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Astron. Astrophys. 335, 281-286 (1998)

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5. Conclusion

With the present work we have tried to see if there is some consistency between the data of the solar system and the theory of Scale Relativity. Surprisingly, one finds almost always a good fit, except maybe for Neptune where there is a lack of data for close objects. This analysis reinforces then the confidence one can have in Nottale's description of large scale gravitational systems in terms of quantified systems. But the method also allows predictions: some levels are unoccupied. It means that either, for some unknown reason, there are no objects on the corresponding orbits, or they have not yet been discovered. Further analysis should take into account short time-scale resonances, and be extended to second order terms linked with the 3-body problem.

Notice that, on level 1, there is never any object. The most we have are objects in fragmented sublevels in case of Saturn, Uranus, Neptune, and for the outer solar system. Notice also that for every planetary system, the radius of the central object has a value wich seems also to fit in a specific rank.

It is also remarkable to notice that the orbital velocity corresponding to the rank n of the inner solar system is equal to 144 km/s. It is the same value as the one found by Tifft in the double galaxies (Tifft, 1977). This point has already been approached by Nottale in his last theoretical work (Nottale, 1997b).

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© European Southern Observatory (ESO) 1998

Online publication: June 12, 1998