The work by J.M. Souriau on the solar system. (p:2)
The theoretical prediction agrees well with the observational data, except for the Neptune-Pluto resonant pair, as expected.
What about the Titius-Bode law?
From the above theoretical result, Souriau immediately constructs a "golden law":
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1.9n
Next, the golden law and the Titius-Bode law are compared, the latter corresponding to:
2.4 ( 0.4 + 0.3 2n)
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Fig. 5: Comparison of the laws giving
the orbital distance in logarithmic values.
If we consider its rotation period, the Sun follows this law. The interpretation is as follows: Souriau supposes that the entire system is shaped by dissipative processes due to tidal effects.
He then applies his method to the satellites of Saturn:
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Fig. 6: Fourier transform analysis for
the orbital periods of Saturn's satellites.
The two typical peaks reappear. Selecting these two lines, Souriau constructs the inverse Fourier transforms. The result is shown in Figure 7. Note that the Sun "behaves like a satellite of Saturn."
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Fig. 7: Expected values of the orbital periods P of Saturn's satellites, derived from a spectrum limited to the two lines ω
and ω2
Incidentally, Saturn's rings fit the golden law very well.
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Fig. 8: Expected values of the period P of Saturn's rings, based on an inverse Fourier transform limited
to the two lines ω
and ω2
Similar results are obtained for the set of Jupiter's satellites.
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Fig. 9: Fourier transform based on the measured values of the orbital periods.
The inverse Fourier transform yields the expected values of the orbital periods of Jupiter's satellites. Some fit well, others do not.
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Fig. 10: Expected values of the orbital periods P of Jupiter's satellites, calculated from an inverse Fourier transform based on the two lines ω
and ω2
Note the presence of the Sun, considered as "a satellite of Jupiter."
