Background

Johann E. Bode developed an equation that is used to approximate the distances of the planets from the Sun. Bode did not actually develop the equation, it was actually devised by a German mathematician named Johann D. Titius in 1766 who never got around to publishing it. At this time Uranus, Neptune, and Pluto were yet to be discovered. It became associated with Bode because he published it in 1772 and it became known as Bode's Law.

This law operates according to a simple formula. Take the numbers 0, 1, 2, 4, 8, 16, 32, 64, 128, and 256. Each figure in the series after four is obtained by doubling the previous number. Then add .4 to the number and divide by 10. The table below shows the formulas and actual 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 inconsistencies cause many scientists to question the significance of Bode's Law in the study of planetary orbits.