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Astronomy
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 Quote by v2kkim I feel better in understanding universe and physics from this dialogue. I have a new question: Suppose that we got a new spectrum picture from a star, and that picture shows several dark lines with shift, and we speculate the object might be moving very fast but do not know the distance. Now from that shift pattern can we tell if it comes from space expansion or local motion ?

The answer is no. One cannot tell just from the shift pattern whether it is Doppler from local motion or stretch-out redshift from the whole history of expansion during the light's travel time.

In fact one can do a complicated mathematical analysis involving a chain of overlapping patches---it's ridiculous but one can do it---so there might be a million observers between you and the object---and actually analyse cosmological redshift in terms of a million little Doppler shifts. But it is a clumsy and useless way to think about it.

 Quote by v2kkim Regarding the distance advanced by light in expanding universe , I did some calculation to get the result: $$D(T)\ = {c \over r} (\left( 1 + {r*dt} \right)^{T \over dt} -1)$$ Taking the limit dt going to 0, $$D(T)\ = {c \over r} (e^{rT} -1)$$ where D(T): distance advanced by light during period T. c: speed of light T: time from emission to present. r : space expansion rate 1/140 % per million. dt: the arbitrary small time intervals in T. ** In case r goes to 0, D(T) goes to c*T as expected. I got this formula by adding each light path segment advanced for each dt, that is after the last dt, the D0 (distance advanced of the last dt) is D1=c*dt*(1+r*dt), and the 2nd last one D2=c*(1+r*dt)^2, and so on .. Dn=c*(1+r*dt)^n. From summing D1 D2 ..Dn, I got above formula. I do not want to use the word speed to avoid confusion, but it is just the distance of light advanced after a period T.
I'm impressed. I haven't examined this closely enough to guarantee it but I think it should give approximately right answers if it is used over short enough distances that the rate r does not change significantly during the light's travel time.

When I quote this figure of 1/140 of a percent, what I mean is that this is the current percentage rate of distance expansion. It has been larger in the past.
Vakkim, do you know the Hubble time? 1/H where H is the current value of the Hubble rate?

Have you ever calculated the Hubble time for yourself? I think you should, because you understand calculation, if you have not already.
What value of the Hubble rate do you like to use? I use 71 km/sec per Megaparsec.
Suppose I put this into google
"1/(71 km/s per megaparsec)"
What google gives me back is 13.772 billion years. I could round that off and say the Hubble time is 14 billion years.
Saying "1/140 of a percent per million years" is just a disguised form of this.

If the Hubble time (1/H) is 14 billion years, then the Hubble rate itself (H = 1/(1/H)) is 1/(14 billion years)
That is the same as 1/14 per billion years.
That is the same as 1/14000 per million years.
That is the same as 1/140 of one percent per million years.

In other words having calculated the Hubble time we could say the rate was "1/137.72 of a percent per million years", except that would be overly precise and we round off to two significant figures and say 1/140.

I expect this may be self-evident to you but want to make sure we know where the figure comes from, and that it gradually changes over time.