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A lead scientist of the Planet Nine theory said that "The period with which it goes around the sun is a rational multiple of the periods of all the furthest Kuiper Belt objects"

To what degree of precision can Konstantin Batygin make that kind of measurement? Has it been backed up by other physicists with a degree of certainty?

He also says that they think it's near it's aphelion "because it hasn't been seen, so it's far away", not because of the above period coincidence, why can't they say where it is more convincingly?

Does that mean that they have very strong mathematical evidence for Planet Nine?

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  • $\begingroup$ I wonder what "rational multiple" means?? $\endgroup$
    – Fattie
    Commented Nov 5, 2016 at 10:34
  • $\begingroup$ It means that for every 18 times a Trans Neptunian object goes round, for example Sedna which is 2000km diameter, Planet Nine goes around 33 times, it means an integer multiple... in the interview he said, "an Integer multiple, no sorry a Rational multiple" so i figure he means they have orbit coincidence like 18/33, 21/55 and so on, and that propulses them far away in a stable resonant path same as pushing a child on a swing every 1/3 times he swings. It seems to be a very vague model at the moment because the orbit of the planet is 10000/20000 years, Sedna is 11000 years. $\endgroup$
    – bandybabboon
    Commented Nov 5, 2016 at 10:52
  • $\begingroup$ Yes, a rational number (so, any integer divided by any other) seems very broad; (ok, so it's "128361283/18263716" - heh) I assume it implies "small integers ratio" (2/3, 7/4, etc) - I guess there's no specific word for such a harmonic. $\endgroup$
    – Fattie
    Commented Nov 5, 2016 at 10:55

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I did a little digging and I found this article.

It's worth noting that the initial publication wasn't about resonances but the fact that all 6 objects came from the same side of the sky, from somewhat similar directions, which, given that they were the 6 most distant at the time, is statistically unusual and it was both similar direction and similar inclination to the plane, so the statistical improbability was high enough to investigate. Orbital resonance wasn't the primary argument, it was tacked on later as a secondary.

From the article:

Their analysis also offered suggestions as to what kind of resonance the planet has with the KBOs in question. Whereas Sedna’s orbital period would have a 3:2 resonance with the planet, 2010 GB174 would be in a 5:2 resonance, 2994 VN112 in a 3:1, 2004 VP113 in 4:1, and 2013 GP136 in 9:1. These sort of resonances are simply not likely without the presence of a larger planet.

“For a resonance to be dynamically meaningful in the outer Solar System, you need one of the objects to have enough mass to have a reasonably strong gravitational effect on the other,” said the research team. “The extreme Kuiper belt objects aren’t really massive enough to be in resonances with each other, but the fact that their orbital periods fall along simple ratios might mean that they each are in resonance with a massive, unseen object.”

But what is perhaps most exciting is that their findings could help to narrow the range of Planet 9’s possible location. Since each orbital resonance provides a geometric relationship between the bodies involved, the resonant configurations of these KBOs can help point astronomers to the right spot in our Solar System to find it.

now, I want to point out that it's them, not me who did the typos on 2 of the objects, I'm pretty sure (based on Wikipedia and the chart below) that it should be 2004 VN112 (not 2994 VN112) that has the 3:1 and 2012 VP113 (not 2004 VP113) that has the 4:1.

This chart below also has a typo, it should be 2010 GB174 not 2012 GB174. I guess nobody proofreads letter/number assignments. Correct names will help if anyone wants to run the numbers see how see how close the resonances come to each other.

enter image description here

As to the degree of statistical certainty? If you're a good enough statistician, you can run the numbers. 3/2, it seems to me, would be the most common resonance based on Jupiter's abundant Hildas and the Plutinos and only 1 of the 5 potentially resonant objects has a 3/2, but 3/2 is also very far from the sun and hardest to detect, so that's not a deal breaker.

I'd guess that the degree of certainty from these orbital resonances is OK but not great - but that's entirely a guess. I also don't know enough about astronomy to know how close numbers have to be to provide some evidence of orbital resonance. Jupiter's resonant moons, for example, if you check their orbits, are off by 1 or 2 percentage points from each other.

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