Titius-Bode laws in the solar system. 2: Build your own law from disk models

Details Titius-Bode laws in the solar system. 2: Build your own law from disk models Titius-Bode laws in the solar system. 2: Build your own law from disk models

Feb 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994a%26a...282..269d&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 282, no. 1, p. 269-276

Astronomy and Astrophysics

Astrophysics

13

Accretion Disks, Astronomical Models, Hydrodynamics, Planetary Gravitation, Protoplanets, Solar System, Systems Stability, Boundary Conditions, Invariance, Mathematical Models, Planetary Evolution, Scale (Ratio), Wentzel-Kramer-Brillouin Method, Solar System, Planets, Satellites, Disks, Model, Theoretical Studies, Hydrodynamics, Stability, Rotation, Gravity Effects, Timescale, Density, Parameters, Calculations, Analysis, Comparison, Symmetry, Boundaries

Scientific paper

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 a 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 rhod)-1/2, where rhod is the disk density. This model links the separation between different density maxima with the ratio MD/MC of the masses of the disk and the central object; for instance, MD/MC 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 Wentzel-Kramer-Brillouin (WKB) approximation.

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