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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
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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
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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
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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
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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
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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
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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
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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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