Posted: Sat Nov 05, 2011 12:34 pm
The other ratios are also interesting. Applying the Titius Bode law to the 'empty' space between Jupiter's and Mars' orbits, you get 2.8 applying one of Kepler's laws to it (cube of the distance (in AE) = square of the orbit period (in years) you get 4.685. The ratio to Jupiter's orbital period is 2:5. The same is the case if Jupiter's orbital period is calculated according to Titius Bode law. I also compared it with Mars' period according to Titius Bode and got ca. 3:7. Mars' actual orbit deviates somewhat from the rule and gives a resonance of 2:5 to the main belt. Both these resonances are present in the Kirkwood gaps, but it should be noted that the wikipedia diagram is only about ratios to Jupiter. Ratio of (the real orbits of) Mars to Jupiter is 1:6.3(close to 2.5*2.5=6.25).zoidsoft wrote:By destroying the planet lying between Jupiter and Mars, it went from the visible to the invisible. What might that suggest about the predominating realm it now operates in? Of course the 3:1 ratio has a special place in sacred geometry...
For absence of a planet in the 17th century, Kepler got an elegant solution. Kepler discovered that the places between the orbits could be related with the five platonic solids and related the place between Mars' and Jupiter's orbit with the tetrahedron. http://upload.wikimedia.org/wikipedia/c ... stem-1.png http://en.wikipedia.org/wiki/Johannes_K ... ographicum
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I referred to it in the Pluto thread but here's something that might indicate the early use of Uranus as Aquarius' ruler. Raphael in 1828: "As yet there are no peculiar houses assigned him, but we have reason to think (from several thousand observations) that the sign Aquarius(italics Raphael's) is one wherein he much delights; .. " http://books.google.nl/books?id=u4RF3OL ... el&f=false page 71.