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Astron. Astrophys. 361, 379-387 (2000)

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Scale-relativity and quantization of exoplanet orbital semi-major axes

L. Nottale 1, G. Schumacher 2 and E.T. Lefèvre 3

1 CNRS, DAEC, Observatoire de Paris-Meudon, 92195 Meudon Cedex, France
2 Observatoire de la Côte d'Azur, Département Augustin Fresnel, UMR 6528 du C.N.R.S., avenue Copernic, 06130 Grasse, France
3 8, rue des Lampes, 92190 Meudon, France

Received 14 April 1999 / Accepted 9 June 2000


In a recent study (Nottale 1996b), it was found that the distribution of the semi-major axes of the firstly discovered exoplanets was clustered around quantized values according to the law [FORMULA], in the same manner and in terms of the same constant [FORMULA] km/s as in our own inner Solar System. The ratio [FORMULA] actually stands out as a gravitational coupling constant. The number of exoplanets has now increased fivefold since this first study, including a full system of three planets around Ups And. In the present paper, we apply the same analysis to the new exoplanets and we find that their distribution agrees with this structuration law in a statistically significant way (probability [FORMULA]). Such a [FORMULA] law is predicted by the scale-relativity approach to planetary system formation, in which the evolution of planetesimals is described in terms of a generalized Schrödinger equation. In particular, one was able to predict from this model (Nottale 1993) the occurrence of preferential distances of planets at [FORMULA] and [FORMULA] from their parent stars. The observational data supports this theoretical prediction, since the semimajor axes of [FORMULA] of the presently known exoplanets cluster around these values (51 Peg-type planets).

Key words: relativity – gravitation – solar system – planets and satellites – planetary systems

Send offprint requests to: laurent.nottale@obspm.fr

© European Southern Observatory (ESO) 2000

Online publication: September 5, 2000