message. As I recall, there is little or no doubt that solar cycles are linked to changes in the solar barycenter. That has been known since about 1965, whether or not Leif understands the mechanism.

    Without any arithmetic, I strongly suspect that changes in the solar barycenter shift the position of the Sun’s pulsar core relative to that glowing sphere of waste products (91% H, 9% He) that Leif calls the surface of the Sun.

    Our scientific community has been plagued by decades of lock-step, politically correct, post-modern, consensus thinking that is designed to save the world from the threat of nuclear war and control mankind’s aggressiveness.

    Details on the deception about the energy source that creates and destroys elements and sustains life are summarized here:

    As this conflict draws to an end, may we have the wisdom to avoid any form of violence or retaliation and adopt the procedure that worked so well in South Africa: Establish a “Truth and Reconciliation”-type commission to restore integrity to science, rights of citizens, and citizen control over government,without reviving racism, threat of nuclear war, or retaliation for deception.

    With kind regards,
    Oliver K. Manuel

  4. gallopingcamel says:

    The abstract of a recent paper states:
    “The main conclusion is that in its essence: planetary influences are too small to be more than a small modulation of the solar cycle.”

    See: “The influence of planetary attractions on the solar tachocline”, Dirk K. Callebaut a, Cornelis de Jager b,n,1, Silvia Duhau

    This makes perfect sense to me, just as the idea that tiny changes in the amounts of CO2 in the atmosphere are too small to produce a significant modulation in global average temperature.

    The folks who want to believe that CO2 is a significant factor affecting climate simply postulate “feedbacks” to increase the effect of their feeble “forcing”.

    Given the complex nature of the sun and our limited understanding of it why not postulate a mechanism that amplifies the tiny effect of the planets on our sun. The sun appears to have many modes of oscillation. Suppose some modes have a high “Q” factor?

    Here on Earth sea level oscillates over an amplitude of a few feet on an 12.4 hour cycle driven mainly by the Moon’s gravitational attraction. Travel to Eastport, Maine and you will find that the tide amplitude is fifty feet thanks to the Bay of Fundy having a resonance with a period of ~12.6 hours.

  5. Ian W says:

    The planets and all of the particles in the Sun are in free fall toward the barycenter. Is the barycenter the bottom of the gravity well – or is the Sun the bottom and other distortions (dips) in the gravity well are caused by the other planets?

  6. E.M.Smith says:

    @Ian W:

    Well, the actual gravity wells are at the solar system bodies. The barycenter is just a mathematical averaging of all those effects into one place where one could pretend there was a center about which things rotate. That means, IMHO, the actual math solution would require using the distances of the actual planets in a hideous bit of math that is not solvable to compute what happens to the sun.

    That something happens is not in doubt, even that something beyond tidal forces happens is not in doubt. That I can’t calculate it is also not in doubt 8-}

    I did find a bit of a NASA paper on HOW to calculate the gravitational forces, including the gravity gradient torque, for a satellite including source code. ( In ADA, fer crying out loud. Last time I saw ADA was about 1982 … )


    Click to access 19940025085_1994025085.pdf

    for enough math to make your head swim. But at least it DOES show a fairly clear way to calculate the values. ( It would be nice if more of their terms were defined in the paper, but it looks like one needs to swim up stream to a prior paper or two for actual definitions of terms).

    Again my main takaways were just that:

    There IS a non-tidal interaction that causes torque forces.

    It’s way complicated to compute and figuring it out in some simple intuitive description is unlikely to happen…

    It’s largely demonstrated for solids and point sources in any case, and we’re dealing with a non-point source fluid Sun (unless Oliver is right and we CAN treat it as a solid, but even then the ‘surface’ is fluid and subject to bizarre motions…)

    So, IMHO, the lengths folks have to attend to compute this torque pretty much shows that it IS important and that it is NOT just a one line tide function. (And even THAT is just for the gravity gradient issue. Magnetic and electrical forces may well be larger and more important. Maybe I need to calculate the homopolar torque on the Earth from the known current delivered at the poles and see what it would do to LOD over, say, a month… just to get a feel for importance vs irrelevance. All the numbers are known, IIRC, and the formula is fairly easy.)


    I think that the planetary forces are small, but that they result in large torques. Look at a typical gyro (and that’s what the sun is after all), even a tiny dust speck can cause it to stumble and wobble (and don’t get me started on gyro tumbling…) It doesn’t always go in the direction you expect, but some minor inputs can have major outputs.

    This effect is used to great advantage in satellites where the attitude control systems may use very small energies to create relatively large torque forces.

    There was a pretty good literature on that when searching for satellite attitude control information.

    An intro here:

    Control moment gyros
    Main article: Control moment gyroscope

    These are rotors spun at constant speed, mounted on gimbals to provide attitude control. While a CMG provides control about the two axes orthogonal to the gyro spin axis, triaxial control still requires two units. A CMG is a bit more expensive in terms of cost and mass, since gimbals and their drive motors must be provided. The maximum torque (but not the maximum angular momentum change) exerted by a CMG is greater than for a momentum wheel, making it better suited to large spacecraft. A major drawback is the additional complexity, which increases the number of failure points. For this reason, the International Space Station uses a set of four CMGs to provide dual failure tolerance.

    So modest gyros can make large torque from small energy…

    Though the wiki also claims gravity gradient effects are a form of tidal force. Perhaps a tidal force without a tide?

    Gravity-gradient stabilization
    Main article: Gravity-gradient stabilization

    In orbit, a spacecraft with one axis much longer than the other two will spontaneously orient so that its long axis points at the planet’s center of mass. This system has the virtue of needing no active control system or expenditure of fuel. The effect is caused by a tidal force. The upper end of the vehicle feels less gravitational pull than the lower end. This provides a restoring torque whenever the long axis is not co-linear with the direction of gravity. Unless some means of damping is provided, the spacecraft will oscillate about the local vertical. Sometimes tethers are used to connect two parts of a satellite, to increase the stabilizing torque. A problem with such tethers is that meteoroids as small as a grain of sand can part them.

    [edit] Magnetic torquers
    Main article: Magnetic torquers

    Coils or (on very small satellites) permanent magnets exert a moment against the local magnetic field. This method works only where there is a magnetic field to react against. One classic field “coil” is actually in the form of a conductive tether in a planetary magnetic field. Such a conductive tether can also generate electrical power, at the expense of orbital decay. Conversely, by inducing a counter-current, using solar cell power, the orbit may be raised. Due to massive variability in Earth magnetic field from an ideal radial field, control laws based on torques coupling to this field will be highly non-linear. Moreover, only two-axis control is available at any given time meaning that a vehicle reorient may be necessary to null all rates.

    Has an interesting point in it. It gives a magnitude of force for a particular Earth satellite:

    Gravity-gradient stabilization (a.k.a “tidal stabilisation”) is a method of stabilizing artificial satellites or space tethers in a fixed orientation using only the orbited body’s mass distribution and the Earth’s gravitational field. The main advantage over using active stabilization with propellants, gyroscopes or reaction wheels is the low use of power and resources. It was first used for low Earth orbit and tested unsuccessfully for geosynchronous orbit in the Applications Technology Satellites ATS-2, ATS-4 and ATS-5 from 1966 until 1969.

    The principle is to use the Earth’s gravitational field and tidal forces to keep the spacecraft aligned in the desired orientation. The gravity of the Earth decreases according the inverse-square law, and by extending the long axis perpendicular to the orbit, the “lower” part of the orbiting structure will be more attracted to the Earth. The effect is that the satellite will tend to align its axis of minimum moment of inertia vertically.

    An example of gravity-gradient stabilization was demonstrated during NASA’s TSS-1R mission. Just prior to tether separation, the tension on the tether was about 65 N (14.6 lbs)

    So a dinky thing in Earth gravity can get 65 N ( 14.6 lbs) of tension just from the different gravity field over a fairly short distance.

    It sure looks like their ought to be enough difference over a one solar diameter range to cause a fluid to be stirred… or the stirring to change with variations in the gravity net vector.

  7. David says:

    A different take on “I found this bit of ‘correction advice’ particularly interesting as it point toward an exchange of orbital angular momentum for rotational angular momentum, which is exactly what I’ve been trying to show happens on a macro scale (so SIM could ‘stir’ the sun).”

  8. R. de Haan says:

    Comment from Scafetta at WUWT
    Nicola Scafetta says:
    April 15, 2012 at 9:20 pm
    Anthony says “Looks to me like Barycentrism just took a body blow – Anthony”

    I think that Anthony was too exited. The things are quite more complex, and they are already extensively explained in my latest published paper:

    N. Scafetta, “Multi-scale harmonic model for solar and climate cyclical variation throughout the Holocene based on Jupiter-Saturn tidal frequencies plus the 11-year solar dynamo cycle.” Journal of Atmospheric and Solar-Terrestrial Physics in press (2012).

    Click to access Scafetta_JStides.pdf

    First, the new paper by Callebaut, de Jager and Duhau [2012] simply repeats the argument that the planetary tides are quite small, which is well known, and de Jager simply repeats the arguments on the same topics in his 2005 papers.

    A response to these people is already contained in my paper at page 13, where I wrote

    “For example, de Jager and Versteegh (2005) further developed the classical argument that planetary tidal elongation on the Sun is tiny. However, this critique simply requires the existence of a strong amplification feedback mechanism that may be provided by a tidal stimulation of the nuclear fusion rate (Wolff and Patrone, 2010), which perhaps may be also helped by collective synchronization resonance effects.”

    Note that Callebaut et al., do not say anything about the above issues.

    However, the best response to Callebaut et al. [2012] is written in de Jager and Versteegh (2005) itself where in the conclusion the authors say:

    “Therefore they cannot significantly influence the solar dynamo unless a completely different hypothesis is forwarded”.

    So, the things are simply not as by Callebaut, de Jager and Duhau think that they are.

    About the other arguments referring the reproduction of the longer cycles such as the Grand Minima, the millennial cycles and so on, I am sorry for Anthony, but my paper answers them all.

    From the abstract of my paper:

    “The major beat periods occur at about 115, 61 and 130 years, plus a quasi-millennial large beat cycle around 983 years. We show that equivalent synchronized cycles are found in cosmogenic records used to reconstruct solar activity and in proxy climate records throughout the Holocene (last12,000years) up to now. The quasi-secular beat oscillations hindcast reasonably well the known prolonged periods of low solar activity during the last millennium known as Oort, Wolf, Sporer, Maunder and Dalton minima, as well as the seventeen 115-year long oscillations found in a detailed temperature reconstruction of the Northern Hemisphere covering the last 2000 years. The millennial three-frequency beat cycle hindcasts equivalent solar and climate cycles for 12,000 years. Finally, the harmonic model herein proposed reconstructs the prolonged solar minima that occurred during 1900-1920 and 1960-1980, the secular solar maxima around 1870-1890, 1940-1950 and 1995-2005, and a secular upward trending during the 20th century.”

    About the claim that Humkin Solheim, Stordahl [2011] do not confirm my results in my 2010 paper that focused on the decadal multidecadal scale, this is funny. Humkin et al. are using an ice core record to study the Holocene that does not have the precision of the global surface temperature records and anly the secular and above scale could be well detected. Humkin et al. study also a shorter local record since 1900 and this confirms my finding. Finally, Solheim wrote me many times saying that they are finding my same cycles.

    This paper is no a body blow of any kind. Just a poor paper repeating things that are already very well known.

    The thing are quite more complex.

    Also have a read at Tallbloke’s Talk Shop and our friend Geoff Sharp’s Beyond Landscheidt.

  9. R. de Haan says:

    Sometimes, a small number can come with huge implications:

    Mass moon as a percentage of Earth mass: 0.0123%

    This distance from our earth to the moon varies but it’s around 10 times the earth diameter.

    Just saying.

  10. omanuel says:

    Thinking out loud about interactions between the Sun and its planets, . . . there are at least three things to consider:

    1. Before suddenly vanishing, Peter Toth noted in 1977 that the Sun oscillates like a pulsar* [“Is the Sun a pulsar?” Nature 270, 159-160 (1970)]

    2. The orbiting planets are probably composed mostly of “expanded”, atomic matter – matter made of atoms.

    3. The core of the Sun is “compacted” nuclear matter but its mantle is mostly “expanded” atomic Fe and its atmosphere is mostly “expanded’ atomic H.

    There may be differences between the interactions of atomic matter in planets with

    a.) “Expanded” atomic matter in the Sun’s skin and
    b.) “Compacted” nuclear matter in the Sun’s core

    *Peter Toth’s analysis of solar oscillations and our analysis of isotopes and elements in meteorites [1-5] were complimentary, but Peter vanished and we didn’t know about his work until much later.

    1. “Elemental and isotopic inhomogeneities in noble gases: The case for local synthesis of the chemical elements”, Trans. Missouri Acad. Sci. 9, 104-122 (1975).

    2. “The xenon record of element synthesis”, paper presented at the April 1976 Annual Meeting of the American Geophysical Union [Trans. Am. Geophys. Union, Eos 57, 278, 1976].

    3. “Xenon record of the early solar system”, Nature 262, 28-32 (1976).

    4. “Strange xenon, extinct superheavy elements and the solar neutrino puzzle”, Science 195, 208-209 (1977).

    Click to access StrangeXenon.pdf

    5. “Isotopes of tellurium, xenon and krypton in the Allende meteorite retain record of nucleosynthesis”, Nature 277, 615-620 (1979).

  11. R. de Haan says:

    gallopingcamel says:
    16 April 2012 at 1:45 am
    “This makes perfect sense to me, just as the idea that tiny changes in the amounts of CO2 in the atmosphere are too small to produce a significant modulation in global average temperature.”

    Don’t use the small number argument to make a point.
    And don’t link this subject with the CO2 CAGW subject.

    Just concentrate on the specifics of the subject.

    Just want to prevent the ancient discussion theme that came with the “birth” of the climate skeptics that only a small amount of a poison can kill you so small amount of CO2 can do the same.
    This argument polluted the blogs for weeks and we don’t want this kind of shit happening again.

    Unfortunately it does.

    We now see people at WUWT doing exactly the same thing.

    Believe me when I say it’s a kind of embarrassing, see my earlier posting about small numbers, big effects.

    In our attempts to advance our understanding we should not get small numbers to block our way.

  12. adolfogiurfa says:

    There will be many surprises in the future, for those who, when finding anything inexplicable (almost everything :-) ), say that it was a “surprise”. This makes me remember “Pedro Navaja” (Fred the knife) lyrics in spanish:

  13. adolfogiurfa says:

    La vida te da sorpresas, sorpresas te da la vida ay Dios. Life gives you surprises, ….
    In a few years, or , perhaps worse, months, ….we will know about the Sun.

  14. R. de Haan says:

    adolfogiurfa says:
    16 April 2012 at 4:38 pm
    “This makes me remember “Pedro Navaja” (Fred the knife) lyrics in spanish”

    I think you mean “Mack the Knife”, a translation from the original lyrics from “Meckie Messer”, a song composed by Kurt Weill with lyrics by Bertolt Brecht, first performed by Hildegard Kneff in 1963.

    Anyway, thanks for posting this.

  15. adolfogiurfa says:

    And this is the cold blood end of Pedro Navaja/Meckie Messer astrophysics tale:

  16. R. de Haan says:

    Would be nice to have this in a readable version or a proper voice presenting the stuff.
    Really, the tin hat digital voice is horrible.

    [This is not the alternate reality you were expecting (waves hand….) -E.M.Smith]

  17. omanuel says:

    Patience is required to decipher a mystery that started about the time Hiroshima vanished!

    Professor Kees De Jager invested a week of his life at the Bilderberg Hotel in April 1967 helping leaders of the solar science community hammer out consensus opinions that would dominate solar science for the next four decades. See: “The Bilderberg model of the photosphere and low chromosphere,” Solar Physics 3, 5-25 (1968) – Ref #3 in “Deep roots of the global climate scandal”

    Click to access Climategate_Roots.pdf

    The key phrase in that paper that regarding climate change is in the abstract “in equilibrium”

    Only two years earlier Dr. P. D. Jose reported that the orbital motion of planets may induce solar cycles and changes in earth’s climate [“Sun’s motion and sunspots”, Astron. J. 70, 193-200 (1965)]:

    The mechanism was a mystery:

  18. MarbellaBoy says:

    I’m afraid the maths is beyond me, but that GIF of the rotating cat had me positively mesmerised! I’ll look at Smudge with a new respect from now on.

  19. E.M.Smith says:


    I presume “Smudge” is a cherished feline…

    It’s amazing to me how much a simple graphic can communicate sometimes; but yes, seeing something happen trumps a dozen intellectual arguments…


    I’ve read all the comments but I’m a bit too emotionally worked up (from the latest posting about The Whore) and I’m a few shots of Tequila too ‘relaxed’ to respond appropriately… I could do a rational response, but, frankly, I’m too in touch with my emotional state when “doing Tequila” to be dispassionate, so things will have to wait ;-)

    At a minimum I have to watch R. de Haan’s Mack The Knife video first ;-)

  20. E.M.Smith says:

    OH, and it’s worth stating out loud:

    I’m quite happy to have a multi lingual blog. I’m good with Spanish, French, and German and kind of OK in Italian, Portuguese and a couple of others. So feel free to put things up in your native language. For me, it’s a feature ;-)

  21. E.M.Smith says:

    @R. de Haan:

    You Bastard! How dare you make me fall for a woman who was way older than my 10 years of age when she sung a song I’d not know for several more years!!! ;-)

    The cyber world is way unfair. Here I am an ‘almost 60 something’ falling for a ’30 something’ who was at least a decade older than me when she sung a song in a language I’d not study for another decade….

    Damn. This is only going to get worse as time passes. I’m smitten by a woman who is likely a 70 something if she is still alive at all… Is there no justice !!! ;-)

  22. R. de Haan says:

    E.M.Smith says:
    17 April 2012 at 12:37 am

    No Justice E.M.

    Hildegard Kneff was a remarkable lady.

  23. R. de Haan says:

    Here is my favorite for many years: Ilse de Lange, an extremly talented young lady who writes her own lyrics and music.

  24. R. de Haan says:

    E.M.Smith says:
    17 April 2012 at 12:14 am
    OH, and it’s worth stating out loud:

    “I’m quite happy to have a multi lingual blog.”

    Talking languages: Marlene Dietrich in 1962 doing her own introduction of the song “Sag Mir Wo Die Blumen Sind” in English and French, performing the song in the German language.

  25. R. de Haan says:

    One more Ilse de Lange

  26. omanuel says:

    Before leaving the topic of solar gravity gradient torque, a quick scan of events in the evolution of science from 6 Aug 1945 to present is illuminating:


    1945: Hiroshima vanishes because E = mc^2: 6 Aug 1945
    1945: United Nations Charter is ratified: October 24, 1945

    __Immediate U-turn: Changes interior of Sun from Fe to H
    __See: “Home Is Where the Wind Blows” (1994) p153-154

    1946: Solar interior changed*: Iron (Fe) into Hydrogen (H)
    1956: Publication blocked of Earth’s natural “nuclear fires”
    1965: PD Jose, “Solar motion: Sunspots,” Astron J 70, 193**

    __ Homogeneous Sun in hydrostatic equilibrium***

    1967: The Bilderberg model, Solar Physics 3, 5-25 (1968)
    1975: Evidence of local element synthesis in Sun is hidden
    1977: The scientist that reported the pulsar Sun vanished
    1983: SW evidence of iron(Fe)-rich solar interior ignored
    1986: Challenger disaster**** delays Jupiter confirmation
    1989: Government tries to discredit cold fusion discovery
    1993: Possibility of nuclear reactor reported in Earth core
    1995: NASA hides Jupiter data confirming Iron (Fe) Sun
    1998: CSPAN***** captures NASA’s release of Jupiter data
    2001: Neutron repulsion solves the Solar Neutrino Puzzle
    2001: 178 SNO scientists report solar neutrino oscillations
    2001: Twin Towers disaster****** reunites nations to cause
    2008: Nature assigns credit for natural reactors to others
    2009: Climategate emails and documents show deception
    2012: Dr. Peter Gleick’s actions reveal AGU/NAS at work


    * Read opinions of Sir Fred Hoyle and Sir Arthur Eddington before 6 Aug 1946 [Fred Hoyle, “Home Is Where the Wind Blows,” University Science Books, 1994, pp. 153-154]. “We both believed that the sun was made mostly of iron, . . .

    ** P. D. Jose (1965) Barycentric-motion induced sunspots

    Click to access jose.pdf

    *** The Bilderberg model, Solar Physics 3, 5-25 (1968)….3….5G

    ****CNN video of 1986 Challenger disaster:

    *****CSPAN shows NASA releasing Jupiter data to confirm pre-1946 Iron (Fe) Sun:

    ******Twin Tower disaster 11 Sept 2001

    – Oliver –

    PS: Ancient advice for major battle: “Having made yourself alike in pain and pleasure, profit and loss, victory and defeat, engage in this great war and you will be freed from sin.” I.e., just do what is right and let go of the results.

  27. E.M.Smith says:

    I was going to put up a comment on a thread over at WUWT, but it got ‘comments closed’ between my start of writing and the time of hitting post. So I’m going to just stick it here instead.

    I’m not going to add much to the squabble, other than to point out that it is very hard to ‘prove a negative’ which is what this paper claims to do. At best it proves that they looked at the wrong things or that the cause is something they do not understand. I once had a Doctor say that I could not have a particular illness because he could not test for it. This is in the same range of “logic”. ( I later self treated with veterinary products and cured my “non-existent” rash… )

    Basically “I can’t see it” is not that same as “it isn’t there”.

    FWIW, the claim that the cyclicality of the sun has not been predicted is wrong. THIS solar minimum was predicted. Furthermore, Charvatova
    has found an ‘about 2300’ year cycle, in the 2402 year cycle. Her solar motion patterns match the times of grand minima AND the times that pop up on the 2400 year range.

    Interesting presentation with graphs and photos here:

    Click to access Charvatova,%20Hejda%20Aug08%20-%20A%20possible%20role%20of%20the%20solar%20inertial%20motion%20in%20climatic%20changes.pdf

    I took a crack at trying to figure out what might be going on but ran smack into some tensor calculus that I didn’t want to tackle (it’s been way too many years). The simple POV is that there are rotational / gyroscopic effects that can be quite large from even modest movements of a gyroscope, and at very low energy inputs. We use these properties to control satellites and prevent them from going into unstable modes due to gravity variations with distance. You might calculate the gravity field variation at 25,000 miles from the earth and find it ‘too small to matter’ but it is enough to either stabilize a satellite or kill it, depending on the particular design. It can be controlled with a very small input energy via spinning wheels…

    I don’t have an answer, but I admire the problem qualitatively here:

    So IMHO, no, not a ‘body blow’. Barely even a ‘swing and a miss’. I could just as easily say that I can’t calculate how a nuclear reactor works and it doesn’t have enough mass for chemistry to make much heat so they will never make much energy. Demonstration of an ignorance is not proof of exclusion.

    What it does do is demonstrate some limits and bounds, both on energy and on method, by which the actions can be effected. It narrows the space in which the “Planets Do It” folks can operate. But it leaves open some very large unexamined areas.

    As I’ve noted elsewhere, orbital resonance means that many things are coincidental in space. One, the cycles of lunar tides, clearly impacts weather on Earth. It, too, has many cycles that “accidentally” match various solar and planetary cycles. So it may well be that Earth climate cycles are legitimately tied to solar cycles, but without the sun as causal. Orbital resonance can synchronize different motions of parts of the whole, leaving ‘wiggle matching’ as a sure way to find correlations with false causality.

    But the paper cited does not ask about Earth weather, it asks about solar cycles. Left unexamined is the question of things like 1800 year lunar cycles on climate and how the orbital motions DO modulate lunar orbital cycles via orbital resonance.

    With that, I’m going to step back from the “does so – does not” argument. Just asking that folks keep an open mind that a strong weather correlation exists and that we don’t know how it works, it cold be something as simple as the lunar tidal cycle.

    ( Don’t know what ‘side’ that puts me on. I’m not on the “it can’t” side, but I’m more in the “maybe something, keep digging” middle?)

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