| Titius-bode Law |
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DISCOVERY AND HISTORY It was discovered in 1766 by Johann Daniel Titius and "published" without Attribution in 1772 by the director of the Berlin Observatory, Johann Elert Bode , thus the name. However, some say it was first proposed by Christian Wolff in 1724 . FORMULATION The original formulation was : where ''n'' = 0, 3, 6, 12, 24, 48 ..., with each value of ''n'' twice the previous value. The modern formulation is that the mean distance ''a'' of the planet from the Sun is, in Astronomical Unit s: : where ''k''=0,1,2,4,8,16,32,64,128 (0 followed by the powers of two) For the outer planets, the first term becomes more and more negligible, and the interpretation is that each planet is roughly twice as far from the sun as the last one. This leads to a weaker formulation with no Geocentric point of view and less " Ad-hocism ": ''The distance of one planet to the innermost one is about twice as much as that of the previous one.'' Here are the distances of planets calculated from the rule and compared with the real ones: 1 The Asteroid Belt has to be considered a planet in order to make something satisfy k=8. Being spread out as it is, the number taken for the distance to the Sun (2.77 AU) is actually that of the Belt's biggest asteroid Ceres , which was at one time considered a planet as well. 2 Neptune violates the law by falling halfway between k=64 and k=128. Instead, Pluto takes up the place where the next planet after Uranus is expected to be based on the "rule". However, Pluto's Status Of Planet Is Actually Under Dispute ). Here is a plot of this law against real planet distances: http://rozeta.com.pl/~jochym/tblaw.png THEORETICAL EXPLANATION There is no solid theoretical explanation of the Titius-Bode law, and it is not known whether this is just a numerical coincidence or a more fundamental Celestial Mechanics rule. When originally published, the law was satisfied by all the known planets — Mercury through Saturn — with a gap between the fourth and fifth planets. It was regarded as interesting, but of no great importance until the discovery of Uranus in 1781 which fit neatly into the series. Based on its new credibility, Bode urged a search for a fifth planet. Ceres , the largest of the asteroids in the Asteroid Belt , was found at the predicted position of the fifth planet. Bode's law was then widely accepted until Neptune was discovered in 1846 and found not to satisfy it. Currently the most likely explanation other than chance is that orbital resonance from major orbiting bodies creates regions around the Sun that are free of long-term stable orbits. Results from simulation of planetary formation seem to support the idea that laws like the Titius-Bode law are a natural consequence of planetary formation, according to the current theories in this area. Given the limits of current Telescopy , there are a decidedly limited number of systems on which Bode's law can be tested. Two of the solar planets have a number of large moons that appear possibly to have been created by a process similar to that which created the planets themselves. The four large satellites of Jupiter plus the largest inner satellite — Amalthea — adhere to a regular, but non-Bode, spacing with the four innermost locked into orbital periods that are each twice that of the next inner satellite. The whole lot are thought to be moving outward under the influence of Tidal Drag to lock to the period of the outermost large moon Callisto . The large moons of Uranus have a regular, but non-Bode, spacing. {Link without Title} Recent discoveries of extrasolar planetary systems do not yet provide enough data to test whether the rule applies to other solar systems.
With the ratios approximating 2:1, pure speculation might lead us to posit something on the order of Orbital Resonance , similar to that of the objects of the Kuiper Belt but on a much greater scale of space and time. REFERENCES External links |