## Scale-relativity and quantization of exoplanet orbital semi-major axes
^{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
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 , in the same manner and in terms of the same constant km/s as in our own inner Solar System. The ratio 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 ). Such a 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 and from their parent stars. The observational data supports this theoretical prediction, since the semimajor axes of of the presently known exoplanets cluster around these values (51 Peg-type planets).
## Contents- 1. Introduction
- 2. Theory: a short reminder
- 3. On the nature of the fundamental ratio : a gravitational coupling constant
- 4. Comparison with observational data and statistical analysis
- 5. The triple system around Upsilon Andromedae
- 6. The planet around HD 209458 and other 51 Peg-like planets
- 7. Discussion
- 7.1. Theory
- 7.2. Error analysis
- 7.3. Consequences for exoplanets
- 8. Conclusion
- Acknowledgements
- References
© European Southern Observatory (ESO) 2000 Online publication: September 5, 2000 |