Two French scientists issued articles in “Astronomy and Astrophysics” (282, pages 262 to 269) arguing that the so-called Titius-Bode law, may be a natural property of the solar system, and not a mere numeric coincidence.

The Titius-Bode law was established in 1766 by the astronomers Johann Daniel Titius (1725-1796) and Johann Elert Bode (1747-1826), consisting in the interesting property of the distances from the sun to the planets to form a sequence in which every number doubles the previous one. Trying to explain it, Robert Matthews (“New Scientist”, 04-09-2001) suggested a) to write the series 0, 3, 6, 12 and so on, b) sum 4 to each number, and, finally, c) to divide those sums by 10. Expressing the figures of the new series in AU, we see that the distances between the sun and the planets correspond roughly to the numbers on the sequence.

The planets already discovered at that time fit perfectly in several positions of the series. Some of the positions were empty. Bode, who had great confidence in the law he elaborated took the task of promoting it among the astronomers, encouraging them to discover new planets to fill in the empty spaces of the series. In 1781, Herschel announced the discovery of Uranus, which was placed precisely over one of the positions of the law, what represented a great achievement to the proposition. Right after, still under Bode’s influence, it was discovered the asteroid Ceres, in the asteroid belt, which corresponds to a small planet orbiting between Mars and Jupiter. Later, John Couch Adams and Urbain Le Verrier discovered signs of the existence of Neptune, which soon after was detected visually.

However, the discovery of Neptune had a flavor of defeat: its position, relatively to the series, was somewhat away from the predicted. Things got worse in 1930 with Pluto, which orbits the sun far apart from the spot reserved for it in the sequence.

Both Frenchmen, following an astronomical and mathematical study of planets formation concluded that the models studied posses two important symmetries and predict, in general, a gas and heavy materials cloud inside the proto-planetary disks. The study of the symmetries may explain the deviations from the original theory of Bode-Titius observed in the behavior of the solar system.

Have you heard of it?

Do you mean, heard of the Titus-Bode law, or of the Astronomy and Astrophysics paper? Who were the French scientists? Maybe we can find an online link.

The paper. The scientists are François Graner and Bérengère Dubrulle, from the Midi-Pyrenées Observatory at Toulouse, France.

It would be fine to discuss. Unfortunately I can't give you a link, cause I read it in a physical medium. I didn't take the time to search it over the net.


<font size=-1>[ This Message was edited by: Argos on 2002-04-09 06:37 ]</font>

Do you know the date of the paper? Astronomy and Astrophysics has an online version (articles are only available to print subscribers though), but the magazine seems to have changed publishers, and they only have the last two years online.

TITIUS-BODE LAWS IN THE SOLAR-SYSTEM .1. SCALE-INVARIANCE EXPLAINS EVERYTHING
GRANER F, DUBRULLE B
ASTRONOMY AND ASTROPHYSICS
282 (1): 262-268 FEB 1994

Document type: Article Language: English Cited References: 31 Times Cited: 15

Abstract:
According to the Titius-Bode law, the planetary distances to the sun follow a geometric progression. We review the major interpretations and explanations of the law. We show that most derivations of Titius-Bode law are implicitely based on the assumption of both rotational and scale invariance. In absence of any radial length scale, linear instabilities cause periodic perturbations in the variable chi = ln(tau/tau(0)). Since maxima equidistant in chi obey a geometric progression in the variable tau, Titius-Bode type of laws are natural outcome of the linear regime of systems in which both symmetries are present; we discuss possible nonlinear corrections to the law. Thus, if Titius-Bode law is real, it is probably only a consequence of the scale invariance of the disk which gave rise to the planets.

Author Keywords:
PLANETS AND SATELLITES, GENERAL, SOLAR SYSTEM, FORMATION, HYDRODYNAMICS, INSTABILITIES

KeyWords Plus:
INSTABILITY, PLANETARY, DISK

Addresses:
GRANER F, UNIV PARIS 06,ENS,CNRS,PHYS STAT LAB,24 RUE LHOMOND,F-75231 PARIS 05,FRANCE
UNIV PARIS 07,F-75231 PARIS 05,FRANCE
OBSERV MIDI PYRENEES,CNRS,URA 285,F-31400 TOULOUSE,FRANCE

Publisher:
SPRINGER VERLAG, NEW YORK

IDS Number:
MW312

ISSN:
0004-6361

TITIUS-BODE LAWS IN THE SOLAR-SYSTEM .2. BUILD YOUR OWN LAW FROM DISK MODELS
DUBRULLE B, GRANER F
ASTRONOMY AND ASTROPHYSICS
282 (1): 269-276 FEB 1994

Document type: Article Language: English Cited References: 11 Times Cited: 5

Abstract:
Simply respecting both scale and rotational invariance, it is easy to construct an endless collection of theoretical models predicting a Titius-Bode law, irrespective to their physical content. Due to the numerous ways to get the law and its intrinsic arbitrariness, it is not an useful constraint on theories of solar system formation.

To illustrate the simple elegance of scale-invariant methods, we explicitly cook up one of the simplest examples, an infinitely thin cold gaseous disk rotating around a central object. In that academic case, the Titius-Bode law holds during the linear stage of the gravitational instability. The time scale of the instability is of the order of a self-gravitating time scale, (G rho(d))(-1/2), where rho(d) is the disk density. This model links the separation between different density maxima with the ratio M(D)/M(C) of the masses of the disk and the central object; for instance, M(D)/M(C) of the order of 0.18 roughly leads to the observed separation between the planets. We discuss the boundary conditions and the limit of the WKB approximation.

Author Keywords:
PLANETS AND SATELLITES, GENERAL, SOLAR SYSTEM, GENERAL, HYDRODYNAMICS, INSTABILITIES

Addresses:
DUBRULLE B, OBSERV MIDI PYRENEES,CNRS,URA 285,14 AV E BELIN,F-31400 TOULOUSE,FRANCE
UNIV PARIS 06,ENS,CNRS,PHYS STAT LAB,F-75231 PARIS 05,FRANCE
UNIV PARIS 07,F-75231 PARIS 05,FRANCE

Publisher:
SPRINGER VERLAG, NEW YORK

IDS Number:
MW312

ISSN:
0004-6361

Thanks, Karl.

Full articles available on ADS:
http://adsabs.harvard.edu/cgi-bin/np...d39ae933f15536

http://adsabs.harvard.edu/cgi-bin/np...d39ae933f15536

Thanks, again.