Renaissance Astronomy, Page 31: [Previous Page] [Next Section] [Class Home Page] Textbook pages 62 - 64

Bode's Rule (also called The Titius-Bode Law) is a rough rule that predicts the spacing of the planets in the Solar System. The relationship was first pointed out by Johann Titius in 1766 and was mathematical formulated by J.E. Bode in 1778. It lead Bode to predict the existence of another planet between Mars and Jupiter in what we now recognize as the asteroid belt. The law relates the mean distances of the planets from the sun to a simple mathematic progression of numbers.

Here's the mathematical progression. Start with the following sequence of numbers (each is simply twice the value of the previous number): 0 3 6 12 24 48 96 192 384 Then add 4 to each number, and divide by 10. You get: 0.4 0.7 1.0 1.6 2.8 5.2 10.0 19.6 38.8 But this is nearly identical to the measured planet-sun distances:

Body Actual distance (A.U.) Bode's Law Mercury 0.39 0.4 Venus 0.72 0.7 Earth 1.00 1.0 Mars 1.52 1.6 2.8 Jupiter 5.20 5.2 Saturn 9.54 10.0 Uranus 19.19 19.6

What's more, this works for the Moons around planets, too! Here we've plotted the distance of the Moon's of Uranus from Uranus. However, Bode's law fails for Nepture and Pluto. The 'explanation' is that it may be a natural consequence of planetary spacing (about a factor of two between planets). But fundamentally, it is nothing more than a numerical toy. Indeed, one can still find plenty of examples of numerological thinking in present-day sciences.