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A comment on What If Planet 9 Is a Primordial Black Hole?. Parent comment

Re:What If Planet 9 Is a Primordial Black Hole? by semi-extrinsic on Thursday September 26, 2019 @11:14AM (#21081633)
The Roche limit depends on the density difference between the two bodies in question. For a black hole (of any size), the density is basically infinite compared to regular planets, so the Roche limit is basically zero. As in, less than one meter.

The radius of the event horizon for a black hole even the size of Jupiter is only 2.5 meters.

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Re:What If Planet 9 Is a Primordial Black Hole? by CodesInChaos on Thursday September 26, 2019 @11:25AM (#21081790)
The gravity field of a spherical object only depends on its mass and not its density/radius. So for the Roche limit only the density/radius of the object at risk of breaking apart (called minor object on wikipedia) (earth) should matter, not the one of the major object (black hole).

Wikipedia gives the formula d=R_m*(2m_M/m_m)^{1/3} which matches that intuition.

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Re:What If Planet 9 Is a Primordial Black Hole? by semi-extrinsic on Thursday September 26, 2019 @01:52PM (#21083451)
Ah, you're right.

So plugging in numbers you get 2.15 times the radius of Earth, which becomes 13 750 km.

For comparison, Earth-Moon distance is approx. 400 000 km.

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Re:What If Planet 9 Is a Primordial Black Hole? by perl4ever on Saturday September 28, 2019 @07:51PM (#21103909)
Yes, but you don't have to be within the Roche limit to have substantial tidal effects, which could destroy habitability at a much greater distance. Just look at Io.
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