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Bode's law


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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.

Bode's law

Planet

Mercury

Venus

Earth

Mars

Ceres

Jupiter

Saturn

Uranus

Bode's law distance

4

7

10

16

28

52

100

196

Actual distance (10−1 AU)

3.9

7.2

10

15.2

28

52

 95

192

Subjects: Astronomy and Astrophysics.


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