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As transits of Venus come in pairs, each separated by 8 years, wouldn't that imply an accurate ratio between Earth's and Venus' revolution period? I've found the ratio to be about 0.681. I presume one could see a resonance of 2/3 in that number, but as other resonances in our solar system as for example Thethys and Enceladus (4:3) are far more accurate, could it be "just" coincidental? And if so, why the regularity in the transits?

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Quoting http://eclipse.gsfc.nasa.gov/transit/catalog/VenusCatalog.html

"When a transit of Venus occurs, a second one often follows eight years later. This is because the orbital periods of Venus (224.701 days) and Earth (365.256 days) are in an 8 year (2922 days) resonance with each other. In other words, in the time it takes Earth to orbit the Sun eight times, Venus completes almost exactly thirteen revolutions about the Sun. As a result, Venus and Earth line up in the same positions with respect to the Sun. Actually, the two orbital periods are not quite commensurate with each other since Venus arrives at the eight year rendezvous about 2.45 days earlier that Earth. After the third eight-year cycle, Venus arrives too early for a transit to occur."

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  • $\begingroup$ Why is NASA describing this as a "resonance" when clearly it is just coincidentally the case that the ratio is close to 13:8? $\endgroup$ – ThePopMachine May 18 '15 at 18:21
  • $\begingroup$ If you google "resonance", the first hit (the one that doesn't even have a link apparently) gives definition 4 for astronomy as "the occurrence of a simple ratio between the periods of revolution of two bodies about a single primary." Also en.wikipedia.org/wiki/Orbital_resonance $\endgroup$ – barrycarter May 18 '15 at 20:32
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    $\begingroup$ 13:8 is neither a simple ratio, nor it is even exactly 13:8. They are using the term wrong. Resonance implies that the items are interacting (in this case through gravity) to stably maintain a fixed ratio. $\endgroup$ – ThePopMachine May 19 '15 at 14:54
  • $\begingroup$ Well, the definition just requires the "occurrence" of a ratio, not a reason for it, but, as you point out, it's not true resonance. Take it up with NASA, I guess :) $\endgroup$ – barrycarter May 19 '15 at 16:15
  • $\begingroup$ Just for future readers' sake and for accuracy: The Wikipedia page you referenced gives this definition: "In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers." $\endgroup$ – ThePopMachine May 19 '15 at 17:14

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