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.

Collins Dictionary of Astronomy © Market House Books Ltd, 2006

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.

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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.

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References in periodicals archive

Bode's Law Distance from Distance from Predicted Sequence sun sun (AU) distance Planet (millions km) Mercury 58 0.39 0.40 0 Venus 110 0.71 0.70 0.3 Earth 150 1.00 1.00 0.6 Mars 230 1.52 1.60 1.2 Asteroids 440 2.93 2.80 2.4 Jupiter 780 5.20 5.20 4.8 Saturn 1430 9.50 10.00 9.6 Uranus 2880 19.20 19.60 19.2 Neptune 4516 30.10 38.80 38.4 Pluto 5940 39.60 77.20 76.80 Table 2.

The music of the celestial spheres

Maybe, but "looking for patterns in chaos is what great editors do," says Murch, who can play the ratios described by Bode's Law on the piano.

Murch's interest in Bode's Law isn't just a diversion from his life's work but an extension of it--he hopes to complete a book on the subject by the end of the year.

From Jupiter to 'Jarhead': legendary cutter Walter Murch has a theory about editing, and it involves the heavens

Bode's law didn't seem to have much scientific significance.

Nevertheless, it fit Bode's law, and Piazzi named it Ceres, after the Roman goddess most closely associated with Sicily.

Ceres

In fact, the submission guidelines for Icarus, the leading journal of planetary sciences, specifically state that it "does not publish papers that provide 'improved' versions of Bode's Law, or other numerical relations, without a sound physical basis." Had Adams and Le Verrier been working in the 21st century, their predictions never would have found their way into a peer-reviewed journal!

Neptune comes full circle: as Neptune completes a full orbit since its discovery, it's a good time to reflect on one of the greatest stories in astronomy lore

The authors of this book have done a superb job connecting all the relevant factors that led up to the Vulcan episode, from Johannes Kepler's formulation of his laws of planetary motion, to Isaac Newton's gravitational theory, then through cometary motions, the discovery of Uranus, Bode's law, and the discovery of the brighter asteroids.

In Search of Planet Vulcan