Bodes law

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 and now regarded as a dwarf planet, 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 have argued that the deviation of Neptune from its predicted positions signifies that it is no longer at its 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.

Bode's law A numerical sequence announced by J. E.Bode in 1772 which matches the distances from the Sun of the six planets then known. It is also known as the Titius–Bode law, as it was first pointed out by the German mathematician Johann Daniel Titius (1729–96) in 1766. It is formed from the sequence 0, 3, 6, 12, 24, 48, 96, 192 by adding 4 to each number. The planets were seen to fit this sequence quite well—as did Uranus, discovered in 1781. However, Neptune and Pluto do not conform to the ‘law’. Bode's law stimulated the search for a planet orbiting between Mars and Jupiter that led to the discovery of the first asteroids. It is often said that the law has no theoretical basis, but it does show how orbital resonance can lead to commensurability.