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Since many stars are hundreds of light years away from the Earth and therefore, what we observe of them today is really their distant past, how can we say anything with certainty about their composition, size and nature? Betelguese, for example, is said to be in the last stage of stellar evolution, but taking into consideration its approximately 640 light years of distance from the Earth, aren't we actually making assertions about the star that are 640 years old? If that is the case, how can we claim to know the actual present status of the star?

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Well, we don't claim to know the status of the star at the present time. If the star is close enough (within our galaxy, or local neighbourhood), we measure the distance in light years, or parsecs. If they're further away than that, it's easier to quantify their distance in terms of a redshift.

When we say that a star has some properties (size, temperature etc.) in that statement is the knowledge that the light received is delayed, so it won't reflect the state of the star right now.

Even though knowing the state of a star as it was several thousand years ago may not seem like it's a useful thing, it's the only tool we have to probe the evolution of stars, and the evolution of the universe. Since the further away something is, it will reflect conditions of the universe at earlier and earlier times. Which is where we can test cosmological theories of the evolution of the universe, or our theories of the evolution of galactic or stellar systems.

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Indeed, what we infer about stars from the light we see at the Earth is "old news". However for almost all practical purposes in stellar astrophysics this doesn't matter. The phases of a star's life last millions if not billions of years and most of the individual stars that are studied are within say 30 thousand light years of the Earth.

The example you picked is an interesting one. Betelegeuse is probably in the very last phase of its life before exploding as a supernova. This final phase is about the shortest in a stellar lifecycle and it is possible that Betelgeuse has already exploded, though more likely we will have to wait a few tens of thousands of years more.

Another interesting example is that when it comes to other galaxies, it is possible to study individual luminous (most massive) stars. So, if we study very massive stars in the Andromeda galaxy (2.5 million light years away) it is likely that many of these stars (the most massive stars have the shortest lifetimes) have already exploded as supernovae.

If we want to say what a star is like now, then we have to rely on an extrapolation forward in time of our stellar evolution models. This is not of great concern because (a) the extrapolation is not that great for most stars (see above) and (b) even where the extrapolation is a large fraction of the stellar lifetime, the models are tested using different stars at all phases of their lives so we have reasonable confidence in them.

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