Here is a rather poor image of part of Emile Sevin’s 1946 paper I have dug up off the net:
Comptes rendus de l’ Academie des Sciences 1946 tome 222 p220.
Astronomy:- On the structure of the solar system (Prevision of a new planet)
Note of M. Emile Sevin presented by M.Ernest Esclangon
Using the logarithms of the periods T of revolution of planets, expressed for example in days, let us form the following sums:
log T (Venus) + log T (Pluto) = 7,309;
log T (Earth) + log T (Neptune) = 7,342;
log T (Mars) + log T (Uranus) = 7,324;
log T (asteroids) + log T (Saturn) = 7288;
log T (Jupiter) + log T (Hidalgo) = 7,344;
These sums being very appreciably constant, the general structure of the solar system rises to an intricacy, of which the double period lies between those of Jupiter and Hidalgo; and as it would be surprising that only Mercury did not have one combined, has led us to envision that there exists, beyond the orbit of Pluto, a planet which constitutes the same limit of the solar system and which we will designate by letter X.
Under these conditions, the planets were left again in two groups: that of the planets inferiors, whose periods are shorter than the period doubles and who includes/understands Mercury, Venus, Earth, Mars, the asteroids and Jupiter that of the planets superiors, of which the periods are on the contrary longer than the period doubles and or one meets Hidalgo, Saturn, Uranus, Neptune, Pluto and X. It is not without surprise that in 1920 Baade has discovered Hidalgo, a small planet of 22km of ray, strayed, seemed it, a little further that Jupiter; in fact, it is thus the first higher planet and, as we will further specify it, among the others its place is, mathematically, very clearly marked.(1.)
(1 .)Of course, it could be that Hidalgo was not isolated, but found to be the type of a certain number of other asteroids, with periods close, which remain to be discovered.
According to our view, it is a cataclysm, to which the Sun has been subjected to, which can generate planets, whereas the satellites of those would come of secondary cataclysms. And one can think that it is in particular that these secondary cataclysms which one must allot the slight differences that the periods observed present, compared to those which result of a perfect involution (intricacy), However the involution (intricacy ) is still rather well preserved so that it is possible to recognize that the period of vibration of the Sun, i.e. the period of its infrasonic vibration (1/9 of day), has played an essential role in the distribution of the superior planets.
So indeed, one calculates the periods of revolution for which the equations of light “C” (the time that that light traverses the equatorial radii of the orbits) are equal has successively the period of the infrasonic vibration multiplied by 3/10, 1/2, 1, 3/2, and 2, one finds the periods of revolution of Hidalgo, Saturn, Uranus, Neptune, and Pluto (which are separated by considerable intervals) with the relative variations written here:-1/223,+1 / 84, +1/1 39,-1/18 and 1/27. [Garbled text recognition in these figures]
As for planet X, we will show that it is the multiplier 4 which is applicable for him. It locates the limits of the period of revolution and the average movement of planet, 247.275 days or approximately 677 years, 5, 24113, sizes that, relatively, one can considerer like exact has some hundreths close. And one obtains in excellent agreement with the sums indicated above.
This text was referred to by Valery Kotov and S. Koutchmy in their 1985 paper ‘A Possible Relation Between Planetary Distances and the 160-Minute Solar Pulsation’. In that paper, they reformulated Sevin’s insight and put the relationship between the 160 minute solar pulsation (hypothesized(?) by Sevin and empirically observed by them) on a sounder footing which didn’t require the use of Tiny Hidalgo. Their reformulation of Bode’s law recieved validation in 2005 with the discovery of Eris, a small planet around the size of Pluto, with a moon, Dysnomia. But Eris’ semimajor axis is not at the distance expected by Sevin, due to its high eccentricity. Sevin predicted a multiplier of four on the 160 minute light-speed wavelength which Kotov calculated to be L = 19.24a.u. In fact, Eris’ Aphelion is at 5L, perihelion is at 2L and the semimajor axis is at 3.5L. This gives Eris and orbital period of 557 years, rather than the 677 years Sevin predicted.
Kotov wrote a paper in 2007 ‘There are ten, not eight planets’ in which he expressed his annoyance at the downgrading of Pluto to ‘dwarf planet’ status following Eris’ discovery.
In 1946, E. Sevin postulated the global vibrations of the Sun with a period P 0 = 1/9 day and a “wavelength” L 0 = c x P 0 = 19.24 AU and predicted the tenth planet at a mean distance of 4.0 x L 0 = 77.0 AU from the Sun (c is the speed of light). The global vibrations of the Sun, precisely with the period of 1/9 day, were actually detected in 1974. Recently, the largest Kuiper Bell object 2003 UB313, or Eris, with an orbital semimajor axis = 3.5 x L 0 = 67.5 AU was discovered. We adduce arguments for the status of Eris as our tenth planet: (i) the object is larger and farther from the Sun than Pluto and (ii) the semimajor axis of Eris agrees well with the sequence of planetary distances that follows from the resonance spectrum of the Solar system dimensions (with the scale L 0 and for all 11 orbits, including those of Pluto, Eris, and the asteroid belt). We point to a mistake of the Prague (2006) IAU Assembly, which excluded Pluto from the family of planets by introducing a new, highly controversial class of objects-’dwarf planets.’
I think he has a point. If the relationships between the orbital distances of the planets and the Sun’s activity can be discerned, then they are of a family, even if some of them are small. Calling the small ones ‘dwarves’ is very un-PC these days. :)
What then of Sevin’s idea of adding the logarithms of the revolution periods of the pairs of planets? This is an interesting consonance, because it doesn’t rely on splitting the planets into two groups as Kotov did (inner planets and outer planets, with Jupiter at the ‘hinge’), though as we saw with Sevin’s inclusion of Hidalgo, it does require some creative thinking.
Sevin expected ‘planet X’ to have a period of 677 years (via Kepler’s third law: The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.) on the assumption of a 4L semimajor axis length. But Eris has a semimajor axis of 3.5L not 4L, so how might the circle be squared to account for this apparent disharmony in his scheme?
Both Eris and the planet at the other end of the solar system he wanted to pair it with, Mercury, have high eccentricity orbits: 0.206 for Mercury and 0.441 for Eris. This gives their aphelion distances as 0.466a.u for Mercury and 97.56a.u for Eris.
Orbits at these distances would take 116days and 351963 days respectively
Orbits at their semimajor axis distances give a figure of 7.2523
But if we take the log of Mercury’s perihelion orbit and add it to the log of Eris’ aphelion orbit we get
Which is right in the frame of the added logs of Sevin’s other planetary pairs. I think that given the fact Eris’ semimajor axis falls nicely on a zero crossing node at 3.5 times Kotov’s L value derived from the speed of light multiplied by the 160 minute solar pulse, we can therefore count Eris as one of our family, if a slightly wayward one who as her name suggests introduces a discordant and offbeat note into the music of the spheres. Her Moon daughter is after all Dysnomia, Δυσνομία, which translates as ‘lawlessness’.
Incidentally, Mike Brown from the discovery team, who chose the names ‘Eris’ and ‘Dysnomia’ must surely have read Robert Anton Wilson’s and Robert Shea’s ‘Illuminatus’ trilogy. Who says astronomers don’t have a sense of humour?
Hail Eris! All hail Discordia! – Final proof that we are comparing apples with apples! :)