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Originally Posted by Hornblower
Here are some of the numbers I calculated. _____Mass (Earth = 1)__Torque (Jupiter = 1)_________Barycenter displacement (Jupiter = 1) Sun___333,000______________147,000____________ Moon____.0123______________326,000_____________ Mercury____.04__________________.018_____________. 00001 ______________________Max.__Mean____Min Venus______.82_________17___.363____.071_________. 0003 Mars________.11_________.821___.049___.003________ .0001 Jupiter_____318_________2.28____1.00___.52________ _1.00 Saturn______95__________________.048_____________. 548 Uranus______15__________________.0009____________. 169 Neptune_____17__________________.0003____________. 312.
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Thanks Hornblower, this sets a quantitative context for my argument.
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The large amounts of barycenter displacement from the three outermost planets made the familiar 179-year pattern clearly visible, but look how tiny the corresponding torque shares are compared with Jupiter. For a remote outer planet of any given mass, the barycenter displacement is proportional to its distance from the Sun, but its precession-inducing torque on Earth is inversely proportional to the cube of the distance. On a graph of this torque the 179-year cycle would be virtually invisible.
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You have showed that Neptune and Saturn have miniscule direct causal effect on the precession period. This falsifies the hypothesis that the outer planets are a main direct causal factor governing the precession period. It is great to set the discussion in a quantitative context. However, it does not address my observation that these harmonised cosmic patterns participate in a system-wide resonance period of 179 years, as does the earth.
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Meanwhile Venus packs a wallop at each inferior conjunction, peaking about 17 times Jupiter's average amount. Mars comes close to Jupiter at close oppositions.
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This gives the data behind
Warren Platts earlier comment that torque means Venus is a much bigger contributor to the precession period than Saturn, Uranus and Neptune. Warren also pointed out there are 112 Venus-Earth cycles in 179 years. I think this suggests the Venus torque is a strong regulator for the precession period. This Venus cycle is in common ratio with cycles of the outer planets, all of which share a common pulse period of 179 years. Considering planets as like
regulators, such as on a
steam engine, the overall harmonic phasing of the system remains a scientific issue open to further research.
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Clearly, Venus, Mars and Jupiter are the heavy hitters, and their effects are very much lightweights compared with those of the Sun and Moon. I stand by my arguments in a prior post that even relatively strong torque pulses would not shepherd the precession rate into a resonance, and the effects of the tiny magnitude of the pulses from the outermost planets appear to be vanishingly small.
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Thanks for the good summary. My view is that your finding on Venus did indeed show a relatively strong torque pulse that WOULD shepherd the precession rate into a resonance. Essentially, we have Venus buzzing by us every just under phi years, a period in quite precise resonance to the Jupiter-Saturn-Neptune cycle over 179 years. So, there are a set of related harmonic ratios in the solar system, with both gravity and torque producing events which share a 179 year period. I am asking if there is some underlying harmonic resonance which combines gravity and torque in complex cycles.