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Thread: Sun and Barycentre Period

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    Sun and Barycentre Period

    A paper on the sun’s motion http://adsabs.harvard.edu/full/1965AJ.....70..193J by Paul D. Jose published in 1965 in the Astronomical Journal states “the variation in the motion of the sun around the center of mass of the solar system has a periodicity of 178.7 years.”

    In researching this topic, I have found indication of a possible small error in Jose’s calculation, with a strong periodicity at 178.86 years in the NASA JPL Horizons calculations of the distance of the sun from the barycentre over 6000 years. I am interested to seek comment on my method for deriving this figure, and help in explaining the 0.16 year difference from Jose’s figure.

    My attached charts show my results. The first chart, showing Solar System Barycentre Variance in Solar Distance, compares the change in solar distance to the SSB over different time periods, ranging from one year to 244 years. The resulting line has a clear minimum at 179 years, and a clear axis of symmetry at 89.5 years, indicating periodicity at 179 years. It shows that after 179 years, the variance in distance is 7% of the peak variance. The oscillation in the chart matches the Jupiter-Saturn 20 year cycle, with variance greatest at points separated by 10, 30, 50 etc years and smallest at points separated by 20, 40, 60 etc years.

    The 179 year minimum occurs when Jupiter, Saturn and Neptune are at the same relative position, which makes sense since these three planets have the biggest effect on the SSB. The very clear axis of symmetry in the graph at 89.5 years reflects the fact that if these three planets come together every 179 years, their ‘outward’ and ‘inward’ journeys on that cycle will be close to mirror images.

    In seeking finer resolution of the observed 179 year period, my second chart indicates a minimum, and therefore an average periodicity, at 178.86 years. My method for this calculation was to use the JPL data with granularity 0.27 years to find the average difference for periods from 177 to 194 years, producing the following table.

    Code:
    Average Variance in Distance from Sun to SSB (Solar Radii)	Years
    0.252923908	177.1379
    0.216642582	177.4112
    0.179511942	177.683
    0.141957922	177.9549
    0.104649252	178.2349
    0.070030527	178.5054
    0.047409704	178.78
    0.052477895	179.0573
    0.081795385	179.3306
    0.118153163	179.6024
    0.155814897	179.8743
    0.193518583	180.1489
    0.230623183	180.4221
    0.266936145	180.694
    0.302168912	180.9658
    0.336327244	181.2445
    0.455907453	194.9303
    The minimum at this level of detail is 178.78. Plotting the data and extending the arms of the curve gives a minimum of 178.86, which also matches my previous research calculating the period from the difference between turning points in the JPL graph.

    I would be grateful for advice on best mathematical method to calculate the exact minimum of the curve that best fits to the above data. I tried this using the following websites but could not get a close enough curve. https://mycurvefit.com/ https://www.derivative-calculator.net/https://www.symbolab.com/solver/step-by-step/

    My reason for thinking that 178.86 is more likely than Jose's 178.7 is based on my previous analysis of the spectral power. Decomposing the JPL data by Fourier Transform shows that components with period multiples just slightly more than 179 provide 33% of the wave power, balancing the 41% of the wave power from the multiple of the Jupiter-Saturn cycle at 178.67 years.

    I posted on this a few years ago at https://forum.cosmoquest.org/showthr...69#post2057269 and am now posting again because this new research validates and expands my observation of a stable 178.86 year SSB wave function.

    Robert Tulip
    Attached Images Attached Images

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    You're contrasting your value of 178.86 years with his value of 178.7 years, and your granularity is .27 years?

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    Quote Originally Posted by grapes View Post
    You're contrasting your value of 178.86 years with his value of 178.7 years, and your granularity is .27 years?
    Yes. The input data produces curve points separated by 0.27 years, synthesising 6000 years of the NASA calculation. The minimum point on the curve can be calculated to a far more precise value than this range.

    It is like if you have a parabola with points (-3,9), (-1,1), (8,64), you can calculate the minimum point (0,0).

    I had another go at fitting the curve, and came up with the attached, showing how 178.7 is well short of the turning point, which is clearly between 178.85 and 178.9, as the two arrows indicate. My calculation from two separate methods was 178.86 as shown, at the turning point of this curve just using visual inspection.
    Attached Images Attached Images

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    I see how you're determining the end-of-cycle point, but how did you determine the starting point? The graph starts out so much lower.

    O, I see. You've taken your higher Fourier components and combined them into a synthetic curve, which then essentially starts with all the planets together on the same side of the sun. That's your "zero" point. Then you determine your period by the distance (time) to the next extreme low point (which you have interpolated).

    ETA: However, that distance is going to change over time. Run it out ten or twenty more iterations--you just have to calculate the values around the suspected low points, maybe 4000 years from now. I suspect that the average value will tend towards a multiple of the period of the Jupiter-Saturn component, since that is clearly the dominant one. Probably the value that appeared in the article was derived from the periods of Jupiter and Saturn. Using ( https://nssdc.gsfc.nasa.gov/planetary/factsheet/ ) Jupiter period of 4331 days and Saturn period of 10747, we get 10747*4331/(10747-4331), 7254.56 days, or divided by 365.242 times nine periods (very close to 165 years, the period of Neptune) is 178.76 years. Looking at the article, it seems they use 178.77, so maybe that's how they got it.

    OK, looking at that NASA chart I linked to above, those periods are tropical not sidereal, these webpages ( https://nssdc.gsfc.nasa.gov/planetary/planetfact.html ) from the same website make the distinction, and the sidereal values are 4332.589 and 10759.22, and the calculation is 10759.22*4332.589*/(10759.22-4332.589), 7253.455 days, times nine periods is 178.73 years.
    Last edited by grapes; 2018-Jan-14 at 10:12 PM. Reason: ETA

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    Calculation Method

    Quote Originally Posted by grapes View Post
    I see how you're determining the end-of-cycle point, but how did you determine the starting point? The graph starts out so much lower.
    Assuming you are speaking about the first graph, with file name SSB Variance 179 yr.png, and showing Solar System Barycentre Variance in Solar Distance over 244 years.

    My method for producing this graph was as follows.
    1. Obtain 22,000 data points from NASA JPL Horizons showing calculated distance from the sun to the SSB over 6000 years from 3000 BC to 3000 AD.
    2. Extract from this 4096 annual data points, noting that the SSB-sun vector change over one year is smooth and regular.
    3. Tabulate every difference in vector over a specified time gap. At points separated by 0 years the difference is 0, which is why the graph starts at 0. At points separated by one year, the difference is calculated by averaging the differences between all data points separated by one year, giving a result of 0.14 solar radii.
    4. This process is repeated iteratively for every annual gap, 2, 3, … 244 years. For example at the observed chart minimum point (not counting zero), 179 years, the difference is calculated by averaging the differences between all data points separated by 179 years. This figure is 0.046 solar radii by my calculation. So any two sun-SSB vectors separated by 179 years will on average differ by 0.046 solar radii, one third the difference between points separated by one year, and 7% of the maximum average difference of 0.7 radii.
    5. Redo the above using all 22000 data points to calculate the average vector between 177 and 181 years (with 194 as outlier) with granularity 0.27 years to produce second graph.
    6. Interpolate the minimum point of this second graph as the axis of symmetry between its arms.

    It is very interesting to me that the first curve, with annual data to 244 years, shows the change in SSB vector as such a smooth and symmetrical pattern with strong periodicity driven by the gas giant planets.

    The difference between my calculation of the SSB period, 178.86 years, and Jose’s 178.7 years, is 365.25 x 0.16 = 58.44 days.
    Quote Originally Posted by grapes View Post
    O, I see. You've taken your higher Fourier components and combined them into a synthetic curve, which then essentially starts with all the planets together on the same side of the sun. That's your "zero" point. Then you determine your period by the distance (time) to the next extreme low point (which you have interpolated).
    No, it is not Fourier components. It is just average differences in distance. It doesn’t start with all the planets together, which would pull the SSB more than a solar radius out of the sun, but just starts at the difference between any point and itself, zero, as explained above.

    There is no interpolation in this initial chart. But in the second chart, file name SSB variance 178.86 years.png, I interpolate the theoretical minimum point of the curve of best fit, which I then show again at the Fit My Curve picture in my second post.

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    If Jose was using a different data set, I would say the results are in remarkably good agreement, when you consider that the waveform only roughly repeats from one cycle to the next. After all, the planets' periods are not small integer multiples of one another and the orbits have significant eccentricity.

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    Quote Originally Posted by Hornblower View Post
    If Jose was using a different data set,
    That looks likely since his paper is from 1965 and the JPL analysis of the SSB is more recent.
    Quote Originally Posted by Hornblower View Post
    I would say the results are in remarkably good agreement,
    Yes true, which means this is a revision. I have not been able to find any other references except false ATM claims that there is no regular SSB cycle at all. It seems the main interest in Jose’s paper was just in relation to prediction of sunspot cycles.
    Quote Originally Posted by Hornblower View Post
    when you consider that the waveform only roughly repeats from one cycle to the next.
    Not true that the repetition is only rough. The repetition from one 179 year cycle to the next is very close, with only a slow drift in the shape of the wave at period of about 1000 years.
    Quote Originally Posted by Hornblower View Post
    After all, the planets' periods are not small integer multiples of one another
    The integer multiples occur around the 179 year point, which is within 0.5 years of 9 x JS, 5 x SN, 14 x JN and 13 x JU.
    Quote Originally Posted by Hornblower View Post
    and the orbits have significant eccentricity.
    Yes, that is a very good point to raise. I am sure eccentricity is a factor in the millennial drift of the wave form, but doubt it makes much difference at the 179 year comparison between successive periods.

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    Quote Originally Posted by Robert Tulip View Post
    That looks likely since his paper is from 1965 and the JPL analysis of the SSB is more recent. Yes true, which means this is a revision. I have not been able to find any other references except false ATM claims that there is no regular SSB cycle at all. It seems the main interest in Jose’s paper was just in relation to prediction of sunspot cycles. Not true that the repetition is only rough. The repetition from one 179 year cycle to the next is very close, with only a slow drift in the shape of the wave at period of about 1000 years.The integer multiples occur around the 179 year point, which is within 0.5 years of 9 x JS, 5 x SN, 14 x JN and 13 x JU. Yes, that is a very good point to raise. I am sure eccentricity is a factor in the millennial drift of the wave form, but doubt it makes much difference at the 179 year comparison between successive periods.
    Very close but not exact, with changing shape from one cycle to the next. Multiples close to but not exactly small integers. That is my idea of being roughly periodic. You and I appear to have different ideas of what roughly means. So be it.

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    Quote Originally Posted by Hornblower View Post
    Very close but not exact, with changing shape from one cycle to the next. Multiples close to but not exactly small integers. That is my idea of being roughly periodic. You and I appear to have different ideas of what roughly means. So be it.
    Here is a diagram of the SSB wave function showing how close the shape is from one 179 year SSB cycle to the next. There are almost no visible gaps between successive lines. The drift in shape occurs over much longer time.
    Attached Images Attached Images

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    Why are you not looking at a circular plot as posted in the other thread or compare it with the planets which separates out the effects of Jupiter and Saturn and the lesser effects of all the other planets? You seem to be finding the effect of Neptune's orbit for example which lines up with Jupiter, Saturn about every 170 years ( that's an approximation from memory) it is also messed up a bit by pluto's weird orbit.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by Robert Tulip View Post
    Here is a diagram of the SSB wave function showing how close the shape is from one 179 year SSB cycle to the next. There are almost no visible gaps between successive lines. The drift in shape occurs over much longer time.
    At that image scale with no coordinate grid lines I cannot read the interval between successive crests with any certainty.

    Is there some variation from one cycle to the next in the interval between successive crests? If not, then why jump through a lot of curve fitting hoops to get a period?

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    This is silly in my opinion, the biggest drivers are Jupiter and Saturn and they conjunction every 11 years or so and then a lesser driver is Neptune with a slower orbit which sometimes also conjunction Jupiter and Saturn. All predictable and so no surprise that you find an extreme point depending on how many years you take into account. What point are you seeking? The regular periods are altered as you would expect by the other planets. Either with or opposing the big ones.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by profloater View Post
    This is silly in my opinion, the biggest drivers are Jupiter and Saturn and they conjunction every 11 years or so and then a lesser driver is Neptune with a slower orbit which sometimes also conjunction Jupiter and Saturn. All predictable and so no surprise that you find an extreme point depending on how many years you take into account. What point are you seeking? The regular periods are altered as you would expect by the other planets. Either with or opposing the big ones.
    And don't forget Uranus.

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    Quote Originally Posted by Hornblower View Post
    At that image scale with no coordinate grid lines I cannot read the interval between successive crests with any certainty.
    The method to produce this diagram was to take the NASA Sun-SSB data over 6000 years, divide it into 178.9 year segments, and stack these segments on top of each other. This form of presentation came from the late Carl Smith. It is a way to show the speed of drift in the SSB wave form. When there is no white space between two lines, the interval between successive crests, defined as the variance in solar vector over 178.9 years, is negligible. White points between lines appear when the shape of the curve is changing over centuries from a local concavity to convexity. However, the small number of these white points illustrates the stability of the wave, and that its pattern is regular rather than rough. My interpretation of the data is that the stability comes from the interaction of Jupiter, Saturn and Neptune as the main drivers of the SSB position with respect to the sun in its repeating 178.9 year pattern, while the occasional faster periods of change shown by the few white points between the lines may come from the influence of the planet Uranus.
    The purpose of this thread is to quantify the interval between successive crests, so I appreciate your putting the problem in those terms. As per the explanation in the opening post, overall the variance between the vertically connected points in this graph of 6000 years of data is actually 7% of the random difference between the length of any two SSB-sun vectors. While 7% may seem a lot, it is only enough to produce the slow millennial drift seen in the wave form, which overall has a strong orderly stability. Its nine subpeaks are caused by the Jupiter-Saturn 20 year cycle and each successive line is strongly similar to the preceding and succeeding wave forms.
    Quote Originally Posted by Hornblower View Post
    Is there some variation from one cycle to the next in the interval between successive crests?
    Yes, as per my opening post, this variation is 7% of random, ie very small. In addition, this 7% variation is itself orderly, reflecting directional patterns that cause the gradual change of the shape of the wave over thousands of years.
    Quote Originally Posted by Hornblower View Post
    If not, then why jump through a lot of curve fitting hoops to get a period?
    The curve fitting exercise in my second post was purely designed to illustrate the method to quantify the exact SSB period and to explain how the data granularity can produce a more exact result. As I use the curve fit to show, supporting the initial method of analysing the axis of symmetry around 179 years, the 1965 close estimate by Jose of 178.7 years was out by two months, and the best estimate of the actual SSB wave period is 178.86 years.

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    The exact conjunction of all the planets is very rare and the same is true of groups of conjunctions so the roughly 178 year pattern will not exactly repeat, I don't know if it ever does and the spiral diagram of the relative positions of the sun centre and barycentre illustrates the 2D complexity, let alone the 3D complexity. I have been interested in the tidal effects these movements might and indeed must cause inside the sun. The recent pictures of Jupiter and its vortices shows how the moons stir Jupiter, plus the internal heat, so Jupiter is like an analog of the sun situation.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    If we are interested in the possibility that the planets might have a physical role in the Sun's activity, let's avoid falling into the trap of thinking the barycentric displacement of the Sun is the key quantity. Any physical stress on the Sun is in the form of tidal stretch, and for any given planetary mass this falls off as the cube of the distance to the planet, while the barycentric loop increases with distance. A remote planet puts greatly reduced gravitational action on the Sun but keeps it up a very long time, thus causing the Sun to move in a relatively large loop.

    The relative amounts of tidal stretch are as follows:

    Mercury 0.8 units 12% of total
    Venus 2.5 37
    Earth 1.0 15
    Mars 0.03 <1
    Jupiter 2.3 34
    Saturn 0.1 1
    Uranus 0.002 --
    Neptune <0.001 --

    These are for mean distances. Note that Venus exceeds Jupiter's average amount, and that Saturn contributes less than the amount that Mercury varies in its highly eccentric orbit. Let me add that any two planets will raise the same amount of spring tide when on opposite sides of the sun as when in conjunction on the same side, regardless of where the overall barycenter is. For this problem, assuming the tidal action has any effect on the circulation of the Sun's material, my inclination is to concentrate on the first three inner planets and Jupiter and ignore everything else. It is my opinion that the barycentric excursion is merely a mathematical curiosity when analyzing action in and very near the Sun. For gravitational action on Voyager 2 and outlying comets and KBOs, by all means take it into account.

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    Quote Originally Posted by Hornblower View Post
    If we are interested in the possibility that the planets might have a physical role in the Sun's activity, let's avoid falling into the trap of thinking the barycentric displacement of the Sun is the key quantity. Any physical stress on the Sun is in the form of tidal stretch, and for any given planetary mass this falls off as the cube of the distance to the planet, while the barycentric loop increases with distance. A remote planet puts greatly reduced gravitational action on the Sun but keeps it up a very long time, thus causing the Sun to move in a relatively large loop.

    The relative amounts of tidal stretch are as follows:

    Mercury 0.8 units 12% of total
    Venus 2.5 37
    Earth 1.0 15
    Mars 0.03 <1
    Jupiter 2.3 34
    Saturn 0.1 1
    Uranus 0.002 --
    Neptune <0.001 --

    These are for mean distances. Note that Venus exceeds Jupiter's average amount, and that Saturn contributes less than the amount that Mercury varies in its highly eccentric orbit. Let me add that any two planets will raise the same amount of spring tide when on opposite sides of the sun as when in conjunction on the same side, regardless of where the overall barycenter is. For this problem, assuming the tidal action has any effect on the circulation of the Sun's material, my inclination is to concentrate on the first three inner planets and Jupiter and ignore everything else. It is my opinion that the barycentric excursion is merely a mathematical curiosity when analyzing action in and very near the Sun. For gravitational action on Voyager 2 and outlying comets and KBOs, by all means take it into account.
    Actually, because the sun is fluid, a point mass on the sun is being attracted toward say Jupiter by Newtonian gravity inverse distance squared as the sun spins, not uniformly as a solid would, but at different rates. This is like the oceans on earth pulled sideways by the moon (and sun) however the Suns radial heat flows are greatly complicated and dominated by magnetic forces on the plasma,. My idea was that the variation of the tidal effect as the sun spins disrupted radial flow but annoyingly the Jupiter effect swing s from in phase to out of phase with the sunspot cycle. So I don't know whether that forcing has an effect as a damped oscillation.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by profloater View Post
    Actually, because the sun is fluid, a point mass on the sun is being attracted toward say Jupiter by Newtonian gravity inverse distance squared as the sun spins, not uniformly as a solid would, but at different rates. This is like the oceans on earth pulled sideways by the moon (and sun) however the Suns radial heat flows are greatly complicated and dominated by magnetic forces on the plasma,. My idea was that the variation of the tidal effect as the sun spins disrupted radial flow but annoyingly the Jupiter effect swing s from in phase to out of phase with the sunspot cycle. So I don't know whether that forcing has an effect as a damped oscillation.
    My bold. That is what tidal stretching is all about, that is, the difference between the gravitational "pull" on the near side and the far side. It drops off as the cube of the distance, not the square, which explains why the giant planets seem so weak compared to the inner terrestrials. The lack of correlation between the position of Jupiter and the sunspot activity suggests that the effect of the tidal action is too slight to affect the circulation of the Sun's innards with their tangles of magnetic fields.

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    Brace yourselves for just how feeble the tidal action of the planets on the Sun really is. I estimated that the Earth's component will elongate the Sun by about a trillionth of its diameter, or roughly a millimeter in over a million kilometers. Of course I did not do a rigorous equipontential surface calculation because I don't have that kind of knowhow, but I did a sanity check with the same calculation for the Earth and Moon, and my result was about the same order of magnitude as the tides we actually observe. With all of the planets and the Sun in syzygy, giving the ultimate compound spring tide, we get a few millimeters. I would say the physical effect on the Sun in comparison with its Coriolis effect and magnetic entanglements is utterly negligible.

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    That's an interesting fun Sun fact for 1 mm!
    We know time flies, we just can't see its wings.

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    What is the comparable figure for the Moon's or Sun's tidal effect
    on the Earth? Something like half a meter or so?

    -- Jeff, in Minneapolis
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    "I find astronomy very interesting, but I wouldn't if I thought we
    were just going to sit here and look." -- "Van Rijn"

    "The other planets? Well, they just happen to be there, but the
    point of rockets is to explore them!" -- Kai Yeves

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    Yes that is right for the normal radial tidal movement which is tiny. But I propose that you miss the tangential point for fluids just like the ocean tides which are sideways accelerations at constant radius. The gravity pull integrates up for approximately the quater turn of the sun, then negligible for another quarter turn , then it reverses. I am not talking about the tiny radial lift which is negligible compared with the gravity of the main body, sun or earth. It's a tiny pull maintained for a long time and not resisted in a fluid while, of course it is resisted by a solid. Fluids accelerate and pick up velocity and Coriolis applies too.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Numbers, taking G as 6.67 10^-11, Jupiter mass and distance 1.9.10^27 kg 778.10^6 km,
    Using Newton
    The force on one kg is 2.10^-3 N
    Acceleration same in m/s^2
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    See this paper from Cambridge University:

    https://www.google.com/url?sa=t&rct=...sYZ8o7Ky4LhKWq

    Click on the link, and then on the PDF tab that appears in lower left corner.

    The author's rigorous calculation of an equipotential displacement in a fluid Earth-sized body gave the same order of magnitude as my oversimplified rough-and-dirty estimate. Thus I stand by my estimate for the Sun and my expectation that physical consequences of the tides raised by the planets will be vanishingly small.

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    Oh dear, I hate to disagree but the tidal calculation using the near and far side is not what I am talking about . that radial tidal bulge along the two body centre line is indeed tiny.
    I hope I can explain again.
    If we consider a particle at the surface, free to move at constant radius because it is floating, it sees a sideways gravitation pull toward, let's say just one distant body for moment, Newton gives us the equation just as that paper does but we do not need to consider r.
    I choose to consider a particle at the extreme outside, ninety degrees from the centre line between the bodies. So this small force is at right angles to the main gravity force holding the particle to the body.
    That particles sees an inverse square sideways force and it is free to move sideways toward the distant body.
    The earth case is easier and it was Euler who spotted this important way to analyse the tides.
    The major tidal force is the effect of those tangential accelerations as the earth rotates.
    The sun case is obviously more complex because a gas is even freer than a water ocean and it churns so I accept the tides may still be insignificant, but not so insignificant as that cube of the distance suggests.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Maclaurin used Newton's theory to show that a smooth sphere covered by a sufficiently deep ocean under the tidal force of a single deforming body is a prolate spheroid (essentially a three-dimensional oval) with major axis directed toward the deforming body. Maclaurin was the first to write about the Earth's rotational effects on motion. Euler realized that the tidal force's horizontal component (more than the vertical) drives the tide. In 1744 Jean le Rond d'Alembert studied tidal equations for the atmosphere which did not include rotation.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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