TitiusBode laws in the solar system. 1: Scale invariance explains everything
Abstract
According to the TitiusBode 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 TitiusBode 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/r_{0}). Since maxima equidistant in x obey a geometric progression in the variable r, TitiusBode 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 TitiusBode law is real, it is probably only a consequence of the scale invariance of the disk which gave rise to the planets.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 February 1994
 Bibcode:
 1994A&A...282..262G
 Keywords:

 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;
 Astrophysics; Planets