Quote:
Originally Posted by Robert Tulip
Attached picture shows the solar system as a set of sine waves mapped on a cylinder.
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I like your sine wave diagram actually. Brings out orbital resonance quite clearly. Unfortunately, I went and did some reading, and it turns out that most orbital resonances involving planets are illusions. At least according to
wiki:
Quote:
A number of near-integer-ratio relationships between the orbital frequencies of the planets or major moons are sometimes pointed out. However, these have no dynamical significance because there is no appropriate precession of perihelion or other libration to make the resonance perfect.
Such near-resonances are dynamically insignificant even if the mismatch is quite small because (unlike a true resonance), after each cycle the relative position of the bodies shifts. When averaged over astronomically short time-scales, their relative position is random, just like bodies which are nowhere near resonance.
For example, consider the orbits of Earth and Venus, which arrive at almost the same configuration after 8 Earth orbits and 13 Venus orbits. The actual ratio is 0.61518624, which is only 0.032% away from exactly 8:13. The mismatch after 8 years is only 1.5° of Venus' orbital movement. Still, this is enough that Venus and Earth find themselves in the opposite relative orientation to the original every 120 such cycles, which is 960 years. Therefore, on time-scales of thousands of years or more (still tiny by astronomical standards), their relative position is effectively random.
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BUT, luckily for you, it goes on to say:
Quote:
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The presence of a near resonance may reflect that a perfect resonance existed in the past, or that the system is evolving towards one in the future.
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As for your 3D attempts, I think you're running into the same problems as I had with mine (
see above post). You need a 3D
display to fully bring out their advantages. On a 2D surface, it just looks confusing. Stick to 2D as much as possible is my advice.