2000A&A...361..379N

In a recent study (Nottale, 1996A&A...315L...9N), 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 a/GM=(n/w₀)², in the same manner and in terms of the same constant w₀=144km/s as in our own inner Solar System. The ratio α_g=w₀/c 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 ≃10^–4). Such a n² 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 Schroedinger equation. In particular, one was able to predict from this model (Nottale, 1993, Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity (World Scientific)) the occurrence of preferential distances of planets at ≃0.043AU/M_☉ and ≃0.17AU/M_☉ from their parent stars. The observational data supports this theoretical prediction, since the semimajor axes of ≃50% of the presently known exoplanets cluster around these values (51 Peg-type planets).