Johann Elert Bode | Biography

Johann Elert Bode was born in Hamburg, Germany, on January 19, 1747. Self-taught in astronomy, he became director of the Berlin Observatory in 1786 and issued an enormous catalog of star positions in 1801. He is most famous, however, for Bode's law, a simple formula that gave a mathematical relationship between the distances of the known planets and the Sun. It was not even conceived by Bode, but by Johann Titius (1729-1796) of Wittenberg in 1766. Titius was forgotten when Bode brought the law into prominence in 1772.

Titius discovered that if one considered the distance from the Sun to its closest planet, Mercury, as 4 units, one could begin by adding 3 to the distance of Mercury (4 + 3 = 7) to derive the distance of Venus from the Sun. Then, each time one doubled the second number in the equation, one would get the distance of the next planet--the Earth was 4 + 6 = 10, and Mars was 4 + 12 = 16. Jupiter, however, was at 4 + 48 = 52, and Saturn was at 4 + 96 = 100, so there was an empty space at 4 + 24 = 28.

Bode was captivated by the sequence. He made one slight modification to the scheme (he decided the distance to the Earth should equal "one unit" so he divided all of Titius's numbers by ten), and gave the resulting calculations wide publicity.

Since nothing could be seen where, according to the formula, there should have been a planet between Mars and Jupiter at 4 + 24 ÷ 10 = 2.8 units, astronomers began looking for something there. While searching within the gap in 1801, Giuseppe Piazzi (1746-1826), director of an observatory on Sicily, discovered a small object that was eventually named Ceres. German mathematician Carl Friedrich Gauss made calculations to determine its orbit and, sure enough, Ceres was in orbit where the formula predicted it would be. Countless other asteroids were soon found orbiting there as well. A few years earlier, in 1781, English astronomer William Herschel had discovered a new planet. Bode gave it the name Uranus and it, too, was found to fit the formula nearly precisely at the next available position after Saturn: 4 + 192 ÷ 10 = 19.6.

Would the next planet to be discovered lie at the next position, 4 + 384 ÷ 10 = 38.8 units? Astronomers had observed that Uranus seemed to be pulled from its predicted orbit by an unseen neighbor. In the 1840s, English astronomer John Couch Adams and French astronomer Jean Urbain Le Verrier (1811-1877) independently began to make calculations based on that fact. They provided figures that quickly led to the discovery of Neptune in 1846, but it was found at a distance of 30.07 units, nowhere near the 38.8 units predicted by Bode's law. Bode's law had broken down and soon lost its importance, but Bode never knew that; he had died in 1826.

That Bode's law eventually broke down should not surprise us. The so-called "law" is entirely arbitrary, with no basis in anything of physical significance. Titius had picked an arbitrary number (4), added an arbitrary number to it (3), and then come up with an arbitray formula to create a sequence of numbers that concidentally matched the spacing of the planets. Bode's law is not science; it is one of those numerical coincidences that inevitably occur in nature. An essential--and difficult--job of the scientist is to separate meaningless coincidences, which appeal so much to the human mind's love of regularity and pattern, from true physical phenomena. Unfortunately for nineteenth-century astronomy, Titus and Bode were unable to do this.