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Bode's law
[for J. E. Bode], also known as Titius's law or the Titius-Bode law, empirical relationship between the mean distances of the planets from the sun. If each number in the series 0, 3, 6, 12, 24, … (where a new number is twice the previous number) is increased by 4 and divided by 10 to form the series 0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10.0, 19.6, 38.8, 77.2, … , Bode's law holds that this series gives the mean distances of the planets from the sun, expressed in astronomical units. When this relationship was discovered by Titius of Wittenberg in 1766 and published by Bode six years later, it gave good agreement with the actual mean distances of the planets that were then known–Mercury (0.39), Venus (0.72), Earth (1.0), Mars (1.52), Jupiter (5.2), and Saturn (9.55). Uranus, discovered in 1781, has mean orbital distance 19.2, which also agrees. The asteroid Ceres, discovered 1801, has mean orbital distance 2.77, which fills the apparent gap between Mars and Jupiter. However, Neptune, discovered 1846, has mean orbital distance 30.1, and Pluto, discovered 1930, has mean orbital distance 39.5; these are large discrepancies from the positions 38.8 and 77.2, respectively, predicted by Bode's law. Some theories of the origin of the solar system have tried to explain the apparent regularity in the mean orbital distances of the planets, arguing that it could not arise by chance, but must be a manifestation of the laws of physics. Some astronomers hold that the deviation of Neptune and Pluto from their predicted positions signifies that they are no longer at their original positions in the solar system. However, since Bode's law is not a law in the usual scientific sense, i.e., it is not universal and invariant, it alone should not be taken as evidence for such a conclusion.