# Bode's law

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## Bode's law

[for J. E. BodeBode, Johann Elert
, 1747–1826, German astronomer. From 1772 to 1825 he was astronomer of the Academy of Science, Berlin, and from 1786, director of the Berlin Observatory.
], 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 unitsastronomical unit
(AU), mean distance between the earth and sun; one AU is c.92,960,000 mi (149,604,970 km). The astronomical unit is the principal unit of measurement within the solar system, e.g., Mercury is just over 1-3 AU and Pluto is about 39 AU from the sun.
. 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 planetdwarf planet,
a nonluminous body of rock or gas that orbits the sun and has a rounded shape due to its gravity. Unlike a planet, a dwarf planet is not capable of clearing its orbit of smaller objects by collision, capture, or other means.
, 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

(boh -dĕz, bohdz) (Titius–Bode law) A relationship between the distances of the planets from the Sun. Take the sequence 0, 3, 6, 12, 24,…, where each number (except the 3) is twice the previous one, add 4 to each, and divide by 10. The resulting sequence (0.4, 0.7, 1.0, 1.6, 2.8, 5.2,…) is in good agreement with the actual distances in astronomical units (AU) of most planets, provided that the asteroids are included and considered as one entity at a mean distance of 2.8 AU. The law fails to predict the correct distances for Neptune and Pluto. Some astronomers think that the relationship may have some significance with respect to the formation of the Solar System; most consider the sequence purely fortuitous. Named after Johann Bode (1747–1826), who published it in 1772, it was formulated by Johann Titius (1729–96) of Wittenberg in 1766.

## 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.

## Bode's law

[′bōdz ‚lȯ]
(astronomy)
An empirical law giving mean distances of planets to the sun by the formula a = 0.4 + 0.3 × 2 n, where a is in astronomical units and n equals -∞ 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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