Close encounters of the dark kind: how close to a black hole can you shoot and still miss?
As Newton said once, all things attract all other things (I have it on audio if you don’t believe me), so if you are reckless enough to go for a warning shot, don’t aim too close to your target, or you might hit it by accident, because gravity. You have to make sure that the point of closest approach is not inside your target. Comets in the Kuiper belt or in the the Oort cloud aiming to zoom really close to the Sun often make this fatal mistake. Now, this blog’s author has an unhealthy fascination with black holes, so let’s try to near-miss one of those. Let’s shoot a projectile such that it passes real close to the event horizon before coming back out on the other side. How hard can it be, just keep aiming closer and closer…
Uh, no. Yes, you can aim closer and closer, up to a point. If you aim too close, you would notice that your tracer bullets, instead of circling the black hole decide to dive into it. If you shoot just close enough for the point of closest approach (peri-blackhole-ion?) to be somewhere around 2-3 black hole radii, depending on how speedy your bullet is, it (the imaginary bullet) circles and comes out, but if you shoot any closer, it does not. There is no trajectory such that the bullet comes close to grazing the event horizon before coming back out.
So, a regular bullet cannot come close to the horizon and live to tell the tale. How about a really fast bullet? If it flies faster, wouldn’t it be able to come closer compared to the slower one? After all, it spends less time in the danger zone. The answer is a qualified “yes”. The higher is the bullet’s velocity, the closer its peri-hole-ion is. But there is a limit of how fast things can fly. Even a near-light speed bullet can’t get all the way down and then back up. The best it can do is to come down to 1.5 black-hole radii. There it can linger a bit, make a turn or two or 10, then spiral back out. Any closer, and it’s a goner. This closest approach orbit is known as the photon sphere. Not that there are many extra photons there, they either fall in, or come out, or even both.
This is the black hole ballistics. But not being able to graze the event horizon with a bullet does not mean that you cannot come close to it, at least theoretically, with a powered star ship. You could, if your ship is powerful, if you can stand bone-crushing g-forces and if you are very careful.
For a solar mass black hole, if you want to stop and hover near the photon sphere, the g-forces you would feel are about 10 billion times the Earth’s gravity. Less if you want to have a quick flyby, but still probably more than a human can handle. Or a ship built out of any known material, for that matter. But what about inertial dampers? No, sorry, no messing with gravity while we are studying gravity, only non-gravitational physics allowed.
But suppose you and your ship are made out of spider silk or carbon fiber, and you have antimatter source for fuel. The matter and antimatter annihilate and the resulting radiation is emitted as propellant to provide reaction. That’s as efficient as one can get without warp drives and other gravity-based tech. Why would you need to be careful? Because… well, you might end up inside the horizon without realizing it, and then it’s too late. I’ll return to this question next time. Maybe.