Is it true that we are looking billion years back when we look at stars?

In short, yes we do. When we look out at the stars shining in the vast darkness around them, we're actually looking at them when they were much younger. The same stars may today be expanding into a red giant, colliding with some other star, or may even be dead. What we're seeing is their past.

Now, the detailed answer.
We all must have learnt sometime in school that speed = distance / time. The same fact is used to actually realize this phenomenon. The speed of light, approximately 300,000,000 m/s, is the fastest that could ever be. When a star emits light, the light travels towards us with that great speed. However, the distances are much, much greater. For example, the star closest to us following the Sun, Alpha Centauri, is still around 44 quadrillion meters away. How large is that number?
44,000,000,000,000,000 m.
Now, when light leaves Alpha Centauri, it has to travel, at its immense speed, 44 quadrillion meters to reach our home, the Earth. So, using the above mentioned formula, light should take around 4.4 years to reach us. So when we look at the light of Alpha Centauri, we're looking at its state 4.4 years ago. But then again, that's the closest one. A bright star, Vega is around 237 quadrillion m away, thus light takes around 25 years to reach our home. Thus we're seeing it as it was 25 years ago. Similarly, we have stars much much farther away. The farthest star system we've found is 13 billion quadrillion meters away. How huge is that number?
13,000,000,000,000,000,000,000,000 m
When we look at it, we look 13 billion years in the past! Imagine the brilliant history that the sky lays in front of you when you look at the stars in the night. Just looking at the stars shows us how the universe around us was, years before we were born. When you look at the sky, you not only look very, very far out in space, but also look very, very back in time. The night sky is our time machine to observe the universe in its childhood.

Many of such stars are billions light years ago.

It is a unit of distance.

So light takes about billion years to come from these stars to us.

This causes it is true that we are looking billion years back when we look at stars.

Avinash Agarwal, Programmer, Stargazer, Otaku
Answered Apr 21, 2015
You always see past in the night-sky. The light emitted by that star millions of years away will reach us after a million years, and in theory you could see the star as long as it emitted radiation in its entire lifetime and until the light directed towards us has dissipated, as already mentioned in another answer.

When you're seeing the star, it might actually be dead. But what you're observing is the light emitted by that star millions of years ago , and not now, i.e. you're looking into the past. The astronomers would witness the entire lifespan of the star as long as it emitted radiation continuously until it dies in a supernovae. It wouldn't simple disappear in the nightsky.

If a star, visible to us today, about 2 billion light years away, dies now. We would come to know of its death only when the light from its supernovae reaches us, after 2 billion years .

Consider a star in one of the farthest known galaxies in the observable universe some 13 billion light years away. Assuming a star is born in this galaxy now, and a static universe, we would witness its birth after 13 billion years and the star would have already died by the time we witness its birth. Though after 13 billion years the star would appear in our nightsky and remain until its entire lifespan for as long as it had emitted radiation. If the star lived for 5 billion years, we would see the star for 5 billion years in the sky and know of its death after 18 billion years.

But there are still parts of the universe that will remain hidden to us forever.
By hubbles law we know the universe is not static and is expanding, and the rate of expansion is faster for more distant objects. In fact, for objects far enough, the rate of expansion is faster than the speed of light (and yes, it doesn't violate relativity). Objects this far enough will never be visible to us, since light from that region could never reach us. So yeah, if a star is born in this region, your person X will never be able to see the star.

Whats more, the expansion of the universe is accelerating, so even though as time passes and the size of the observable universe increases, there is a a "future visibility limit", and in theory we will never be able to see more than above twice the no of galaxies in the observable universe today.

(a) Stars we can see (Our Sun falls into this category, Fortunately!)

(b) Stars which died BUT which left some sort of interesting residue. (e.g. The Crab Nebula)

But you’re correct about the ‘missing your chance’ thing. If Alpha Centauri A actually exploded four years and nineteen weeks ago – then you will still be seeing it. But sometime tomorrow, it will disappear. The last light that star ever emitted will pass the Earth and there won’t be any more. If the explosion leaves some debris (e.g. a nebula) then you can continue to watch the Alpha Centauri Nebula – but you won’t see the star again. And if your daughter is born next week, then she will never see the star. You can show her the nebula (if there is one) but Alpha Centauri A will just be a story to her.

By the time earth's light goes out 300.000.000 billion light years into space …earth will be dead.

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