The Law of Bode
Bode's law is an equation for representing the approximate distances of the planets from the sun. Contrary to most beliefs Bode actually did not develop this law. It was originally devised by a German mathematician in 1766 by the name of Johann D. Titius. Only when Titus developed this formula it was not published and the planets Uranus, Neptune, and Pluto had not been discovered yet. This law is associated with Johann E. Bode because he published the it in 1772.
This law operates according to a simple formula. Take the numbers 0, 3, 6, 12, 24, 48, 96, 96, 192, 384, and 768. Each figure in the series after four is obtained by doubling the previous number. Then add four to the number and divide by ten. The table below shows the formulas and distances for all the planets in the solar system. Compare the numbers calculated by Bode's law to the actual distances of the planets. These distances are measured in astronomical units which equal about 93 million miles (150 million kilometers).
Planet n Distance by Bode's Law Actual Distance
Mercury 0 .3x0 + .4 = .4 0.39 Venus 1 .3x1 + .4 = .7 0.72 Earth 2 .3x2 + .4 = 1.0 1.00 Mars 3 .3x4 + .4 = 1.6 1.52 (Asteroids) 4 .3x8 + .4 = 2.8 --- Jupiter 5 .3x16 + .4 = 5.2 5.20 Saturn 6 .3x32 + .4 = 10.0 9.55 Uranus 7 .3x64 + .4 = 19.6 19.18 Neptune 8 .3x128 + .4 = 38.8 30.06 Pluto 9 .3x256 + .4 = 77.2 39.30
The distances calculated by Bode's law are approximately the actual distances for Neptune and Pluto. Also there is no planet that corresponds to the distance between Mars and Jupiter, but some asteroids are about this far. The inconsistancies cause many scientists to question the significance of Bode's Law in the study of planetary orbits.