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In case you haven't heard already, researches at the California Institute of Technology discovered mathematical evidence of large object orbiting the sun at a distance about 20 times further than that of Neptune.

Because mathematical observations like this have not been made up until very recently, and the planet itself has yet to be observed, how can we be sure that this is in fact a planet, and not a more distant black hole?

My hyopthesis is based around the fact that, A.) We haven't observed the planet, and B.) There was a rumor a week earlier that gravitational waves had been observed at LIGO.

My knowledge of black holes pertains that, we would be able to observe such an object by viewing how light becomes obscured as it approaches the event horizon. But given that we are not able to look in every direction at the same time, the probability of missing such an occurance would not be low.

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All we can tell (assuming of course that the conclusions of the CalTech team are correct) is that there is a large mass in a distant orbit around the Sun. The mass could in principle be anything, but some things are more likely than others.

It seems very plausible that the mass could be a planet that got ejected from an orbit nearer the Sun because:

  • we know at least one planet of that mass has formed i.e. Neptune

  • computer simulations show planets can be ejected (with a significant probability)

You suggest that the object could be a black hole rather than a planet, but we know of no mechanism that could cause a 20 Earth mass black hole to be orbiting the Sun. That doesn't make it impossible, but it does make it very much less likely than that the mass is a planet.

Commenting on rumours is a somewhat pointless exercise, but for the record the rumour is that a black hole merger has been seen by LIGO. A solitary black hole would not create any detectable gravitational radiation. It's conveivable there might be gravitational waves if the black hole interacted with some other massive body, but in that case we'd get a flood of gamma rays that would certainly have been detected by now.

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    $\begingroup$ @OlegSilkin: at the distances we are talking about both a planet and a black hole would appear as a point mass. They would also follow the same orbit, which is indeed hypothesised to be elliptical and very eccentric. $\endgroup$ – John Rennie Jan 21 '16 at 17:31
  • $\begingroup$ @OlegSilkin: the orbit is predicted from the observations of objects in the Kuiper belt. A larger object (black hole or otherwise) at a greater distance would not match the observations. Whatever it is would have to be following an orbit pretty close to the one the CalTech team describe. $\endgroup$ – John Rennie Jan 21 '16 at 17:40
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In principle, any body with the mass of the proposed planet would have the same gravitational effect as the planet. Therefore, it would explain the orbit of those other bodies equally well.

We know of a lot of planets in orbit around stars (and we have theories about how they form). However, I don't think we've ever seen or theorized black holes in orbit around stars. So planet sounds more likely.

Someone should work out the Hawking radiation for a black hole of the proposed mass and see if it would stand out in any way. According to wolfram alpha it's massive enough to not radiate a lot. There are other observable differences (a hot disk of infalling matter, possibly jets of matter shooting out of the poles) which suggest a black hole would have been detected earlier.

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    $\begingroup$ Would an approaching mass explain the orbits? If not, there's no point proposing it. As regards proving it's not a black hole, look at my answer. Most observable differences require pointing a telescope at it. $\endgroup$ – ignacio Jan 21 '16 at 17:27
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"Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is."

It seems like the night sky isn't so very big, so it should be easy to observe objects, right? Wrong. Once you use telescopes, the night sky becomes huge and if you don't know what you are searching for, you'll only find out about it by coincidence. The biggest problem is that the planets only reflect light, which makes them barely shine, so we don't really know where to look and most ordinary telescopes will be unable to detect this. This planet is so far from the sun that sunlight is not stronger than our moon, so the reflected light will be much less (see https://astronomy.stackexchange.com/questions/13282/how-bright-would-the-sun-appear-from-the-hypothetical-planet-nine-proposed-by-ca).

But let me quote directly:

If the planet happens to be close to its perihelion, Brown says, astronomers should be able to spot it in images captured by previous surveys. If it is in the most distant part of its orbit, the world's largest telescopes—such as the twin 10-meter telescopes at the W. M. Keck Observatory and the Subaru Telescope, all on Mauna Kea in Hawaii—will be needed to see it. If, however, Planet Nine is now located anywhere in between, many telescopes have a shot at finding it.

So part A) is too weak to form a good basis for the hypothesis.

Part B) is also not a good basis, because first of all, they are rumours (which could turn out to be false positives) and second of all, we have no idea what else can be said about them and where they maybe originated - because, well, they are only rumored to be observed.

This together is enough to dismiss your theory as highly unlikely.

Can we do more? First of all, we know the mass of the supposed ninth planet. It's not very big, just a couple of times the earth's mass. This means, it is far from sufficient to have originated from a star. This is the only known mechanism for the creation of black holes today, which means that from my limited knowledge, we are left with two possibilities: either this would be a small primordial black hole (if those exist) or a black hole that has nearly evaporated (if black holes evaporate). Both of these are hypothetical and we don't have an accepted theory for the formation of black holes of this size - let alone a single observation.

Second, we have not yet observed any solar system with a black hole not at its centre (recall that we have not observed small black holes), but we have already found a lot of systems with a lot of planets where nobody thinks they are black holes. However, our solar system seems special among these. This new planet would change this (once again from the authors):

"One of the most startling discoveries about other planetary systems has been that the most common type of planet out there has a mass between that of Earth and that of Neptune," says Batygin. "Until now, we've thought that the solar system was lacking in this most common type of planet. Maybe we're more normal after all."

This is even more evidence that this might just be a planet.

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