"Philosophy is written in this grand book — I mean the universe — which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth."[2]Johannes Kepler is known as much for the Kepler conjecture, that the face-centered cubic packing of spheres is the most efficient at filling space, as his astronomy. Having such geometry on his mind would explain his model of the spacing of the planets in the solar system shown in the figure.

An illustration of Kepler's planetary model, as it appears in the 1910 book by Francis Rolt-Wheeler, "The Science-History of the Universe," as figure 37 on page 112.(Scan by Sue Clark, via Wikimedia Commons). |

a = 0.4 + 0.3(2As the graph shows, the equation quite well matched the distances to the planets known at the time. Ceres was included in the law, since it seemed to fit, and it stood as a placeholder for the entire asteroid belt. The asteroids would have formed a planet were it not for the gravitational effects of Jupiter.^{n}), n = -∞, 0, 1, 2, 3...

Actual distances (orange), and distances predicted by the Titius-Bode Law (green), for the planets. In this case, Ceres and Pluto are considered planets. (Rendered by author using Gnumeric). |

Deviation from Bode's Law.(Rendered by author using Gnumeric). |

Artist's conception of a protoplanetary disk around the brown dwarf, OTS 44.(Image: NASA Spitzer Space Telescope Collection, NASA/JPL-Caltech/T. Pyle). |

- E.P. Wigner, "The unreasonable effectiveness of mathematics in the natural sciences," Communications on Pure and Applied Mathematics, vol. 13, no. 1 (February, 1960). pp. 1-14. A PDF file is available, here.
- Galileo quotations on Wikiquotes; Selections of a translation of The Assayer; Stillman Drake, "Discoveries and Opinions of Galileo," Doubleday & Co.(New York, 1957), pp. 231-280.
- Daniel Stolte, "Popular Solar System Orbits Result in 'Planet Pileups'," University of Arizona Press Release, March 19, 2012
- R.D. Alexander and I. Pascucci, "Deserts and pile-ups in the distribution of exoplanets due to photoevaporative disc clearing," arXiv Preprint Server, February 24, 2012.