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No. 51: May-Jun 1987

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Were titius and bode right?

For a couple of centuries, astronomers have been trying to explain in physical terms why the empirical and very simple formula of Titius and Bode works so well. It is only an unimposing geometric progression, which, if one inserts the earth's average distance from the sun, yields the distances of the other planets with enough accuracy to perturb astronomers. You see, all scientists abhor numerology. They must insist that the Titius-Bode Law has physical underpinnings.

S. Weldenschilling and D. Davis now propose that the planets owe their present positions to a combination of two effects:

  1. The frictional drag of the gas in the solar nebula, which favors the presence of small planets in the inner solar system.

  2. Gravitational perturbations that create favored places for the coalesceing of planets.

C. Patterson has expanded on this suggestion and finds that a model based on these effects works quite well for Jupiter and beyond, where planets are "bound together" in an interlocking system of orbital-period resonances. (See diagram.)

Several important anomalies persist, however. That vacant niche between Uranus and Neptune is presently unexplained. In the inner solar system, the presence of Mercury is "embarrassing." (Anonymous; "Were Titius and Bode Right?" Sky and Telescope, 73:371, 1987.

Reference. The "problem" of Mercury is treated in AHB2 in The Moon and the Planets. This catalog is described here.

C. Patterson's model of the outer planets In C. Patterson's model the outer planets accreted at those spots where their orbital periods formed simple ratios. Planet ? ? is indicated by this theory, but has never been found.

From Science Frontiers #51, MAY-JUN 1987. 1987-2000 William R. Corliss

Science Frontiers Sourcebook Project Reviewed in:


  • "A sourcebook of unexplained phenomena is therefore a valuable addition to a collection of scientific literature. William R. Corliss has provided this in the past with his source books of scientific anomalies in several subjects, and now he has provided it for astronomy. He has done an excellent job of collecting and editing a large amount of material, taken in part from scientific journals and in part from scientific reporting in the popular or semi-scientific press." -- "The Mysterious Universe: A Handbook of Astronomical Anomalies", reviwed by Thomas Gold, Cornell University, in Icarus, vol.41, 1980

  • "An interesting, systematic presentation of unusual weather [..] This book is recommended for a general audience" --"Corliss, William R., Tornados, Dark Days, Anomalous Precipitation, and Related Weather Phenomena, Sourcebook Project, 1983.", revieweed in Choice, September 1983
  • "..the science is necessarily somewhat speculative, but Corliss's symthesis is based on reputable sources." -- "Corliss, William R. (Compiler). Lightning, Auroras, Nocturnal Lights, and Related Luminous Phenomena" reviwed by Joseph M. Moran, Univ. of Wisconsin in Science Books and Films, Sep/Oct 1983

  • "Before opening the book, I set certain standards that a volume which treads into dangerous grounds grounds like this must meet. The author scrupulously met, or even exceeded those standards. Each phenomenon is exhaustively documented, with references to scientific journals [..] and extensive quotations" -- "Book Review: The moon and planets: a catalog of astronomical anomalies", The Sourcebook Project, 1985., Corliss, W. R., Journal of the Royal Astronomical Society of Canada, Vol. 81, no. 1 (1987), p. 24., 02/1987