Astronomy and Astrophysics – Astrophysics
Scientific paper
Feb 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994a%26a...282..262g&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 282, no. 1, p. 262-268
Astronomy and Astrophysics
Astrophysics
27
Astronomical Models, Hydrodynamics, Invariance, Protoplanets, Scale (Ratio), Solar Orbits, Solar System, Broken Symmetry, Distance, Mathematical Models, Planetary Evolution, Planetary Gravitation, Systems Stability, Solar System, Planets, Satellites, Origin, Formation, Hydrodynamics, Stability, Theoretical Studies, Dynamics, Kinematics, Calculations, Symmetry, Position (Location), Distance, Rotation, Scaling, Density, Gravity Effects, Planetary Systems, Orbit
Scientific paper
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 x = ln(r/r0). Since maxima equidistant in x obey a geometric progression in the variable r, 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.
Dubrulle Bérangère
Graner Francois
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