Remember that gravity falls off in strength with the square of distance. The gravitational field around such a black hole would be immensely strong and absolutely miniscule. The event horizon would be the size of a few atoms.
Locally, the black hole would swallow any atoms it comes into contact with and would probably scatter nearby molecules, but that's it. It'd pass straight through you.
The gravitational field would be enormous: 1,000–500,000 times Earth gravity, at one meter's distance, for the range of PBH masses this paper mentions. That's balanced out by the relative speed being a brisk 200 km/s, so the interaction time would be short (microseconds). Still a pretty significant momentum impulse if one flew by.
This is analyzed in the paper. There are two sources of problems: gunshot-wound-like, and the effect of transiently highly increased gravity on nearby tissues. The first one seems worse, and is the limiting factor. PS. The paper is very easy to read :)
If Bob is floating in space in a capsule, and a very heavy asteroid floats past, the amount that Bob's capsule is moved is dependent on the speed of the asteroid?
Does that sort of thing have to be considered when planning the orbits of probes etc?
Is Earth traveling fast enough, from the viewpoint of Alice floating near the sun, to have a gravity "tail" or "wake" trailing after it? (Alice near the sun thing is my attempt at a mostly static observer) And of course due to relativity, if Alice was orbiting retrograde to the big heavy object, she'd observe even more effect?
I think I need about 6 more cups of tea before I can think about this!
> If Bob is floating in space in a capsule, and a very heavy asteroid floats past, the amount that Bob's capsule is moved is dependent on the speed of the asteroid?
Yes
> Does that sort of thing have to be considered when planning the orbits of probes etc?
Yes, it's a primary concern when sending probes to other planets
> Is Earth traveling fast enough, from the viewpoint of Alice floating near the sun, to have a gravity "tail" or "wake" trailing after it?
If I understand you correctly, then classically (i.e. ignoring relativity), no. Your gravitational acceleration towards the earth depends only your distance to it. If you consider general relativity? It's... complicated.
Force is the derivative of momentum. If you apply a gravitational force for a short time, the derivative is the same but the change of momentum is tiny. If you apply it for a longer time, the change is bigger.
> Locally, the black hole would swallow any atoms it comes into contact with and would probably scatter nearby molecules
More likely, it would go straight through most atoms without interacting with them. They are tiny and move very fast, if you do the math the likelihood of direct, non-gravitational interactions with matter are somewhere near neutrinos, of which trillions passed through you while reading this sentence.
When one does end up eating something, the most significant effect is probably that it wouldn't eat the whole atom, but either just the nucleus, freeing all the electrons, or just an electron, leaving the atom positively charged.
I wonder what happens to the electrons when/if they interact with the black hole. There's already weird stuff going on there with electrons being particles and waves. So, I wonder what happens when you introduce something like a black hole to the equation. Does it have a charge? I'm assuming it'd break through the electron shell; would it absorb the electron/s upon interacting with the shell?
> Locally, the black hole would swallow any atoms it comes into contact with
Would it be capable of doing that? If the radius of the event horizon is significantly smaller than the radius of a proton, would it be capable of swallowing a proton (and how)?
Locally, the black hole would swallow any atoms it comes into contact with and would probably scatter nearby molecules, but that's it. It'd pass straight through you.