Quote:
Originally Posted by tony873004
I don't see 0.1% when I run the numbers. Using orbital periods of 11.85920, 29.657296, 164.79 years for Jupiter, Saturn & Neptune respectively, I see an approximate 15:6:1 resonance. But the real numbers are
15.093766864544 : 6.03561430549838 : 1.08623096061654
which miss a perfect resonance by about 5%. This will certainly cause drift in the plot.
|
Thanks tony873004, my statement was too condensed. What I meant was that Jupiter-Saturn meet nine times every 178.7 years, while Saturn-Neptune meet five times every 178.9 years, and Jupiter-Neptune meet 14 times every 178.9 years. Considering this period as a cycle, JS drifts against SN at a rate of 0.1% per cycle (0.2 years per 180). btw your numbers, ~ 12:30:165 look more like 1:2.5:14 than 1:6:15
Quote:
|
Here's 2000 years of the planets sans Jupiter curving the path of the center of the sun. It's pretty busy, and if I let it run 10s of thousands of years, it would be a solid yellow circle (or perhaps a doughnut as it looks like the middle won't get filled in) because of the width of the plotted line.http://orbitsimulator.com/BA/ssbcsj2k.GIF
|
Thanks! This looks to have over 100 loops, so is already busy. Your picture showing only three loops did not show what would happen when the loops repeat the cycle, which a diagram with about ten or twenty loops would do.
Based on material presented here, I have a further question. Is my understanding of gravity as presented below correct?
The
attached picture illustrates the relative gravitational effect of the four gas giant planets at the sun. I explain the mathematics here. These four waves are the main decomposed sine functions that produce the pattern of the solar system barycentre. The wavelengths correspond to the orbital period of each gas giant, while the amplitude shows the Jupiter function multiplied by the gravity of each planet at the sun, as per the following table, calculated by the inverse square law. This calculation indicates that as a proportion of Jupiter’s gravity, Saturn’s gravitational effect on the sun is 30% as strong, Uranus is 4.6% and Neptune is 5.4%. Eight hundred years are presented.
Code:
Planet Distance from sun (km m.) Mass (x10^22kg) Distance (J=1) Planetary Gravity on Sun (Jupiter=1) Orbital Period (Days)
Mercury 58 33 0.07455 0.00017368 88
Venus 108 487 0.138817 0.00256316 224.7
Earth 150 598 0.192802 0.00314737 365.25
Mars 228 64.2 0.293059 0.00033789 687
Jupiter 778 190,000 1 1 4331.573
Saturn 1,429 56,900 1.836761 0.29947368 10832.33
Uranus 2,871 8,690 3.690231 0.04573684 30799.1
Neptune 4,504 10,280 5.789203 0.05410526 60189.55
Pluto 5,913 1.49 7.600257 0.0000078 90600
Note: Sun (x10^30kg) 1.9891 0
The planetary gravity at sun is calculated by mass of planet x mass of sun ÷ Distance squared ÷ Jupiter result