BODE'S LAW

also called Titius-bode Law, empirical rule giving the approximate distances of planets from the Sun. It was first announced in 1766 by the German astronomer Johann Daniel Titius and only popularized, from 1772, by his fellow countryman Johann Elert Bode. The rule may be given as follows: Write down the sequence 0, 3, 6, 12, 24, etc. To each number add 4. Divide each result by 10. Of the first seven answers (0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10.0), six closely approximate the distances from the Sun, in astronomical units (a.u.; the distance between the Earth and the Sun), of the six planets known when Titius devised the rule: Mercury, Venus, Earth, Mars, Jupiter, and Saturn. At about 2.8 a.u. from the Sun, between Mars and Jupiter, the asteroids (sometimes called minor planets) were later discovered. The rule also holds for the seventh planet, Uranus, which lies at about 19 a.u. Bode's law fails for the eighth planet, Neptune. However, Pluto, the ninth planet from the Sun, is at a distance (39 a.u.) roughly equal to that given by the rule for the eighth planet.