Bode's 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.

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Bode's law

Rule giving the approximate distances of planets from the Sun. First announced in 1766 by the German Johann Daniel Titius (b. 1729—d. 1796), it was popularized, from 1772, by his countryman Johann Elert Bode (b. 1747—d. 1826). It may be given as follows: To each number in the sequence 0, 3, 6, 12, 24, and so on, add 4 and divide the result by 10. The answers closely approximate the distances from the Sun, in astronomical units, of the first seven planets. Bode's law also suggested that a planet should be found between Mars and Jupiter, where the asteroid belt was later discovered. Once thought to have some significance regarding the formation of the solar system, it is now regarded as a numerological curiosity.

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Bode's law [′bōdz ‚lȯ]

(astronomy)

An empirical law giving mean distances of planets to the sun by the formulaa= 0.4 + 0.3 × 2ⁿ, whereais in astronomical units andnequals -∞ for Mercury, 0 for Venus, 1 for Earth, and so on; the asteroids are included as planets. Also known as Titius-Bode law.

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Bode’s Law 

(also Titius-Bode law, Titius-Bode rule), an empirical rule (improperly called a law) that states the relation between the distances of the planets from the sun. The rule was proposed by J. D. Titius in 1766 and became well known owing to works by J. E. Bode published in 1772.

Bode’s law gives the distances of Mercury, Venus, the earth, Mars, the central part of the asteroid belt, Jupiter, Saturn, Uranus, and Pluto (Neptune deviates from the relation) from the sun in astronomical units. To obtain the distances, the number 4 is added to each number in the sequence 0, 3, 6,12, 24, 48, 96,192, 384, which forms, starting with 3, a geometric progression. If the resulting sums are then divided by 10, we obtain the new sequence of numbers 0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10.0, 19.6, and 38.8, which gives the distances of the above-mentioned bodies of the solar system from the sun in astronomical units with an accuracy of about 3 percent. There is no satisfactory theoretical explanation of this empirical relation.