The J.M.Souriau's work about
the solar system. (p:2)
The theoretical prediction fits
well the observational datas, except for the resonant couple Neptun-Pluto,
as expected.
What about the Titus-Bode law ?
From the above theretical result
Souriau builds immediatly a "golden law" :
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1,9n
Next, the golden law and the Titus-Bode
law are compared, the latter corresponding to :
2,4 ( 0,4 + 0,3 2n)
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Fig. 5 : Comparizon of the
laws giving
the orbital distance in logarithmic
values.
If we consider its rotation period,
the Sun follows this law. The interpretation is the follwing: Souriau supposes
that all the system is shaped by dissipative processes, due to tidal effects.
Then he applies his method to the
satellites of Saturn :
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Fig. 6 : Fourier transform
analysis for
orbitation periods of Saturn'
satellites.
The two typical peaks apper again.
Selecting these two lines, Souriau builds the reciprocal Fourier transforms.
The result is given on figure 7. Notice that the Sun "behaves like a satellite
of Saturn".
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Fig.7 : Expected values of
the orbitation periods Pof the satellites of Saturn, derived from a spectrum
limited to the two lines w
et w2
By the way the rings of Saturn fit
very well the golden law.
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Fig.8 : Expected values of
the period Pof Saturn' rings, based on a reciprocal Fourier transform
limited
to the two lines w
and w2
Similar results, for the set of Jupiter'
satellites.
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Fig.9 : Fourier transform
based on the measured orbitation periods values.
Reciprocal Fourier transform gives the expected values of the orbitation
periods of satellites of Jupiter. Some fit well, some not.
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Fig.10 : Expected values
of the orbitation periods Pof Jupiter' satellites, calculated from a reciprocal
Fourier transform based on the two lines w
and w2
Notice the presence of the Sun,
considered as "a satellite of Jupiter".
