Astronomy and Astrophysics – Astrophysics
Scientific paper
Jun 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997a%26a...322.1018n&link_type=abstract
Astronomy and Astrophysics, v.322, p.1018-1025
Astronomy and Astrophysics
Astrophysics
26
Chaos, Diffusion, Gravitation, Planets And Satellites: General, Solar System: General
Scientific paper
The scale relativity theory, by giving up the differentiability of space-time coordinates at very large time-scales, describes the solar system in terms of fractal trajectories governed by a Schroedinger-like equation. The predictions of the theory are expressed in terms of probability densities, that we interpret as a tendency for the system to make structures. Planets can no longer orbit at any distance from the Sun, but instead at preferential distances given at lowest order by: a_n_=(GM/w_0_^2^)n^2^. In this formula, M is the mass of the Sun and w_0_=~145km/s is a fundamental constant which is observed from the planetary scales to the extragalactic scales. Our theoretical predictions agree very well with the observed values of the actual planetary orbital parameters, including those of the asteroid belts. In addition, since Mercury ranks n=3 in the above formula, there is good reason to anticipate a small planet or two between the Sun and Mercury. We propose to check the theory by searching for such an object, on the second orbit which has a semi major axis of =~0.18AU.
Gay Jean
Nottale Laurent
Schumacher Georg
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