3 ms·

I've never liked the "escape velocity >= c" explanation of why you can't get out a black hole. The escape velocity for a body at a given point is the velocity n

by tzs 3y ago

I've never liked the "escape velocity >= c" explanation of why you can't get out a black hole. The escape velocity for a body at a given point is the velocity needed to escape from that point ballistically. If you don't limit yourself to entirely ballistic trajectories you can escape without ever reaching that point's escape velocity. To explain why nothing, not even things on non-ballistic trajectories, cannot get out of black holes you've got to turn to weird headache inducing general relativity stuff.

at_a_remove 3y ago
You are correct. It's a fortunate coincidence and nothing more. It's much easier to think of the gradual warping of spacetime around a black hole so that more and more directions are down. East? No, that's really east and down. Left? Nope, you thought you were going left but it is left and down. Less and less "up" is available to you until you are on a knife edge where you can make an orbit (assuming a non-rotating black hole, no angular momentum) around the event horizon with a photon. Beyond that, everything is some flavor of down.
29athrowaway 3y ago
In 1700s?
- tzs 3y ago
  Yup. Those in the 1700s who wrote about stars with so much mass that light cannot escape would have known that their calculations only applied to ballistic trajectories. They would have believed that non-ballistic objects such as rockets would be able to escape because all they had was Newtonian physics. That when mass becomes high enough that light can't escape nothing else can escape either doesn't pop out of the math until you have general relativity.
martyvis 3y ago
That's right. The Earth's escape velocity is just over 11km/s or 4000km/h. If you have a rocket that only has enough force to propel you at say 100km/h away from the earth you can go anywhere you want in the universe - provided you keep applying that force through thrust. If you stop the rocket you will be subject to gravitational force to bring you back (or until the gravitational pull from other bodies of becomes dominant)
- thfuran 3y ago
  >If you have a rocket that only has enough force to propel you at say 100km/h away from the earth you can go anywhere you want in the universe Unless the rocket collapses into a black hole under the sheer mass of all that fuel.
- albumen 3y ago
  Nitpick: 11km/s escape velocity for earth is ~40,000km/h (not 4,000)
marcosdumay 3y ago
Well, if you go with Newton's explanation for light, it's quite obvious that it can only follow ballistic trajectories. One would certainly not expect elementary particles to function like rockets. But yeah, nobody could come with a description of a black hole anything like the modern one before 1900. Anything older is certain to be very different.
- jahnu 3y ago
  We don’t need to assume a small rocket strapped to a particle ;) Imagine accelerating an electron in some sort of magnetic field, in series. In a Newtonian system any speed is achievable. GR forbids this though.
  - naasking 3y ago
    > GR forbids this though. Does it though? https://youtu.be/9-jIplX6Wjw?si=xbNYKT9YN13VyJrV https://youtu.be/9-jIplX6Wjw?si=xbNYKT9YN13VyJrV

by tzs 3y ago

at_a_remove 3y ago

You are correct. It's a fortunate coincidence and nothing more. It's much easier to think of the gradual warping of spacetime around a black hole so that more and more directions are down. East? No, that's really east and down. Left? Nope, you thought you were going left but it is left and down. Less and less "up" is available to you until you are on a knife edge where you can make an orbit (assuming a non-rotating black hole, no angular momentum) around the event horizon with a photon. Beyond that, everything is some flavor of down.

29athrowaway 3y ago

In 1700s?

tzs 3y ago
Yup. Those in the 1700s who wrote about stars with so much mass that light cannot escape would have known that their calculations only applied to ballistic trajectories. They would have believed that non-ballistic objects such as rockets would be able to escape because all they had was Newtonian physics. That when mass becomes high enough that light can't escape nothing else can escape either doesn't pop out of the math until you have general relativity.

martyvis 3y ago

That's right. The Earth's escape velocity is just over 11km/s or 4000km/h. If you have a rocket that only has enough force to propel you at say 100km/h away from the earth you can go anywhere you want in the universe - provided you keep applying that force through thrust. If you stop the rocket you will be subject to gravitational force to bring you back (or until the gravitational pull from other bodies of becomes dominant)

thfuran 3y ago
>If you have a rocket that only has enough force to propel you at say 100km/h away from the earth you can go anywhere you want in the universe Unless the rocket collapses into a black hole under the sheer mass of all that fuel.
albumen 3y ago
Nitpick: 11km/s escape velocity for earth is ~40,000km/h (not 4,000)

marcosdumay 3y ago

Well, if you go with Newton's explanation for light, it's quite obvious that it can only follow ballistic trajectories. One would certainly not expect elementary particles to function like rockets. But yeah, nobody could come with a description of a black hole anything like the modern one before 1900. Anything older is certain to be very different.

jahnu 3y ago
We don’t need to assume a small rocket strapped to a particle ;) Imagine accelerating an electron in some sort of magnetic field, in series. In a Newtonian system any speed is achievable. GR forbids this though.
- naasking 3y ago
  > GR forbids this though. Does it though? https://youtu.be/9-jIplX6Wjw?si=xbNYKT9YN13VyJrV https://youtu.be/9-jIplX6Wjw?si=xbNYKT9YN13VyJrV