Reflections The Titius-Bode Rule, Part 2: Science or Numerology? by David M. F. Chapman (
[email protected]) ast month, I presented the history postulated the following rule for the radius of the Titius-Bode rule of planetary of the planetary orbits: from Mercury Lorbit spacing in the solar system, through Saturn, including the spectacular concordance of the “predictions” of the rule (also called D = 0.4 + 0.3 n, where n = {0, 1, 2, 4, 8, 16, 32} Bode’s law) in the case of Uranus and the asteroids, and the abysmal failure of the in which D is the semi-major axis in rule with respect to the last two planets Astronomical Units (i.e. DEarth=1 AU). discovered: Neptune and Pluto. This Fellow German Johann Elert Bode month, I will review the quest for a scientific (1747–1826) liked the idea so much that The approximate logarithmic spacing of the basis to this rule. At the time I made this he included it in one of his popular planetary orbits. Filled circles are the exact rash promise, I was going out on a limb, textbooks on astronomy, and everyone semi-major axis values; open diamonds are as I was unsure of what I would be able started calling it Bode’s Law. In fact, there the Titius-Bode law results. Note the excellent to find. To my relief, I found an extensive was a gap at n=8, as no planet was known “predictions” of Ceres (k=5) and Uranus (k=8) body of literature on the subject, including to occupy the zone between Mars and and the poor “predictions” of Neptune (k=9) some recent interesting studies.