Wow. Strange question if you don't mind me saying. I'm on a night
shift with very little to do other than stay awake so I'll have a
crack at it...
To start with I think it would be useful to re-state the question in
clearer terms, and give you the opportunity to clarify.
Mathematically defining the movement of your particles seems like the
least daunting step:
Particle a: Velocity = 10m/s
Particle b: Velocity = 10*2^time
Particle c: Velocity = 10*(1/(1-time))
That was mildy interesting. Haven't worked an equation out since I
left school and took this dead end job. Not to worry I resigned last
week and have a much better one lined up with no more night shifts!
(sorry you'll have to find someone else to do your physics then...)
Now then, moving onto black holes... A basic overview of how they
work might be handy:
A black hole is just a pile of matter that has collapsed into a single
point in space and has absolutely zero volume. When we say an object
is in a black hole, we mean it is past the imaginary point at which
the gravity due to the black hole is so great that it is impossible
for anything, even light, to escape. This is the swartzchild radius I
think. Dunno how you spell it though.
You say the objects are in a black hole and 1m of travel results in
travelling 1 second into the future. This is not an effect normally
associated with black holes - it simply means the object is travelling
at 1 metre per second.
The effects of black holes on objects are described by einstein's
theory of general reletivity. Unfortunately I didn't take that course
at uni. Went to the first lecture and was greatful it was an optional
module! Basically they have the following effect:
If you were very far away from an object near a black hole, it would
appear to you that time was passing more slowly for that object, and
the object would seem to shrink. Eg, if you attached a very large
clock to a rocket and fired it into a black hole, then watched it
though a telescope, it would seem to tick more slowly and would appear
to be contracted. Interestingly, if you were on the rocket it would
tick normally as you would be under the same effect.
Moving on to the question itself - "what is the movement contra speed
contra time for each of the objects" - you would need to define two
more quantities to work this out - the mass of the black hole and the
distance of the particle from the black hole. Even then, you have
specified how the velocity of each particle varies with time which
implies an external force is acting on them, so that part of the
question doesn't seem to make sense. If you simply gave the starting
speed and position reletive to the black hole, it would be possible to
work out the path each particle would take as it spiraled into the
black hole, but don't look at me - the maths would be far too scary!
I'm curious why you asked this specific question. Did you make it up
yourself as an example or did you find it somewhere?
Hope this helps in some way. It killed about half an hour for me,
which was nice. Only 2 1/2 hours to go. I think I'll watch South
Park on telly... |
