In August, Michael Brown and Konstantin Batigyn proposed new data concerning the hypothetical Planet X to explain the orbits of the 19 TNOs. They suggest a perihelion of 300 AU, but might Planet X be even much closer? Is there something like a minimum perihelion it must have to account for the TNOs' highly elliptical orbits?
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1$\begingroup$ This is a proper science based question. I voted up to encourage you to post more questions like this rather than your previous one. $\endgroup$– StephenG - Help UkraineOct 19, 2021 at 21:08
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Well yes, because Brown & Batygin (2021) say the perihelion would be $300^{+85}_{-60}$ au, so there is roughly a 50% chance that the perihelion is smaller than 300 au according to their work.
The quoted error bars represent their estimate of the 16th to 84th percentiles of a probability distribution, so conceivably the perihelion could even be a little lower. One or two of their simulations suggest a perihelion as low as 200 au, but they are less favoured than those with a larger perihelion distance.
This picture from Batygin et al. (2019) is quite helpful. It shows the parameter space for any new planet that is ruled out by other current observations (e.g. infrared surveys by WISE, the limits on perturbations of giant planets ["ruled out by ephemeris"]). The hatched region shows what might still be possible and does admit the possibility of a small planet between 100 and 200 au, but I would think thathas been superseded by Brown & Batygin's recent work.
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$\begingroup$ Thank you. It looks like they assume that beyond 1,000 AU there could't be any more planets but despite one's belief the Sun might capture a rogue one. $\endgroup$ Oct 19, 2021 at 15:29
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1$\begingroup$ @LoveForChrist, a gravity capture requires giving up excess orbital energy to some other planet. In order for a rogue planet to be captured, it would need to approach the Sun at least as close as Neptune's orbit. $\endgroup$– MarkOct 19, 2021 at 22:35
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$\begingroup$ @Mark, in theory, I believe there are ways in which a capture could happen even with a perihelion far beyond Neptune. But all the mechanisms I can think of for that require either an unlikely initial state (e.g. a very loosely bound binary pair of rogue planets passing by the Sun) or an unlikely coincidence (two separate rogue planets passing close to each other in the Sun's vicinity), so I do agree with your comment in general. $\endgroup$ Oct 20, 2021 at 1:28
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$\begingroup$ @IlmariKaronen: I'm used to tidal capture but I don't think that can happen at 300AU. $\endgroup$– JoshuaOct 20, 2021 at 18:11