## Introduction

#### On the distribution of the planets and the satellites

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This study of Maurice Allais contains 69 pages and is
finished with a bibliography naming 29 different research
works dating from 1766 to our present days.

It has not been yet the object of a publication.

Here follow a resume of his paper.

The distances of the sun to the planets of the solar system
and the distances of the planet central of the satellites
of Jupiter, Saturn and Uranus are not just any numbers.

We observe that those distances answer to a mathematical law,
yet not knowing as of today of an explicit reason.

1.	Anterior Works.

The effort to bring to attention the relation of the
proportional distances of and in the solar system as very
ancient origin and Wolf, the German Astronomer has been
one of the first to realize the importance of those
researches in 1741.

Titius, rediscovered it in 1766. Yet it is mainly known
due to Bode who published his work in 1772. It is known
as the Titius- Bode law.

Subsequently numerous contribution have been presented,
some of greater value than others. To the fore ranks of
those contributions, we can situate the formulation of
Gaussin, simultaneously valuable for the planets and
for the satellites of the planets.

2.	Contribution of Maurice Allais.

The research work of Maurice Allais inscribes itself in
the long lineage of all those publications. His formulation
depends only on 2 parameters and situates itself in the way
opened by Gauss in 1880.

The formula is written as:

Where:

dn’ represents the distance of the satellite to the central planet, and
ra the radius of the central planet, and
na* a positive integer.

The parameter A* and na*, represent 2 parameter of adjustment.
The values of the n represent the numerical order of the satellite
to the central planet.

Altogether this formulation gives excellent results for the system
of the Sun, of Jupiter and of Saturn and Uranus.

The estimations of the dn, ra results of the relation of the
Celestial mechanics, which place itself in the isotropic and
Euclidian space.

The considered formulation can be interpreted as corresponding
to a localization of the planets and of the satellites of the
planets at the sinusoids knots of the period T=2 in the space
of the n’.

As of today, no theoretical explanation has been given for this
formulation, which brings the intervention of the neperien
logarithms of the distance in space fundamentally isotrope and
Euclidian of the celestial mechanic. Nevertheless, it certainly
doesn’t diminish its importance and significance.

Author:      Maurice Allais (22-DEC-2003)
Translator:  François Bocquet 01-AUG-2004

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