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I had read that the Betelguese star may be going supernova in may of 2022. Now it is about 500 Light years away, so if we see a supernova explosion in may, then does that mean it occurred about 500 years ago already? So do we put the date of its death 500 years back or this year? (pardon me if its silly doubt)

Another doubt is that let's say if someone measured parameters like the luminosity of such explosion from let's say distance less than a light-year. Now we on earth measure same parameters of that explosion. Will the luminosity and other parameters of the explosion would be different?

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    $\begingroup$ Check your sources... Betelgeuse will not explode this year. It is still way too stable for that to happen anytime soon. $\endgroup$
    – rfl
    Commented Jan 20, 2022 at 11:07
  • $\begingroup$ @rfl Are these not credible source: thecreative.cafe/…, youtube.com/watch?v=D7stJoNJ52o $\endgroup$ Commented Jan 20, 2022 at 11:11
  • $\begingroup$ Related: astronomy.stackexchange.com/q/47523/16685 $\endgroup$
    – PM 2Ring
    Commented Jan 20, 2022 at 11:23
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    $\begingroup$ The first reference does not say that B will go supernova in 2022. And no, it is not a reliable source. The second reference also does not say that B will go supernova in 2022; rather it questions what is meant by the date of an event in the context of relativity. It is a better source than the first, but is still not authoritative. In fact, what's arguably the best answer given to that question has two down votes. $\endgroup$
    – garyp
    Commented Jan 20, 2022 at 11:46
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    $\begingroup$ OMG. No, both those "sources" are not credible. Sigh. ("Scientists have apparently forgotten..."? Ha, so glad that voiceover reminded them.) $\endgroup$
    – rfl
    Commented Jan 20, 2022 at 12:09

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About $168,000$ years ago, a supernova occurred that was observed in $1987$. We called it SN 1987A. Except when the distance to a star is known to within at most a few light months, which is the case for only the nearest stars, one couldn't compute the calendar year in which it really happened. Indeed, trying to impose a human calendar onto events across the galaxy like that is at best misleading, in the light of relativity. So we date them by when observation of them happened, which is much more convenient in discussing the history of the science.

As for your second question, if two observers would be positioned to encounter measurably different measurements we'd have to acknowledge that on a case by case basis, but it doesn't come up much, at least not in the way you describe. You should probably sate your interest by reading about stellar parallax, though, where the two observations are on Earth but at different times of the year.

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