(also known as the Titus-Bode Law) is an interesting mathematical coincidence
, and not a physical law. However, the general form of geometric spacing is valid in Sol-type stable stellar systems
, hence the numerical series that matches planetary distances from Sol and many other stars. Because of resonance, planets form with periods that are rational multiples of each other. As some resonances are stable and others are not, modelling requires complex calculations. The Titus-Bode series predicts the positions of all the planets in the Sol System except Neptune (plus it predicts a planet where the asteroid belt is). In this instance, start with 0.4 (A.U.), then form the series by adding 0, 0.3, 0.6, 1.2, 2.4, etc. (doubling each time after the first). The results it predicts are: Mercury: 0.4 A.U., Venus 0.7 A.U., Earth 1.0 A.U., Mars 1.6 A.U., Asteroid Belt 2.8 A.U., Jupiter 5.2 A.U., Saturn 10.0 A.U., Uranus 19.6 A.U.
[named for Johann Titus and the German astronomer Elert Bode, who did their work in the late 1700's.]