In short, in Orbital mechanics, burning your thrusters deeper within a gravity well, results in a greater increase in kinetic energy than burning them further out.
This is because momentum ~ v, while kinetic energy ~ v^2. If you're travelling faster—as you would be as you approach the black hole and fall deeper and deeper in your orbit—then you can expend to same amount of momentum to receive a disproportionally larger increase in kinetic energy.
Because your potential energy falls off with distance to the black hole at the same rate regardless of the speed you're travelling at, your total energy upon escaping the black hole is much larger than it would be had you burned your thrusters outside its gravity well.
The phenomenon described is not due to the Oberth effect.
What would be happening would be that the human in the spacecraft, and the spacecraft, are accelerating at exactly the same rate because they are accelerating due to gravity. Thus, the human feels no pressure accelerating him (no outside force acting upon him) from e.g. his seat. And his internal organs feel no pressure accelerating them from each other. They (the craft and the human and all his internal organs) are in free fall together and feel no forces acting upon them despite the whole system (craft-human-organs) being accelerated to tremendous velocities.
It's super un-intuitive, but you're indirectly harnessing the gravitational potential energy of lowering your propellant into a gravity well and leaving it there. The overall orbital energy gain of the spacecraft can exceed the chemical energy of the fuel.
In terms of the energies involved, the Oberth effect is more effective at higher speeds because at high speed the propellant has significant kinetic energy in addition to its chemical potential energy.[2]: 204 At higher speed the vehicle is able to employ the greater change (reduction) in kinetic energy of the propellant (as it is exhausted backward and hence at reduced speed and hence reduced kinetic energy) to generate a greater increase in kinetic energy of the vehicle.
If you sit on a merry-go-round, and spin it very fast, you feel the "centrifugal force" trying to keep you in an inertial frame. That's because you're having to hold on to the ride. If you're in a spacecraft in orbit around Earth, you don't feel the force keeping you in a circular motion, because both you and the craft are experiencing the same force.
The worse thing about going past a blackhole would be tidal forces, which would exert differential stretching to your craft and you. I don't know the numbers for a blackhole that small. Also you'd need to aim very precisely - if you miss, it's a long way round to get back there and if you aim too well, it might take a chunck out of your craft and your left foot.
I was wondering that actually if the hole goes through your leg does it leave a hole or does your whole body get sucked in.
I imagine it is the whole body unless you are travelling really fast at the time. Like near speed of light.
Because the gravity outside the event horizon will still be crazy strong going out for several km (earth is a good comparison in the gravity is still fairly strong about 6000km from the centre)
Black holes warp the spacetime around them, so your idea of distance is isn't really valid. Also the idea of time is warped as well, so the black hole doesn't quite just pass through your leg as you expect.
Nor does the black hole "suck" anything in.
What would happen from your perspective if such a black hole were to pass you at high velocity would be the same as if you were to pass the black hole at high velocity. From your perspective, you would begin orbiting that object, carried along with it. So would all the matter near you. But it would be matter, not objects, as the tidal forces would spaghettify all objects very quickly.
> gravity is still fairly strong about 6000km from the centre
Sounds like the centre is what creates gravity. But there's weightlessness at the Earth center. It's the sum gravity force of all Earth particles that creates total gravity.
Depends on the size of the hole. If it's small enough, all you might get is one long bruise due to tidal/gravity effects, without losing a single atom of your body
This is incorrect. Any matter within about three Schwarzschild radii will never escape the black hole - i.e. will be carried along with it - even if the black hole passes you at the speed of light.
And if the black hole passes you at a velocity lower than the speed of light, then the radius grows. That matter will begin orbiting the black hole and will leave your body just as fast as the black hole left.
What's the Schwarzschild radius of a black hole the size of an atom? Or would something that size evaporate before it got a chance to snatch any of my leg?
The whole idea of encompassing an object that warps space into a sphere in our unwarped space is just a little invalid, especially when examining them on the scale of their constituent particles. I really don't know the answer, but I do not think that a black hole could be the size of an atom. I would expect the strong (or was it weak) nuclear force to overcome the mutual gravity and so compact an object would not be able to form.
I'm just a layman on the topic, and would greatly appreciate any insights by physicists in audience.
