Quantum Gravity 404.8: Continuation of 404.7 with Titus-Bode Law and Dermott's Law
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From: Osher Doctorow on 31 Jul 2010 00:26 From Osher Doctorow In Section 404.7, why did I choose the earth-moon distance as the "standard" distance? By intuition, I thought of it as our closest relevant "local" distance to Earth, the moon being quite larger than artificial satellites. But there are also two "laws" of planets and/ or planetary satellites that are relevant and that gives 1/2 or 0.50 and/or 0.44 to 0.49 as either distances or periods. The Titus-Bode Law (see Wikipedia's article of that name) gives for planetary distances "a" from the Sun: 1) a - 4 = n, where n = 0, 3, 6, 12, 24, 48, etc. Therefore: 2) Each planet's predicted distance minus 4 is 1/2 the distance of the next outer planet from the Sun (except of course for n = 0). This works quite well for Venus, Earth, Mars, Ceres (a "dwarf" planet), Jupiter, Saturn, Uranus in that order outward from the Sun (Mercury has n = 0). For Neptune and Pluto individually it is wrong, but to my recollection it is correct for their average. The "Dermott's Law" (see Wikipedia's article of that name online) is for the orbital period T(n) of major satellites (moons) n (nth from the Sun) orbiting planets in the solar system, and is: 3) T(n) = T(0)C^n, where n = 1, 2, 3, 4, ..., and T(0) and C depend on whether the system is Jovian (around Jupiter), Saturnian, or Uranian. 4) For Jovian, T(0) = 0.444 days, C = 2.03. 5) For Saturnian, T(0) = 0.462 days, C = 1.59. 6) For Uranian, T(0) = 0.488 days, C = 2.24. For Jupiter, the 4 innermost moons have orbital periods each twice that of the next inner moon, although as a whole it is called a Non- Bode spacing. These or their next neighbor's ratio correspond well to 1/2 and 0.43 from the previous post as the Probability of the Repulsive set. Osher Doctorow
From: Osher Doctorow on 31 Jul 2010 00:32 From Osher Doctorow Technically, a is the semimajor axis of each planet's elliptical orbit, since a planet's distance changes along an ellipse (also ellipses precess, but this gives the idea). Osher Doctorow
From: Osher Doctorow on 31 Jul 2010 01:17
From Osher Doctorow It's the Titius-Bode Law or Bode's Law, not the Titus-Bode Law. Osher Doctorow |