Take a small bh say 100 sol masses, how long would it take to ingest a Earth size planet?
Depends - I think black holes are hungrier in the mornings, I know I am!
On a serious note - the ingestion rate would be directly proportional to mass of the BH and I suspect the angle/inclination and speed of the approaching object may have an impact. Then again tidal forces may be so strong as to render the approach dynamics irrelevant. There is also reference frames to consider. From the reference frame of the infalling Earth mass, the time would be fairly quick, from the reference frame of a relatavistic observer you would see a different result.
However I suspect the mass would have been smashed into an accretion disk long before all of this matter is gobbled up by the hungry hole.
Any more knowledgeable posts welcome as I find a Black Hole appetite fairly interesting!
A 100-solar mass black hole has a Schwarzchild radius of about 300 km, a lot smaller than Earth's radius. Tidal forces would tear Earth apart as it approached the black hole, creating an accretion disc. Friction in the accretion disc would release vast amounts of energy, blowing a substantial portion of Earth's mass completely away from the interaction (to ∞ and beyond?). So the pedantic answer is forever.
Others have answered your question, so I'll just nitpick: 100 solar masses is pretty big for an astrophysical black hole (though obviously very small for a supermassive one!). We expect most black holes that are not the nuclei of galaxies to be closer to 5-15 solar masses, give or take. I don't think 100 solar mass black holes are nonexistent, just that there are likely a heck of a lot more smaller ones out there, so that I wouldn't call that particularly small.
If I recall correctly the lack of mid size black holes is a hot topic at the moment.
If the Earth gets torn apart by tidal forces and is turned into an accretion disk, what does that mean? Does that mean that the matter in the disk tumbles into the black hole in a spiral?
Thats a fairly accurate layman description. See http://en.wikipedia.org/wiki/Accretion_disc for more info.
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