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