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  #1  
Old September 25th 03, 01:39 AM
Denis Taylor
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Default Cosmology question

In message , Darren
writes
A question has recently been put to me. I thought I'd share it with the
group to see if there is a knowledgeable person able to answer it.

Consider three galaxies. Our own Milky Way and two other galaxies (called A
and B for ease) Galaxies A and B are on exactly opposite sides of the Milky
way at exactly the same distance, right at the edge of the observable
Universe (i.e. where recessional velocity is equal to the speed of light)
For argument's sake, let's say they are 98% of the distance to the edge and
their velocity as seen from our galaxy is 0.98c.

Obviously, if you were in Galaxy A, we would be on the edge of your
observable Universe and Galaxy B would be far beyond it and undetectable.

So, the question is: What is the recessional velocity of Galaxy B from
Galaxy A?

Is it 1.96c?

Is it c?

Or is it something else entirely?

I hope this tickles the grey cells.

I have my own answer, but don't know if there's some weird cosmological
thing that makes my answer wrong.

Have fun,

Darren


Just so nobody shouts at me, I'm new to astronomy and somewhat unsure of
my facts, but I think your answer is 0.98c. I've been reading Roy and
Clarkes' Astronomy, Structure of the Universe, but there are numerous
treatments of special relativity.
Hopefully someone will put me right politely if I'm wrong!

Denis
--
**********************************
Denis Taylor
two ears, one mouth, think first.
**********************************
  #2  
Old September 25th 03, 02:42 AM
Mike Williams
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Default Cosmology question

Wasn't it Denis Taylor who wrote:
In message , Darren
writes
A question has recently been put to me. I thought I'd share it with the
group to see if there is a knowledgeable person able to answer it.

Consider three galaxies. Our own Milky Way and two other galaxies (called A
and B for ease) Galaxies A and B are on exactly opposite sides of the Milky
way at exactly the same distance, right at the edge of the observable
Universe (i.e. where recessional velocity is equal to the speed of light)
For argument's sake, let's say they are 98% of the distance to the edge and
their velocity as seen from our galaxy is 0.98c.

Obviously, if you were in Galaxy A, we would be on the edge of your
observable Universe and Galaxy B would be far beyond it and undetectable.

So, the question is: What is the recessional velocity of Galaxy B from
Galaxy A?

Is it 1.96c?

Is it c?

Or is it something else entirely?

I hope this tickles the grey cells.

I have my own answer, but don't know if there's some weird cosmological
thing that makes my answer wrong.

Have fun,

Darren


Just so nobody shouts at me, I'm new to astronomy and somewhat unsure of
my facts, but I think your answer is 0.98c. I've been reading Roy and
Clarkes' Astronomy, Structure of the Universe, but there are numerous
treatments of special relativity.
Hopefully someone will put me right politely if I'm wrong!


Simply applying Special Relativity to the speeds would give a number a
little higher than 0.98c, but that would lead to the apparently absurd
conclusion that an observer in galaxy A would be able to see galaxy B,
because the galaxies are receding from each other at less than c. An
observer in galaxy A sees a visible universe twice the size of what we
see. The process can be repeated for galaxies on the edge of A's visible
universe, and it would seem that observers there can see twice as far
again, and so on.

One way out of this absurdity is to notice the fact that light has taken
about 15 billion years to get here from galaxy B, so it will take
another 15 billion years for that light to fly past us and reach the
location of galaxy A. When it arrives at galaxy A, the universe will be
about 30 billion years old and could well be twice the size it is now.

Things get more complicated if we notice that those remote galaxies have
moved considerably since the light we now see was emitted from them. Are
we trying to ascertain their relative velocity at the time when the
light we now see was emitted from them, or their relative velocity now
(under the assumption that they're still there)? The answer is very
different in the two cases.

--
Mike Williams
Gentleman of Leisure
  #3  
Old September 25th 03, 05:31 PM
Denis Taylor
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Posts: n/a
Default Cosmology question

In message , Mike Williams
writes
Wasn't it Denis Taylor who wrote:
In message , Darren
writes
A question has recently been put to me. I thought I'd share it with the
group to see if there is a knowledgeable person able to answer it.

Consider three galaxies. Our own Milky Way and two other galaxies (called A
and B for ease) Galaxies A and B are on exactly opposite sides of the Milky
way at exactly the same distance, right at the edge of the observable
Universe (i.e. where recessional velocity is equal to the speed of light)
For argument's sake, let's say they are 98% of the distance to the edge and
their velocity as seen from our galaxy is 0.98c.

Obviously, if you were in Galaxy A, we would be on the edge of your
observable Universe and Galaxy B would be far beyond it and undetectable.

So, the question is: What is the recessional velocity of Galaxy B from
Galaxy A?

Is it 1.96c?

Is it c?

Or is it something else entirely?

I hope this tickles the grey cells.

I have my own answer, but don't know if there's some weird cosmological
thing that makes my answer wrong.

Have fun,

Darren


Just so nobody shouts at me, I'm new to astronomy and somewhat unsure of
my facts, but I think your answer is 0.98c. I've been reading Roy and
Clarkes' Astronomy, Structure of the Universe, but there are numerous
treatments of special relativity.
Hopefully someone will put me right politely if I'm wrong!


Simply applying Special Relativity to the speeds would give a number a
little higher than 0.98c, but that would lead to the apparently absurd
conclusion that an observer in galaxy A would be able to see galaxy B,
because the galaxies are receding from each other at less than c. An
observer in galaxy A sees a visible universe twice the size of what we
see. The process can be repeated for galaxies on the edge of A's visible
universe, and it would seem that observers there can see twice as far
again, and so on.

One way out of this absurdity is to notice the fact that light has taken
about 15 billion years to get here from galaxy B, so it will take
another 15 billion years for that light to fly past us and reach the
location of galaxy A. When it arrives at galaxy A, the universe will be
about 30 billion years old and could well be twice the size it is now.

Things get more complicated if we notice that those remote galaxies have
moved considerably since the light we now see was emitted from them. Are
we trying to ascertain their relative velocity at the time when the
light we now see was emitted from them, or their relative velocity now
(under the assumption that they're still there)? The answer is very
different in the two cases.

I was mindful of the hypothetical situation described in the question
when I mentioned SR, plus I don't have a great grip GR!
My current understanding is that in our space/time continuum light speed
is a constant, objects at light speed are impossible as they would have
infinite mass, therefore all objects in our universe travel at less than
light speed. If our sensor technology had sufficient sensitivity, and
the big bang is real, all objects would be visible, they would just have
greater and greater red shift. Galaxy A would be visible to galaxy B.
I accept the point about the size of the universe, as we can only look
down the 'time slope', and not up it (if that makes sense!).
I am trying not to confuse the reality presented within our frame of
reference (our universe) with the (mathematical) view from outside the
frame of reference.
I'm not at all sure the above makes sense but I am on a steep learning
curve so enlightenment is always appreciated!

--
**********************************
Denis Taylor
two ears, one mouth, think first.
**********************************
  #4  
Old September 25th 03, 05:50 PM
Dr John Stockton
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Posts: n/a
Default Cosmology question

JRS: In article , seen in
news:uk.sci.astronomy, Darren
posted at Wed, 24 Sep 2003 18:27:28 :-

Consider three galaxies. Our own Milky Way and two other galaxies (called A
and B for ease) Galaxies A and B are on exactly opposite sides of the Milky
way at exactly the same distance, right at the edge of the observable
Universe (i.e. where recessional velocity is equal to the speed of light)
For argument's sake, let's say they are 98% of the distance to the edge and
their velocity as seen from our galaxy is 0.98c.


So, the question is: What is the recessional velocity of Galaxy B from
Galaxy A?


About 0.999,795,960,008,161,599,673,536,013,058,559,477, 657,620,894 c

--
© John Stockton, Surrey, UK. / ©
Web URL:http://www.merlyn.demon.co.uk/ - FAQish topics, acronyms, & links.
Correct = 4-line sig. separator as above, a line precisely "-- " (SoRFC1036)
Do not Mail News to me. Before a reply, quote with "" or " " (SoRFC1036)
  #5  
Old September 25th 03, 07:39 PM
Denis Taylor
external usenet poster
 
Posts: n/a
Default Cosmology question

In message , Dr John Stockton
writes

About 0.999,795,960,008,161,599,673,536,013,058,559,477, 657,620,894 c

This is where I bow out and follow the advice of my own sig.
--
**********************************
Denis Taylor
two ears, one mouth, think first.
**********************************
  #6  
Old September 25th 03, 08:29 PM
Gautam Majumdar
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Posts: n/a
Default Cosmology question

On Thu, 25 Sep 2003 17:31:29 +0100, Denis Taylor wrote:

In message , Mike Williams
writes
Wasn't it Denis Taylor who wrote:
In message , Darren
writes
A question has recently been put to me. I thought I'd share it with
the group to see if there is a knowledgeable person able to answer it.

Consider three galaxies. Our own Milky Way and two other galaxies
(called A and B for ease) Galaxies A and B are on exactly opposite
sides of the Milky way at exactly the same distance, right at the edge
of the observable Universe (i.e. where recessional velocity is equal
to the speed of light) For argument's sake, let's say they are 98% of
the distance to the edge and their velocity as seen from our galaxy is
0.98c.

Obviously, if you were in Galaxy A, we would be on the edge of your
observable Universe and Galaxy B would be far beyond it and
undetectable.

So, the question is: What is the recessional velocity of Galaxy B from
Galaxy A?

Is it 1.96c?


Possibly. But no. If you take into account only the proper motion of the
galaxies it would be very close to c.

But recessional velocity depends both on the proper motion of the
heavenly bodies & the rate of the expansion of the space itself which can
exceed the speed of light. In any case Galaxies A & B will be beyond the
horizon (observable universe) of each other.

Simply applying Special Relativity to the speeds would give a number a
little higher than 0.98c, but that would lead to the apparently absurd
conclusion that an observer in galaxy A would be able to see galaxy B,
because the galaxies are receding from each other at less than c. An
observer in galaxy A sees a visible universe twice the size of what we
see. The process can be repeated for galaxies on the edge of A's visible
universe, and it would seem that observers there can see twice as far
again, and so on.

One way out of this absurdity is to notice the fact that light has taken
about 15 billion years to get here from galaxy B, so it will take
another 15 billion years for that light to fly past us and reach the
location of galaxy A. When it arrives at galaxy A, the universe will be
about 30 billion years old and could well be twice the size it is now.

Things get more complicated if we notice that those remote galaxies have
moved considerably since the light we now see was emitted from them. Are
we trying to ascertain their relative velocity at the time when the
light we now see was emitted from them, or their relative velocity now
(under the assumption that they're still there)? The answer is very
different in the two cases.

I was mindful of the hypothetical situation described in the question
when I mentioned SR, plus I don't have a great grip GR! My current
understanding is that in our space/time continuum light speed is a
constant, objects at light speed are impossible as they would have
infinite mass, therefore all objects in our universe travel at less than
light speed.


Objects must travel through empty space at less than light speed but the
space itself can expand at any speed. During inflationary period the rate
of expansion was much higher than light speed.

If our sensor technology had sufficient sensitivity, and the big bang is
real, all objects would be visible, they would just have greater and
greater red shift.


I am afraid not. The Universe is probably much larger than the observable
universe. The current idea is that the speed of the expansion of the
Universe (i.e., space) is increasing. In such an accelerating Universe
more and more objects will disappear beyond our horizon. Only the
gravitationally bound systems, such as our local group of galaxies, will
remain visible.

--

Gautam Majumdar

Please send e-mails to

  #7  
Old September 25th 03, 09:58 PM
Mark McIntyre
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Posts: n/a
Default Cosmology question

On Thu, 25 Sep 2003 01:39:14 +0100, in uk.sci.astronomy , Denis Taylor
wrote:

In message , Darren
writes
A question has recently been put to me. I thought I'd share it with the
group to see if there is a knowledgeable person able to answer it.

Consider three galaxies. Our own Milky Way and two other galaxies (called A
and B for ease) Galaxies A and B are on exactly opposite sides of the Milky
way at exactly the same distance, right at the edge of the observable
Universe (i.e. where recessional velocity is equal to the speed of light)
For argument's sake, let's say they are 98% of the distance to the edge and
their velocity as seen from our galaxy is 0.98c.

Obviously, if you were in Galaxy A, we would be on the edge of your
observable Universe and Galaxy B would be far beyond it and undetectable.

So, the question is: What is the recessional velocity of Galaxy B from
Galaxy A?

Is it 1.96c?

impossible


Is it c?


impossible, unless either one has zero mass


Or is it something else entirely?


yes.

Just so nobody shouts at me, I'm new to astronomy and somewhat unsure of
my facts, but I think your answer is 0.98c.


The answer is to be found in any textbook on relativistic physics, and
as far as I recall its
u' = (u-v)/(1-uv/c^2)
where u and v are the velocites of the two bodies, and u' is the
relative velocity of the two. Hence here you arrive at
u' = 1.96/1.9604 = 0.999796

[Remember that u and v have opposite signs. ]

(I confess to having looked this up in Eisberg and Resnick, which I
still have from my univ days)

--
Mark McIntyre
CLC FAQ http://www.eskimo.com/~scs/C-faq/top.html
CLC readme: http://www.angelfire.com/ms3/bchambless0/welcome_to_clc.html
  #8  
Old September 26th 03, 10:42 AM
SimonP
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Posts: n/a
Default Cosmology question

Denis Taylor wrote in article
...
I think I'm grateful to Darren for raising the question, and I am aware
that he did ask for an expert opinion, so I'm going to drop out and
study a bit more! Thanks to Mike and Gautam. I understand that there
must be a horizon but I'm having trouble with the concept of "empty
space" being outside the constraints of our physics. (I wish my maths
teacher had spoken English, or I could speak German, things would be a
lot easier now :-))


Denis,
Try reading some of Brian Tung's essays on his Astronomical Games page
– I've found them very interesting and understandable. Brian has a
nak of making the complex simple (well simpler).
Specific to this thread try "The Unwinnable Race"
http://astro.isi.edu/

--
Simon
51:31N 0:38W
http://www.cookie-pool.co.uk/Pool1.htm
http://www.maidenhead.astronomical.s...care4free.net/
http://www.popastro.com/home.htm
 




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