Scale relativity and quantization of planet obliquities

We apply the theory of scale relativity to the equations of rotational motion of solid bodies. We predict in the new framework that the obliquities and inclinations of planets and satellites in the solar system must be quantized. Namely, we expect their distribution to be no longer uniform between 0 and π, but instead to display well-defined peaks of probability density at angles θk = kπ/n. We show in the present paper that the observational data agree very well with our prediction for n = 7, including the retrograde bodies and those which are heeled over the ecliptic plane. In particular, the value 23″ 27′ of the obliquity of the Earth, which partly determines its climate, is not a random one, but lies in one of the main probability peaks at θ = π/7.