What If Planet 9 Is a Primordial Black Hole?

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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