Distribution of Orbital Elements of Planets and Exoplanets in Scale Relativity

Details Distribution of Orbital Elements of Planets and Exoplanets in Scale Relativity Distribution of Orbital Elements of Planets and Exoplanets in Scale Relativity

Dec 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004sf2a.conf...75g&link_type=abstract

SF2A-2004: Semaine de l'Astrophysique Francaise, meeting held in Paris, France, June 14-18, 2004. Edited by F. Combes, D. Barret

Mathematics

Probability

Scientific paper

In the framework of scale relativity, we describe the motion of planetesimals in the protoplanetary nebula in terms of a fractal and irreversible process. As a consequence the equation of dynamics can be transformed to take a Schrödinger-like form. Its solutions yield a planetesimal distribution showing peaks of probability for particular values of conservative quantities such as the energy and the Runge-Lenz vector. After accretion, this results in expected probability peaks of the semi-major axis distribution at an = (GM/w2)n2, and of the eccentricity distribution at e = k/n, where k and n are integer numbers, M is the star mass and w is a constant having the dimension of a velocity. The current observational data in our solar system and extrasolar planetary systems support these predictions in a statistically significant way: we show that these systems are hierarchically organized in terms of a sequence of constants which are multiples and submultiples of w = 144.7+/-0.5 km/s. New validations of the theoretical predictions are given concerning the very inner solar system including the Sun itself, the distant Kuiper belt and exoplanets recently discovered very close to their star (at about 0.02 AU/Msol).

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