a703 The work of J.M. Souriau on the solar system. (p: 2)
The theoretical prediction agrees well with the observed data, except for the resonant Neptune-Pluto pair, as expected.
What about the Titus-Bode law?
From the above theoretical result, Souriau immediately constructs a "golden law":
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Next, the golden law is compared to the Titus-Bode law, which corresponds 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 assumes that the entire 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 of the orbital periods of Saturn's satellites.
Two characteristic peaks appear again. Selecting these two lines, Souriau constructs the reciprocal 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 w and w2
By the way, Saturn's rings fit very well the golden law.
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Fig. 8: Expected values of the period P of Saturn's rings, based on a reciprocal Fourier transform limited to the two lines w and w2
Similar results for the set of Jupiter's satellites.
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Fig. 9: Fourier transform based on the measured orbital period values. Reciprocal Fourier transform giving the expected values of the orbital periods of Jupiter's satellites. Some fit well, others not.
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Fig. 10: Expected values of the orbital periods P of Jupiter's satellites, calculated from a reciprocal Fourier transform based on the two lines w and w2
Note the presence of the Sun, considered as "a satellite of Jupiter".