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Originally Posted by tony873004
You can't have a decimal in resonance. They have to be integers. Only at integer multiples of their orbits completed will they line up again. For example, when Jupiter and Saturn are at conjunction, 1:2.5 means that after Saturn completes 1 orbit that Jupiter completes 2.5 and is on the opposite side of the Sun from Saturn. If the pattern repeats every 179 years, then you get the resonance by dividing 179 by the orbital periods:
179/11.85920 = 15.093766864544
179 / 29.657296 = 6.03561430549838
179/164.79 =1.08623096061654
None of these are integers. After 179 years, Neptune has overshot the starting position by 9%, Saturn by 4% and Jupiter by 9%. So there's a 5% difference between Jupiter and Saturn, and between Neptune and Saturn, which is where I got the value of 5% I reported.
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Thank you. What the numbers you provide show is that all three planets have overshot by an amount which brings them together again at a point one twelfth of the way further around the ecliptic. The resonances are shown by comparing the periods of each combined planetary cycle: ie Jupiter-Saturn = 19.85 years, Jupiter-Neptune = 12.78 years, and Saturn-Neptune = 35.8 years. These periods recur at 179 year intervals to within 0.2 years. At
this general science thread I provide diagrams which illustrate how Jupiter, Saturn and Neptune return to conjunction every 179 years, which seems to me to indicate a resonance. These three planets are always about 31 degrees of arc further around the ecliptic than their positions 179 years ago. These orbital JSN periods produce a clear gravitational pattern in the wave function of the solar system barycentre as shown
here.
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Saturn is 1.84 times farther from the Sun than Jupiter (9.58201720 / 5.204267). This makes its gravity (1/1.84^2) = 0.295 as strong as Jupiter's at the distance of the Sun. But Saturn is only 0.3 times as massive as Jupiter, weakening its gravity again. So at the sun, Saturn's gravity is only 0.295 * 0.3 = 0.088 times as strong as Jupiter's.
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Thank you. My understanding was that to calculate the gravitational effect of a body on another body, the mass of both was multiplied and the product divided by the square of the distance. Hence, because the sun has disproportionate mass, Saturn's effect on it is actually very close to 29.5% of Jupiter's.
(Inverse square law)