Mathematics – Probability
Scientific paper
Apr 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003eaeja....11864g&link_type=abstract
EGS - AGU - EUG Joint Assembly, Abstracts from the meeting held in Nice, France, 6 - 11 April 2003, abstract #11864
Mathematics
Probability
Scientific paper
The theory of scale relativity, applied to macroscopic gravitational systems like planetary systems, allows one to predict quantization laws of several key parameters characterizing those systems (distance between planets and central star, obliquity, eccentricity...) which are organized in a hierarchical way. In the framework of the scale relativity approach, one demonstrates that the motion (at relatively large time-scales) of the bodies in planetary systems, described in terms of fractal geodesic trajectories, is governed by a Schrödinger-like equation. Preferential orbits are predicted in terms of probability density peaks with semi-major axis given by: a_n = GMn^2/w^2 (M is the mass of the central star and w is a velocity close to 144 km s-1 in the case of our inner solar system and of the presently observed exoplanets). The velocity of the planet orbiting at this distance satisfies the relation v_n = w/n. Moreover, the mass distribution of the planets in our solar system can be accounted for in this model. These predictions are in good agreement with the observed values of the actual orbital parameters. Furthermore, the exoplanets which have been recently discovered around nearby stars also follow the same law in terms of the same constant in a highly significant statistical way. The theory of scale relativity also predicts structures for the obliquities and inclinations of the planets and satellites: the probability density of their distribution between 0 and pi are expected to display peaks at particular angles θ_k = kpi/n. A statistical agreement is obtained for our solar system with n=7. Another prediction concerns the distribution of the planets eccentricities e. The theory foresees a quantization law e = k/n where k is an integer and n is the quantum number that characterizes semi-major axes. The presently known exoplanet eccentricities are compatible with this theoretical prediction. Finally, although all these planetary systems may look very different from our solar system, they actually present universal structures comparable to ours, so that a high probability to discover exoplanets having orbital characteristics very similar to the Earth's ones can be expected.
da Rocha Daniel
Galopeau Patrick H. M.
Nottale Laurent
Tran Minh N.
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