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...