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Konstantin Batygin has estimated that if Planet Nine was ejected, it would have been ejected 3-10 million years after the formation of the Solar System.

I'm curious as to how he arrived at this figure. Was it through simulations of the early Solar System, a prediction of the alignments of orbits at that time, or something completely different?

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    $\begingroup$ The page you reference appears to be infected with some annoying pop-up/virus. I am unable to locate any source for the statement you are questioning; it does not appear to have been made by Batygin. $\endgroup$ – ProfRob Jan 26 '16 at 7:30
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    $\begingroup$ @RobJeffries It's a stupid scraping site, I have replaced the link $\endgroup$ – user1569 Jan 26 '16 at 13:05
  • $\begingroup$ @RobJeffries I'm so sorry; I thought I had inserted the Wikipedia link, but I must have encountered a redirect somewhere. Thank you for pointing this out; I should have been more careful. $\endgroup$ – HDE 226868 Jan 26 '16 at 13:13
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Page 12 of Batygin & Brown (2016) says that a speculative formation scenario can be drawn from recent solar system formation simulations by Bromley & Kenyon and by Izidoro et al. These suggest that the core of a nascent ice giant may have been ejected very early in the solar system's history in order to explain the properties of the observed planets; the formation of Uranus and Neptune was probably accompanied by at least one other ice giant.

The source of the claim you mention is actually an article by Eric Hand in Science Magazine. He points out that possibly, to explain why this planet was ejected yet still remains part of the solar system in a much wider orbit, then you need it to have been slowed down by residual gas in the protosolar disk. So I assume the 10 million year is an (uncertain) upper limit on the dispersal of the disk and I would guess the 3 million year lower limit is just how long it takes to form a 10 Earth mass ice giant core at the distance of Neptune.

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