Quantization of Planetary Systems and its Dependency on Stellar Rotation

Posted: January 4, 2020 by tallbloke in Analysis, Astrophysics, Celestial Mechanics, solar system dynamics
Tags: ,
Solar system planets [image credit: BBC]

Well this looks interesting. Jean paul Zoghbi has discovered half integer relationships between star rotation rates and their planetary system’s angular momenta. The paper is here

Abstract With the discovery of now more than 500 exoplanets, we present a statistical analysis of the planetary orbital periods and their relationship to the rotation periods of their parent stars. We test whether the structural variables of planetary orbits, i.e. planetary angular momentum and orbital period, are `quantized’ in integer or half-integer multiples of the parent star’s rotation period. The Solar System is first shown to exhibit quantized planetary orbits that correlate with the Sun’s rotation period.

The analysis is then expanded over 443 exoplanets to statistically validate this quantization and its association with stellar rotation. The results imply that the exoplanetary orbital periods are highly correlated with the parent star’s rotation periods and follow a discrete half-integer relationship with orbital ranks n=0.5, 1.0, 1.5, 2.0, 2.5, etc. The probability of obtaining these results by pure chance is p<0.024. We discuss various mechanisms that could justify this planetary quantization, such as the hybrid gravitational instability models of planet formation, along with possible physical mechanisms such as the inner disc’s magnetospheric truncation, tidal dissipation, and resonance trapping. In conclusion, we statistically demonstrate that a quantized orbital structure should emerge from the formation processes of planetary systems and that this orbital quantization is highly dependent on the parent star’s rotation period.

From Table 1, it can be observed from the orbital ranks calculated using the Sun’s presentrotation period that the Solar System exhibits a discrete and quantized orbital structure wherethe planets’ specific orbital angular momenta J n are ranked in discrete half-integer multiplesof the specific angular momentum J 0 at the solar corotation orbit (n=1.0, 1.5, 2.0, 2.5, 3.0,3.5, etc.). TheΔn deviations from integer or half-integer values are included in Table 3 andindicate that 16 out of 19 planetary orbits have absolute deviations|Δn|<0.07. The discretenature of planetary semi-major axes, mean orbital velocities, and orbital periods, in terms of half-integer values, follow logically from the quantized orbital angular momentum results.The inner planets Mercury (n=1.5), Venus (n=2.0), Earth (n=2.5), and Mars (n=3.0) occupythe ranksn= 1.48, 2.07, 2.43, and 2.99 respectively with minimal deviationsΔn from the closest integer or half-integer values. In the main Asteroid Belt, the orbits of the Flora family are ranked atn=3.5, with both Flora and Ariadne occupying n=3.57. At the orbital rank n=4,the main asteroid families of Ceres and Pallas represent the group and both occupy the rank n=4.03. This orbital rank also includes Misa, Eunomia, Lamberta, and the Chloris families at n=3.90, Ino and Adeana atn=3.94, Dora at n=3.96, Elpis, Herculina, Gyptis, Juewa, Minerva,Thisbe, Dynamene, and Eunike are all at n= 3.99, Eugenia and Nemesis at n=4.0, the Lydia,Gefion, and Pompeja atn=4.01, and the Brasilia & Karin families at n=4.09.

  1. oldbrew says:

    Certainly interesting, although quantization is not exactly my forte 😐

    Nearer to home, the Moon’s orbit (and rotation) around the Earth is 13:14 (99.96% true) with the solar rotation of 25.38 days quoted in the paper. 13 lunar orbits is sometimes called the lunar year, i.e. the nearest whole number of lunar orbits to one Earth year = orbit of the Sun.

  2. oldbrew says:

    From p.13 of the paper:
    HD 200964 b 630.00 (orbital period in days)
    HD 200964 c 825.00

    Ratio (divide by 15) = 42:55 = 1:1.3095238 = 2: 2.6194076 (~Phi², or 55/21 in Fibonacci numbers)
    – – –
    ‘Only’ 235.5 light years away, or about 40 billion years at walking speed.

  3. stpaulchuck says:

    I love the age of computers and the men and women who know how to use them. It would have taken a lifetime to manually do the math on this IMHO, but with today’s math modelling this pops out in a few days of programming and a few tics of computer time to validate it.

    Then of course there’s the marvelous folks who look at the stars, and then look farther, and deeper. Such marvelous things they discover and reveal. Thanks.

  4. Jopo says:

    Hi guys, apologies for being off topic but relevant to planetary orbital bodies.

    I recently have stumbled or perhaps guided into a correlation that is to good to be ignored in my opinion. The stuff needs a lot more work. I do not know where to post the stuff where I can hopefully learn a bit more from you guys. Believe me it is this site that got me questioning the climate correlations with our planets many years ago.

    So I have found that by adding the cosines of the planets longitudinal position with reference to the sun with specific reference to to J, S and U. The absolute Sum (ABS) of (Jupiter+ Saturn +Jupiter + Uranus) and then was compared to the correlation of TPW and OLR using the Correl function in excel. The data for the TPW OLR is from NOAA NCEP Reanalysis and the planets is from the Horizons Nasa site.

    Again sorry to be off topic but can I be directed to another section here to discuss. I have more details and correlations of other facets of our planet to our planets polar energy release and the also magnetic variations over time.

    Picture of the correlation is here https://hotcopper.com.au/attachments/060120-1-png.1922146/

  5. oldbrew says:

    Jopo – select Suggestions at the top of our home page, then click on the ‘current page’ link.

    Btw your own link asks for a login to a copper investments site?
    – – –
    General comment – in the paper, see:
    6.5 The Role of Resonance Trapping in Forming Discrete Planetary Orbits Resonance

  6. jpzogby says:

    Hi, thanks for sharing my paper here. The quantization applies to all planetary systems, covering around 500 exoplanets in 2011 (and not just our solar system). I plan to update this research with the recently discovered exoplanets up to 2020 (when I get some free time), just to see if the statistics still hold.
    The planetary orbital quantization in half-integers multiples of the stellar rotation (spin) and is very similar to Bohr’s atomic model.

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