Meta Research Bulletin ©2006

Where It Began – the Titius-Bode Law of Planetary Spacing

            In the latter half of the 18^th century, when only six major planets were known, interest was attracted to the regularity of the spacing of their orbits from the Sun. The table shows the Titius-Bode law of planetary spacing [0.4+0.3*2^n-2], comparing actual and formula distances in astronomical units (au), where n is planet/row number in the table: n = 1-9. This in turn drew attention to the large gap between Mars (at 1.6 au from the Sun, where Earth is at 1.0 au) and Jupiter (at 5 au out), apparently just large enough for one additional planet with the normal spacing ratio. Today we know of tens of thousands of “minor planets” or asteroids with planet-like orbits in that distance range from the Sun.

            With the discovery of the second asteroid in 1802, Olbers proposed that many more asteroids would be found because the planet that belonged at that distance must have exploded. This marked the birth of the exploded planet hypothesis. It seemed the most reasonable explanation until 1814, when Lagrange found that the highly elongated orbits of comets could also be readily explained by such a planetary explosion. That, unfortunately, challenged the prevailing theory of cometary origins of the times, the Laplacian primeval solar nebula hypothesis. Comets were supposed to be primitive bodies left over from the solar nebula in the outer solar system. This challenge incited Laplace supporters to attack the exploded planet hypothesis. Lagrange died in the same year, and support for his viewpoint died with him when no one else was willing to step into the line of fire.

            In modern times, it is widely argued that Jupiter’s gravity interfered with formation of a planet in the gap between Mars and Jupiter. However, this notion is not dynamically viable. The zone near the middle of the main asteroid belt at ~2.5-3.5 au is one of enhanced dynamical stability, not of instability. Elsewhere in the solar system, planets and moons show a preference for the 2-to-1 resonance region rather than an avoidance of it. And computer simulations show that a mass ~30 times that of present-day Jupiter is required to produce instability in the main asteroid belt. Moreover, a new asteroid belt beyond Neptune has no “Jupiter” to produce instability in that region. So the “instability” alternative to exploded planets is no longer a credible alternative to a planet that formed in the normal way and later exploded.