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Review

THE TITIUS-BODE LAW OF PLANETARY DISTANCES:
ITS
HISTORY AND THEORY

  •  M. M. Nieto (Pergamon Press, 1972),$11.00

  •  Reviewed by Irving Michelson

School astronomy teaches that planetary distances have been constant for billions of years, their values happening to be whatever they are as if by chance without rhyme or reason.  Pensée readers are not so sure of this; many favor one interdisciplinary thinker's heretic view that Venus is a newcomer among the planets.  They have also seen that view scornfully rejected by some astronomers in a manner that gives science a bad name.  So it is refreshing to pick up M. M. Nieto's book, reminding us how scientists of great imaginative brilliance—and integrity, too—have grappled for two centuries with this enigma that is a most serious challenge to Velikovsky's assertion.

In addition to restoring faith in astronomers past, Nieto presents his discussion in a manner that brings us up to date on continuing efforts of the highest quality and importance by contemporary scientists.

Nearly everyone who has been to school has wondered about "Bode's Law."  It gives planetary distance rn of planet n, relative to Earth's distance from the Sun taken as 10, by setting n = -¥ for Mercury, 0 for Venus, 1, 2.... for succeeding planets, in the simple formula

rn = 4+3 + 2n

Is it true, accurately?  If so, is it anything more than a coincidence, as many astronomers have felt and still feel?  Or does it betray an underlying order of nature, apprehension of which must ultimately permit deduction of the result directly from general physical laws?

Nieto himself seems unconvinced after examining a great amount of accumulated scientific evidence.  It is the diverse nature of the evidence that has a particular appeal to those who are less than satisfied with the patois of standard celestial mechanics based on consideration of gravitational forces alone.  These were the only cosmic forces known to Isaac Newton who invented the laws of mechanics and gravitation, and to P. S. Laplace who created celestial mechanics two centuries ago.  The fact is that celestial mechanicians, notwithstanding loud claims to the contrary, still stoutly defend and confine their attention to mechanics so narrowly construed.

But now we know that magnetic fields are a ubiquitous component of interplanetary space, and we have had a coherent theory of electromagnetism already for well over 100 years.  Even if some astronomers find no necessity to take note of electromagnetic phenomena, Nieto lucidly describes other cosmogonic studies that have for a long time already been fully cognizant of electromagnetic effects as well as gravitational.  It is in this framework that one not only may but even must consider possible net electric charges of celestial bodies, major electrical discharges and a host of other electromagnetic effects.  Keepers of the traditional wisdom whose prime concern is getting one more decimal accuracy in tables of ephemerides may safely ignore these phenomena—but then they also disqualify themselves from proper discussion of the real questions faced by students of catastrophism.

Bode's Law, as extended by Mary Blagg and by D. E. Richardson earlier this century, has been found to apply not only to planetary spacing, but also to the spacing of the satellite systems of Jupiter, Saturn, and Uranus as well.  Tendentious certainly, but still far short of scientific proof that a formula is a Law.

What is called Bode's Law was in fact first given by J. D. Titius von Wittenberg in 1766.  He gratuitously inserted it as an added note in the main text of a volume he was translating from French to

German.  In 1772 J. E. Bode appropriated it as a footnote in a book of his own without crediting Titius, although he did so later.  But historical priority for the concept of regular planetary spacing belongs neither to Bode nor to Titius, the idea having appeared as early as 1595 in Kepler's musings over nested spheres and regular polygons.  Newton (1642-1726) and Kant (1728-1804) kept the idea alive.  From Bode's time forward it has been known as Bode's Law and is still so identified in Hoyle's popular astronomy work without so much as a mention of Titius.

Law or no law, Titius or Bode, its importance has been inestimable.  Neither J. C. Adams in England nor U. J. Leverrier in France independently of him would have discovered the planet Neptune in 1846 except by assuming in advance that its position would be given by Bode's Law, by setting n = 7.  Yet Bode's Law places Neptune at distance 388, which is quite wrong—it is actually observed to be

at distance 301, considerably closer to the Sun.

The most lively period of the history of the Titius-Bode Law seems to be right now.  Nieto holds that it is by no means proved valid as a physical law, but that if you do believe it is a valid physical law,

then you cannot also believe in recent large-scale evolution of the Solar System.  One or the other, but not both. In other words, he says, Bode's Law and recent catastrophism are mutually exclusive.

But the story does not end there.  Dr. C. J. Ransom points out that by simply replacing the 3 with 6 in the formula shown above, it applies as well (or as badly) as before, without a place for Venus!  Prof. J. W. Warwick has extended the concept broadly by devising what he terms a magnetic Bode's Law. Prof. M. W. Ovenden shows the "law" to be not only quite accurate when a "missing" planet is restored, but gives a physical principle that explains how the planets can settle into the required orbits.  He finds a time scale of the order of billions of years, recognizes other difficulties yet unresolved.  Prof. R. W. Bass reports recent mathematical studies of orbital stability that he believes could shorten the time scale to mere hundreds or at most thousands of years.  If true, then Venus might after all be supposed to have taken its place in the heavens in historical time!  It goes without saying, of course, that many astronomers remain highly dubious—but remember that both they and we have very much shorter personal time scales still, and the opinions of most all of us are probably wrong!

Nieto's book makes exciting reading for the common reader just as much as for the advanced, scientific specialists of astronomy and cosmogony.  Highly recommended.

Bibliographical Addendum:

Bass, R. W. (1974): "Did Worlds Collide," In this issue of Pensée, p. 8.

Ovenden, M. W. (1973): "Planetary Distances and the Missing Planet." Recent Advances in Dynamical Astronomy (Tapley, B. D., and Szebely, V., eds.), Reidel Publishing Company, pp. 319-32.

Ransom, C. J. (1974): "Bode's Law and Changes in the Solar System." Presentation to symposium on Velikovsky and the Recent History of the Solar System, McMaster University, June 16-19, 1974.  See this issue, p. 7.

Warwick, J. W. (1971): "The Relation of Angular Momentum and Magnetic Fields: Schuster's Hypothesis Revisited." Phys. Earth Planet. Interiors 4: 229-32.

PENSEE Journal VIII

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