Re: Singularity destroys planet.

In article <1242682766@xxxxxxxxx>, throopw@xxxxxxxxx (Wayne Throop)
wrote:

: Mike Ash <mike@xxxxxxxxxxx>
: I initially thought of it as traveling through a pipe that's nearly but
: not quite strong enough to avoid being crushed by the BH, with whatever
: radius makes things convenient. The BH will crush the pipe, but this
: will take time, and so it will be crushed behind the BH. The BH moving
: through this pipe will look *something* like this:
:
: ---------------------
: /
: ====< o <- BH (not to scale)
: \
: ---------------------
:
: With the BH moving left to right. You can see that there will be more
: gravitational attraction from the left than from the right, as the
: material on that side is closer.

OK. So, what's the difference in gravitational attraction between
a cylinder of rock N centimeters radius and a kilometer long
(I'll presume that beond a kilometer, there's not much contribution)
and a cylinder of negligable density the same length?

I would have thought it would be negligably small.

Well, that analogy is ok for understanding the mechanism but I don't
think it's very good for coming up with any numbers, since the real
situation will be considerably more dynamic.

I think that the other post which mentioned that a lone particle will
end up on a hyperbolic orbit and will be flung out forward of the black
hole at roughly twice the velocity is a good place to start. I don't
even feel comfortable enough calling this a first approximation, so
let's say it's a zeroth approximation.

The BH cuts through material of density D, and we'll say that everything
within a radius of R gets the hyperbolic orbit treatment. A BH moving at
speed V is then interacting with an amount of material equal to:

pi * R^2 * D * V

If we assume 2.5g/cm^3 for the density, 10m for the radius, and 11km/s
for the speed, that gives us 8.64e9kg/s. That ~9 billion
kilograms/second is getting spit out at 22km/s, which requires a force
of 1.9e14N to accelerate it. Applied to the Chixulub mass of 10e18
grams, that results in 0.19m/s^2, or roughly 2% of the Earth's surface
gravity. This is not huge, but it's significant.

Of course there are a ton of variables here. The most obvious one is the
proper value for R. 10m is a total wild guess. A perhaps more
significant factor is that the particles won't be moving along
hyperbolic orbits, but will interact with each other, a *lot*.

My wild guess is that R will be substantially greater for a BH of this
mass, and that the interaction between the particles will result in the
exit velocity being cut in half. Conceptually, if the particles bang
into each other a bunch, their kinetic energy is transformed into heat,
and they remain in orbit around the BH instead of flying out in front,
resulting in only half the velocity change.

I think this shows that the drag is significant, but I don't think the
above is anywhere close to being able to say just how fast the BH can be
going and still be captured by that mechanism, other than that it's
"somewhere faster than escape velocity".

--
Mike Ash
Radio Free Earth
Broadcasting from our climate-controlled studios deep inside the Moon
.

Relevant Pages

  • Re: Kinetic Energy as a Vector
    ... each with a pair of particles moving inside. ... Let velocity to the right be positive v, ... Net momentum is also conserved, unless boxes are anchored to the ...
    (sci.physics)
  • Re: Particles as lightspeed waves?
    ... The existing relativistic analysis of the behavior of particles in ... spacetime already addresses this, ... objects not moving WRT each other have the same four-velocity ... specifically their velocity components in the "time ...
    (rec.arts.sf.science)
  • Re: SR theory is simplistic
    ... Einstein's postulate on the velocity of light was provided by a number ... which had been emitted by decaying subatomic particles moving at nearly ... different speeds depending on who is going to observe it. ...
    (sci.physics.relativity)
  • Re: Moving mirror experiment, answer to Henri Wilson
    ... >> Consider a light source and a moving observer with a mirror. ... >mirror at rest in it)is moving at v velocity wrt frame Fs. ...
    (sci.physics.relativity)
  • Moving mirror experiment, answer to Henri Wilson
    ... > Consider a light source and a moving observer with a mirror. ... mirror at rest in it)is moving at v velocity wrt frame Fs. ... this same relative velocity between the light ...
    (sci.physics.relativity)
Loading