Two French scientists issued articles in “Astronomy and Astrophysics” (282, pages 262 to 269) arguing that the so-called Titius-Bode law, may be a natural property of the solar system, and not a mere numeric coincidence.
The Titius-Bode law was established in 1766 by the astronomers Johann Daniel Titius (1725-1796) and Johann Elert Bode (1747-1826), consisting in the interesting property of the distances from the sun to the planets to form a sequence in which every number doubles the previous one. Trying to explain it, Robert Matthews (“New Scientist”, 04-09-2001) suggested a) to write the series 0, 3, 6, 12 and so on, b) sum 4 to each number, and, finally, c) to divide those sums by 10. Expressing the figures of the new series in AU, we see that the distances between the sun and the planets correspond roughly to the numbers on the sequence.
The planets already discovered at that time fit perfectly in several positions of the series. Some of the positions were empty. Bode, who had great confidence in the law he elaborated took the task of promoting it among the astronomers, encouraging them to discover new planets to fill in the empty spaces of the series. In 1781, Herschel announced the discovery of Uranus, which was placed precisely over one of the positions of the law, what represented a great achievement to the proposition. Right after, still under Bode’s influence, it was discovered the asteroid Ceres, in the asteroid belt, which corresponds to a small planet orbiting between Mars and Jupiter. Later, John Couch Adams and Urbain Le Verrier discovered signs of the existence of Neptune, which soon after was detected visually.
However, the discovery of Neptune had a flavor of defeat: its position, relatively to the series, was somewhat away from the predicted. Things got worse in 1930 with Pluto, which orbits the sun far apart from the spot reserved for it in the sequence.
Both Frenchmen, following an astronomical and mathematical study of planets formation concluded that the models studied posses two important symmetries and predict, in general, a gas and heavy materials cloud inside the proto-planetary disks. The study of the symmetries may explain the deviations from the original theory of Bode-Titius observed in the behavior of the solar system.
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