Wouldn't we expect such a black hole to slingshot dust and other material to some non-negligible percentages of the speed of light? Wouldn't some of that eventually hit the earth's atmosphere? What would that look like? Tunguska?
Not really, it would just form a (tiny) accretion disk. Dust and other material would fall into it, emit gamma rays and be gone forever. It's a black hole.
Or both. Accretion disks can shoot a tiny bit of matter out the poles while most falls in. IIRC, the dynamics that cause this effect are not well understood.
It does have a special ability to slingshot, because you can get much closer to its center of mass than you could with a planet and get higher accelerations.
I thought slingshot was just another name for a gravity assist. Can you explain in more detail when it is or isn’t useful to get very close to the massive object?
Slingshot uses the motion of the planet around the sun, and pulls the probe along with it in the same direction that the planet is orbiting the sun.
The probe comes in perpendicular to the solar orbit, and leaves parallel to the solar orbit, and faster (relative to the sun). Relative to the planet there is no change in speed.
Kind of like bouncing a ball against a moving car. Relative to the car nothing happened, but relative to the ground the ball is faster.
Gravity burn is more complicated. (Oberth effect)
Imagine a stationary rocket (bolted to the ground). All the energy of the fuel is in the exhaust, and none in the rocket.
Now imagine the reverse - a really fast rocket, now way more of the energy is in the rocket (and less in the exhaust).
So what do you do? You fall toward a planet, and at the point where you are moving fastest, you fire your rocket. Now not only does your fuel have the energy inherent in it, it also has all the energy from falling toward the planet.
And this is the big idea here: You leave that fuel behind as exhaust! So when you climb back out of the planet you don't carry the fuel with you.
Normally falling toward a planet, and leaving the planet exactly cancel out. But you used the oberth effect to leave the fuel behind at the point where the fuel has the most kinetic energy.
That wouldn't get anything up to relativistic speeds. The universal rule of slingshot manoeuvres is that you depart from the slingshotting body at the same speed you approached it, just in a different direction (in the slingshotting body's frame of reference). Therefore, the maximum velocity gain you can achieve with a slingshot is governed by the velocity of the slingshotting body - the black hole. Which, as far out in the extremities of the solar system that it is, is not very fast.
If the black hole is rotating isn't the reference frame in motion about the center of the black hole in addition to the orbital velocity about the sun? i.e. frame dragging?
You mean https://en.wikipedia.org/wiki/Penrose_process - it doesn't look like it is very efficient or effective, and you'd have to get so close to the black hole that you'd be shredded to get anything at all.
