1996A&A...315L...9N

We show in the present letter that the planetary companions recently discovered around nearby stars agree with the predictions made four years ago in the framework of the theory of scale relativity (Nottale, 1993, in Fractal Space-Time and Microphysics: Towards a theory of Scale Relativity). In the simplest case, we expect their periods to be "quantized" as T_n=2{PI}GMn³/w₀³∼3.25(M/M_☉)n³ days. In this formula, which corresponds to the peak of probability distribution of planet positions, M is the star mass, and w₀∼144km/s is a universal constant having the dimension of a velocity, which manifests itself from the Solar System scale to the extragalactic scales (Tifft effect). In particular, three planetary companions, including 51 Peg B, lie at 0.05AU from their star and so achieve the "fundamental level" of the theory for solar-type stars.