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Since all the galaxies are moving further away from each other at a faster and faster rate, eventually we won't be able to see stars from other galaxies. How long until we can't see stars from other galaxies?

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With telescopes getting better and better all the time, the question should be "how long until we CAN see stars in other galaxies"... –  Mr Lister Oct 25 '13 at 12:03
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First of all, we can't see stars from other galaxies (with a few exceptions, Cepheid variable stars for example are regularly used to determine distances to nearby galaxies). As it currently stands, we can only see stars from our own Milky Way (in which I'm including the large and small Magellanic Clouds). Type Ia supernovae aside, it might be possible to see Cepheid variables in the Andromeda galaxy, but anything further is almost certainly not possible.

The relevant number when it comes to the distance one could possibly see in the universe is the comoving distance to the cosmological horizon. This horizon defines the boundary between what can be seen and what cannot be seen, simply because the universe is not old enough for particles to have traveled that far (yes, even at the speed of light; in fact, if we're talking about what we can observe, the photon is the particle we care about).

The definition of the comoving distance is:

$$\chi = \frac{c}{H_{0}} \int_{z=0}^{z=z_{Hor}} \frac{dz^{'}}{E(z^{'})}$$

where the function $$ E(z^{'}) $$ contains your choice of cosmology (the following is for flat universes only):

$$E(z^{'}) = \sqrt{ \Omega_{\gamma} (1+z)^{4} + \Omega_{m} (1+z)^{3} + \Omega_{\Lambda} }$$

This distance can be extrapolated out into the future (given your choice of cosmology), and ultimately will tell you what the distance to the cosmological event horizon will asymptotically reach. This is the distance at which no object beyond could ever come into causal contact with you.

Another simpler way to calculate the particle horizon is to calculate the conformal time that has passed from the beginning of the univirse, and multiply it by the speed of light c, where the conformal time is defined in the following way:

$$\eta = \int_{0}^{t} \frac{dt^{'}}{a(t^{'})}$$

where $$a(t^{'})$$ is the scale factor of the universe, and its relationship to time depends specifically on your choice of cosmology. Again, if the ultimate value of this horizon is desired, you would need to integrate this to infinity.

SUMMARY: I'm having a hard time finding the exact number of the comoving size of the cosmological event horizon, though I'll keep searching. If I can't find it I suppose I'll have to do the calculation when I have some free time. Almost certainly it is larger than the size of the local group of galaxies, making our night sky largely safe from the fate of the universe. Anything further than this horizon, however, will monotonically become both fainter and redder. I also think that it does asymptotically reach some value, rather than eventually increasing infinitely or decreasing passed some point in time. I'll have to get back to you on that.

Here's a nice review of distance measurements in cosmology.

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Thanks for the detailed answer! Regarding not being able to see stars from other galaxies, are you specifically talking about with the naked eye, or through the use of telescopes too? –  Rich Oct 22 '13 at 0:43
    
@Rich Even with telescopes I think you'd have a near impossible time resolving individual stars even in the Andromeda galaxy (nearby large spiral galaxy to the MW). Cepheids and Supernovae are the exception, though. –  astromax Oct 22 '13 at 14:16
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In most cases clusters of galaxies are moving away from each other. The gravitational attraction between galaxies is usually enough in concentrated clusters to overcome the cosmological expansion. The Milky Way and Andromeda, both the largest galaxies in the local group, the cluster of which we are a part of, are close and massive enough to overcome this expansion. Therefore we will never lose sight of the stars in the Andromeda galaxy until the stars within it die and/or fade out, in approximately 10 billion years. However, if you are talking about individual stars, not the collective starlight of stars in a given galaxy, then the answer is we still cant!

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