Roy Martin: How do the planets affect the Sun?

Posted: March 7, 2013 by tallbloke in Analysis, Astrophysics, Cycles, data, solar system dynamics

My thanks to Roy Martin for this guest post, which looks at possible dynamic relations between the planets and Sun which also hint at a Phi/Fibonacci connection to the tidal forces acting on the Sun:

How do the planets affect the Sun ?

By Roy Martin
Jan 5, 2013

“Knowledge is about as durable as green cheese.” anon.

The barycentric motion of the Sun and the tidal forces acting on the Sun are both caused by the motion of the orbiting planets. The first section of this note illustrates the differences between the combination of gravitational forces that cause the barycentric motion of the sun and the tidal forces acting principally on it’s surface layers. I originally intended to use the first part of this in the introduction to a report about further work done on the tidal influence of the planets on solar activity, however it led on to a few interesting, but quite unrelated observations about the synodic relationships between the planets and the José cycle, which would have been out of context, so I have put them into a stand-alone note. As far as I know there is nothing fundamentally new here, just a somewhat different perspective on some older knowledge.

There is an intricate overlapping of features in the two phenomena, and yet they create distinctly different landscapes. This note aims to describe the differences and similarities relevant to my own studies, and which are possibly relevant to other on-going investigations and discussions surrounding the mechanisms by which the planets may effect the solar cycle in particular.

There is significant scope for confusion between the potential effects of the two causes. At least since the publication of José’s 1965 paper: ”Sun’s Motion and Sunspots”, barycentric motion, or solar inertial motion (SIM), has been studied extensively. Many apparent correlations with events on earth and human activity have been identified, but most of those I have examined in any detail have failed to satisfy close scrutiny. The absence of any provable mechanism by which SIM caused by the planets can affect solar activity remains a major objection. SIM is fundamentally a whole-of-body effect, and as such none of the accelerations imposed on the Sun while orbiting the barycentre can differentially affect separate regions. Theories based on spin-orbit coupling appear to come up against the same objections.

During the same period, the possibility that tidal effects could affect solar activity was rejected and largely ignored, but in the last few years increased attention is being directed to this possibility. There is active reseach into suggested mechanisms, and in my own work I have identified close correlations between planetary induced tidal forces and the solar cycle. I now suspect that many of the correlations previously attributed to presumed SIM effects may be due to tidal effects occurring simultaneously.

We need to look at how each individual planet plays quite a different role in relation to SIM compared with tidal forces that may influence solar activity.

Figure 1. below is presented to show the relative effects of the major and minor planets, due to both the gravitational forces that cause barycentric motion, and the tidal effects which many are coming to believe are more likely to affect solar activity. The data plotted is from very simple physics, calculated using the basic formulae for gravitional and tidal forces. It is possible, even likely, that orbital eccentricity and inclination affect both to some extent, but are omitted from this analysis. I reason that if either gravitational or tidal effects are involved in modifying solar activity, it will first have to be shown and proved that the major primary forces due to one or the other are the principal cause. The individual bars represent the percentages of the total of the fully aligned planets.
Figure 1.

It can be seen from Fig.1 and Table 1. that the planets may be viewed as two overlapping groups:
Table 1.

The gravitational group includes Saturn but not Mercury. The tidal group includes Mercury but not Saturn.

The relative magnitudes show the basic differences between the two groups. Jupiter and Saturn dominate the gravitational group, and Jupiter alone accounts for 74% of the total, and the influences of Venus and Earth are also significant. How these combine to create SIM will be looked at a little closer further on. Mercury, Venus, Earth and Jupiter cause 97.8% of the tidal forces, but the component from Jupiter is only 34.7%, which is nearly matched by Venus at 33%. The relative role of Mercury changes from 2.3% to 14.6%, almost equal to that of Earth, and thus has the potential to be a significant influence on tidal effects. The tidal group will be studied in much more detail in another note.

We should note here that the planets do not exist in isolation. It is far too easy to become fixated on one of them as the sole or principal cause of an observed phenomena. Jupiter is a prime candidate for such attention because the orbital period is so close to that of the solar cycle, and it does play a big part in both sets, but in real life it is “…just a player in a rock and roll band.”

But we need to look at the basic forces in conjunction with the synodic periods between the various planets. Table 2. lists the relevant relationships, and we are immediately confronted by the problem that the network of interconnections between the gravitational and tidal planets is so complex that it can lead to the illusion that one is the cause of observed effects, when it is really the other.
Table 2.

In the gravitational group, the dominant synodic period is between Jupiter and Saturn, with a period of 19.8650 years. The 19.8650 x 9 = 178.7853 year multiple is of primary importance, because it appears to be the nominal period underlying the José cycle. I have therefore used it as a base period for comparisons. As shown in the table, the synodic periods of the major planets are all harmonically connected to the nominal 178.8 year period, the consequences of which can lead to endless discussion. Note the small differences between the 178.785 year nominal José cycle length and the nearest multiples for J-V, J-E and V-E.

The gravitational effects of Mercury, Mars, Uranus and Neptune are negligible, but are included to show that their orbits also appear to be harmonically linked to the José cycle.

I tend to scepticism when claims are made that because a value is ‘close to’ another it implies justification for causation, but here the José cycle correlations for all of the significant planets are within +/- 0.2%, and it seems to me this is too close to ignore.

Similarly, we need to be cautious about numbers like the multiples of the synodic periods, because a given number can often be factored in different ways. Should these numbers be accepted as meaningful at all? In this case the factors are all about primes and Fibonacci numbers. We have six of the early primes: 2;3;5;7;11;13, the sum of which is 41, and 2;3;5;13 are also Fibonacci numbers. The sum of the alternate primes 3;7;13 is 23. Within the solar system, such relationships are often observed, and support other observations of the exquisite mathematical balance between planetary orbitital periods. I believe they can be taken seriously.
(Note: The multiple for Mercury could also be taken as 452, with factors 113 x 22, giving the product 178.902 years. Take your pick, the difference matters little here.)

In this context the most important observation is one of the simplest, that nine J-S synodic periods are the dominant cause of the variation of the radius of the orbit of the Sun around the barycentre, as can be seen clearly in a plot of radius vs. time in Fig.2. This type of plot is a rather flat-earth way of presenting solar motion, but it is a much more explicit framework than multiple polar plots for showing the longer term temporal relationships.

Venus and Earth combine to modulate both the amplitude of the radius and the peak-to-peak timing of the nine waves within each José cycle, but the pattern is very close to an exact repeat within each cycle, suggesting a persistent synodic relationship. This repetition also continues for the previous three full cycles. The harmonics of the Venus and Earth synodics are found to form a cycle 22.38 years long, which is very close indeed to one eighth of the José cycle.
Figure 2.
Table 3.

The derivation of the 22.38 year cycle is shown in Table 3. which further extends the relationships between the synodic periods:-
With regard to Ref.1.), by reference back to the multiples in Table 2., we find that for Jupiter-Venus, 276/8 = 34.5; for Jupiter-Earth, 164/8 = 20.5, and the difference between them is 14, the multiple for Venus-Earth. And just for the fun of it, from the set of factors: (3×23)/2 = 34.5, 41/2 = 20.5, and 34.5x(2/3) = 21. The half cycle difference plus and minus from a Fibonnaci number emerges as relevant in the plots of tidal forces on the Sun – further work that I hope to write up in the not too distant future.
With regard to Ref.2.), the multiple differs very slightly from 11.0. The small correction was necessary to reconcile the 12.0037 year cycle period with the value derived from two separate studies on tidal effects. (The precise period is 0.648846 x (37/2) = 12.00365.)

Figure 3a. was drawn to illustrate the effect of combining two sine waves; the basic 19.865 year nine period cycle plus the 22.385 year eight period cycle, appropriately scaled and phased. This approximates the principal characteristics of the plot of actual solar radii for the 1722 to 1901 period in Figure 2., however beyond that it is impossible to reproduce the near chaotic characteristics of the actual orbits with any degree of accuracy.

During the three cycles centred on the start and end dates at 1722 and 1901 the Sun traces successive loops at a relatively large radius from the barycentre, then during the middle six periods the Sun moves through tight loops passing close to the barycentre, but only every second cycle. The effect of this is roughly simulated in Figure 3b. by adding a cycloid with a period of 38.2 years. This is really just a fudge-factor and can only be applied to the middle six cycles, because in reality the movement of the Sun during the start-end cycles and the middle six is somewhat different. In the former the Sun orbits the barycentre in larger loops with generally larger minimum radii, but still moving tangentially at the point of minimum radii, while in the latter the motion in the tight loops becomes almost radial to the centre of the Sun.
Figure 3a.


Figure 3b.

To summarize: the synodic periods between the planets are shared between their gravitational and tidal influneces on the Sun, but whereas the Jupiter-Saturn relationship dominates SIM, Venus-Earth-Jupiter relationships dominate the tidal effects. While some solar and terrestrial phenomena appear to correlate with SIM, the correlations are only partial and, to the best of my understanding, have no known physical connection.

I intend to cover the tidal influences more fully in later notes. They are proving to be a much more productive area of study. Suffice to say briefly in conclusion here; that tidal influences appear to correlate very closely with solar phenomena and with consequent effects on terrestrial phenomena.

As a footnote: In the work on the tidal theory there is a very significant cycle of 110.3 years. It is interesting to note that 110.3 x 1.61803(phi) = 178.48 years, within 0.31 years of the nominal José cycle period as derived above from the Jupiter – Saturn synodic.

Credit: Figure 2.) was plotted using the ephemeris derived from JPL data by Carl Smith, available at

  1. PeterF says:

    “This approximates the principal characteristics of the plot of actual solar radii for the 1722 to 1901 period in Figure 2., however beyond that it is impossible to reproduce the near chaotic characteristics of the actual orbits with any degree of accuracy.”

    Did I understand you right that you say it is impossible to do a calculations involving all planets for a period of e.g 1000 years despite all computing power available?

  2. Roy Martin says:

    “Entertainment or fact?”

    Looks entertaining, not sure if it is fact. Will have a better look tomorrow.

  3. tallbloke says:

    Peter F: Roy is saying the simple sine waves used to represent the planetary motions will go out of phase with the actual planetary motion outside the time envelope he uses. This is because the mutual perturbation between the planets, while calculable using the heavy duty equations underlying the JPL ephemeris (for example) for a period of ~6000 years (3000BC-3000AD), will affect the sine wave ‘analogy’.

  4. tallbloke says:

    Oldbrew: I used that simulator to create my avatar. 🙂
    It’s pretty good, and a lot of fun to investigate.

  5. Chaeremon says:

    PeterF said: “…calculations involving all planets for a period of e.g 1000 years…”

    This is important for research, the accurate eclipse prediction in ancient times (which is affected, if only minimal, but accumulative, by other planet’s orbits). But eclipses can take just minutes and computation is then called “incredible” iff the time of eclipse is missed.

    One critical parameter is “Values of delta T before AD 1600 pre-date the telescope and are based on historic records of naked eye observations of eclipses and occultations.” see

    That is to say: no negative feedback by accurate and trustworthy measurement “what time was it?”, no accurate eclipse prediction, and also no accurate orbits.

  6. Roy Martin says:

    PeterF says:

    “Did I understand you right that you say it is impossible to do a calculations involving all planets for a period of e.g 1000 years despite all computing power available?”

    Not quite what I meant to imply. Fig 3a. is a just simple simulation adding two sine waves. The 19.85 year sine wave is a passable way of illustrating the dominant roles of Jupiter and Saturn in creating the barycentric motion of the Sun. But while using another sine wave to simulate the modifying roles of Venus & Earth is sort of OK, it is already only an approximation. A much more complex integration of the accelerations the planets cause the Sun to undergo is needed to get results accurate enough for space navigation, which is of course what JPL do including all planets, and yes, for very long periods of time.

  7. Ninderthana says:

    Most of what is presented above is confirmation of what I have published or reported at:


    The 179 year Jose cycle appears to be embedded within the relative sidereal
    orbital periods of Venus, Earth, Mars and Jupiter as well, with:

    28 × SVE = 7 x (6.3946 yrs) = 44.763 yrs
    69 × SVJ = 44.770 yrs = synodic period of Venus & Jupiter
    41 × SEJ = 44.774 yrs = synodic period of Earth & Jupiter
    20 × SMJ = 44.704 yrs = synodic period of Mars & Jupiter

    This means that Venus, Earth and Jupiter, in particular, form alignments at
    submultiples of 179.08 years i.e.:

    ½ × 179.08 yrs = 89.54 yrs
    ¼ × 179.08 yrs = 44.77 yrs
    1/8 × 179.08 yrs = 22.39 yrs
    1/16 × 179.08 yrs = 11.20 yrs

    and the references to the VEJ tidal-torquing model at my blog site:

    However, it is good to see it presented in a different way by Roy as it helps to get
    another persons perspective.

  8. Roy Martin says:

    Ninderthana: Good, but it is nearly midnight and I am off to bed. I will put down some further comments tomorrow.

  9. Jeff Krob says:

    If I may…somethings not right. From fig. 1, it looks to show that the majority of the planetary influences on the Sun are from the planets from Jupiter to Mercury (excluding Mars, for the most part). From a post on a previous thread here @Tallbloke, there was a link to the University of Nebraska-Lincoln Astronomy Education

    which had a ‘Influence of the Planets on the Sun’ simulator which shows the 4 gas giants (Jupiter to Neptune) have the greatest influence on the position of the Sun from the barycenter.

    I would tend to agree the gas giants have more of an influence due to their mass but that is just my opinion. Where is the math to support the results in Fig. 1? Which of these two illustrations is correct?


  10. tallbloke says:

    Jeff Krob: I also thought it odd that Saturn gives only 7% ‘gravitational effect’ according to Roy’s figures. I’m wondering if Roy has calculated the gravitational force exerted by these planets on the Sun but not correctly accounted for their effect on the inertial motion.

  11. Chaeremon says:

    Jeff Krob mentioned “…the greatest influence on the position of the Sun from the barycenter.”

    I wait for 2017/2018 perhaps something comes on the radar; IIRC the gas giants return from their aphelion, except Jupiter and Saturn who begin with that around 2017/2018. I’m curious on signals when the big guys together all get closer to the Sun (and to all their inner planets).

  12. PeterF says:

    Roy Martin said: “Not quite what I meant to imply. Fig 3a. is a just simple simulation adding two sine waves.”

    ok, missed the reference to pure sine waves only. Of course that is limited.

    I am looking forward on the tidal discussion, then.

    But as striking and puzzling this numerology with Fibonacci numbers and more is, nobody has an explanation for it (yet), and until its cause can be explained, would a more direct approach be more justified? In other discussions on planetary effect – e.g. by Scafetta – power spectra of planetary motion and temperature or temperature proxy time series are compared, and other striking and puzzling results arise.

    In my mind a more direct approach would be to calculate planetary gravitation and tides backwards (a few) thousand years, and forward a few decades, and see if any structures appear that can be related to features found in temperatures (or proxies for it).

    Are the available ephemeris not good enough for that?

  13. Ulric Lyons says:

    The tidal paradigm pretty much excludes all bar Ju/Ea/Ve/Me, and it’s all fast moving stuff, which why interest in this combo has mostly been confined to those looking at weather effects and solar flares etc. While those looking at climatic scales have looked towards Jovian cycles, but with adopting the mechanistic paradigm of SIM, the Inferior planets are excluded.
    My approach has been to not limit myself with a search criteria, and to examine carefully what is actually happening, and then look to a mechanism which may explain what is observed.
    My key finding is that there is strong interaction between the dominant Inferior planets and the Superior planets, and that the positional orders of the peak configurations do not suggest gravitational mechanisms of either type.
    The Sun may not be able to be effected magnetically from the planets, but the Sun has magnetic connections to each body, and I would propose that the angular relationships of these connections could be what is producing the solar magnetic activity variations.

  14. Ulric Lyons says:

    Jeff Krob says:
    “I would tend to agree the gas giants have more of an influence due to their mass but that is just my opinion.”

    And their distance, if Jupiter was close as Mercury is to the Sun, the barycenter for the two would be only ~5,500km out from the middle of the Sun.

  15. oldbrew says:

    PeterF says:
    ‘But as striking and puzzling this numerology with Fibonacci numbers and more is, nobody has an explanation for it (yet)’

    A link to magnetism could be worth investigating. Its effects are poorly understood IMO if this NASA investigation of Mercury’s magnetic effects represents the state of the art.

    On another thread here we’re looking into a possible correlation of the relative distance between planets and the so-called golden ratio i.e. 1.618. Anyone can do the calcs in 5 minutes with the relevant data to hand. The outcome is within a few per cent of 1.618 for the smaller planets, slightly higher around Jupiter/Saturn.

  16. Bart Leplae says:

    Used this simulator to download the position, velocity, … with 30 day intervals.
    These exports are taken from the perspective of a ‘remote observer’ which differs from taking a perspective relative to the barycenter (which moves as well).

    Subsequently transformed velocity variations towards acceleration.
    And used these accelerations in: “Why does the current Sunspot Cycle stagnate?”
    The acceleration seems to affect solar magnetism which indirectly affects the solar cycle.

    Juper-Saturn have the largest impact on velocity variations.

  17. oldbrew says:

    Updating an earlier comment: re NASA research into magnetism, in particular flux transfer events (FTE)s which seems to have moved on a bit in the last few months.

    ‘The physical process that creates connections between the magnetic fields emanating from the Sun and a planet – a process known as magnetic reconnection – creates a portal through which solar plasma can penetrate the planetary magnetic field. The opening of these portals, known as flux transfer events (FTEs), takes place roughly every 8 minutes at Earth and spawns a rope of streaming plasma.

    Second commenter on the article says:
    ‘A “flux transfer event” or a “rope of streaming plasma” is in fact an electric current (birkeland current), they will find this same phenomenon connecting the Sun to all of its planets.’

  18. tallbloke says:

    Oldbrew: I respectfully suggest we move magnetic discussion to the Bullialdus/Kepler thread.

  19. oldbrew says:

    TB: no problem.

  20. Roy Martin says:

    This comment will respond to comments made by several contributors, and if I do not mention someone specifically I apologize in advance.

    I can see that the comparisons I showed in Fig.1. have not correctly shown the effects the planets have on barycentric motion. The figures are quite correct for what the figure was originally drawn to show, which are the relationships between the actual gravitational and tidal forces exerted by each planet on the sun. However, it is now obvious that some of the notes regarding the relative effects of gravitational forces are really not right. The U. of Nebraska “Influence of the Planets on the Sun” simulator referred to by Jeff Krob does show them correctly.

    Taking the clue from the simulator, I calculated the barycentric radius of the sun for each planet considered separately. A plot of those gives a static view of the results the simulator draws if each planet is selected separately, linked here:

    Jupiter, Saturn, Uranus and Neptune do indeed control most of the barycentric motion of the Sun. The basic mechanics are quite simple: For a planet of a given mass, the radius of the Sun from the barycentre is a function of the distance to the planet. Thus although Uranus and Neptune are both much lighter than Jupiter, the fact that they are also much more distant from the Sun considerably increases their relative effect on the barycentric radius of the Sun.

    At the other end of the scale, the chart shows that the effects of Venus, Earth and Mars on the radius of the barycentre are extremely small. That also seems to explain why the inner planets are observed to orbit the Sun rather than the barycentre, within very close limits.

    [Reply] Roy, thanks very much for taking the trouble to recalculate the effect of the planets on the Sun’s barycentric motion. If you’d like to have the new plot added to the main article with some explanatory text, let me know. I’ll be travelling over the next 36hrs, but I’ll try to update ASAP if you send me the text.

  21. tallbloke says:

    Roy says: That also seems to explain why the inner planets are observed to orbit the Sun rather than the barycentre

    So far as I can tell, all the planets orbit their own Sun-planet barycentre notwithstanding very small perturbations due to their neighbours direct gravitational force upon them.

    For example, Earth’s orbit is perturbed by around 8000km over a 12 year cycle due mainly to its interactions with Jupiter and Venus. This is across an orbit of 0.3×10^9km, and represents a cyclic deviation of around 0.00013% from a smooth orbit of the Earth-Sun barycentre.

    Geoff Sharp tested the Jupiter-SSB distance vs the Jupiter-Sun distance over a period which accounted for Saturn’s motion and if I recall correctly, he found that Jupiter too follows a Jupiter-Sun barycentric orbit closely. My original intuition was that the outer planets, being further away from the centre of the Sun’s gravitational field, mostly responsible for the Solar Inertial Motion themselves, and having relatively stronger mutual interactions, might deviate more and tend towards orbiting the SSB.

    I should make the time to quantify the magnitudes of deviations for each planet more exactly for myself.

  22. […] thanks again to Roy Martin who has done a substantial re-write of the paper he presented here a fortnight ago in response to the feedback he received here at the […]

  23. […] thanks again to Roy Martin who has done a substantial re-write of the paper he presented here a fortnight ago in response to the feedback he received here at the […]

  24. oldbrew says:

    One of these every 20 years should fit into the picture somewhere?

  25. tallbloke says:

    Oldbrew: yes. It’s actually around 19.86 years and Roy commented on it above. 3/2 Jupiter-Saturn synodic periods = 1/6 of the ~179 year Jose cycle.

  26. oldbrew says:

    Speaking of the Jose cycle…

    TB: FYI – for the next four days, I’m heading out into the sticks and (by tomorrow a.m.) the snow, no internet 😉

  27. tallbloke says:

    OB: Have a good trip. I like the pre-spring, it feels so full of potential.