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Just wondering if we can examine individual stars from other galaxies, or if we are pretty much stuck with the billions that are in the Milky Way?

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Yes, Edwin Hubble did that for the first time in 1919. Before that time, it was thought that the galaxies we can observe were just nearby gas nebulae located inside our Milky Way. But Hubble was able to resolve the nearby galaxies like the Andromeda nebula into individual stars. By measuring the brightness of so-called Cepheid variable stars, he was able to calculate the distance to the Andromeda galaxy. Here one uses the fact that the total power radiated by the star is related to the period of the brightness oscillations, so by observing such stars you can deduce the distance to these stars and hence the distance to the galaxy. But later it was found that there were two different types of Cepheid stars and the wrong relation had been used; the distances were actually about twice as large.

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In addition to Count Iblis wonderful answer, consider that supernovae in other galaxies can sometimes be seen with low-powered binoculars. I seem to remember mention of a naked-eye extra-galactic supernova, but I cannot find the reference.

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    $\begingroup$ SNe are not stars. $\endgroup$ – Py-ser Oct 13 '14 at 2:18
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    $\begingroup$ In what way is a SN not a star? You could argue that a SN is a short-lived phase of a star, and I would agree with that. But for purpose of this discussion, in which the asker is interested in seeing spheres of fusing elements in other galaxies, a SN fits the description. $\endgroup$ – dotancohen Oct 13 '14 at 7:09
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    $\begingroup$ A supernova is a process, an event, not an object. Supernova Remnants are objects. $\endgroup$ – Py-ser Oct 13 '14 at 10:27
  • $\begingroup$ An event that occurs to a star. $\endgroup$ – dotancohen Oct 13 '14 at 11:05
  • $\begingroup$ @dotancohen After which the object is not a star. Also, it's more likely you'd see supernova remnants than actual supernovae. $\endgroup$ – HDE 226868 Oct 13 '14 at 12:04

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