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What do we mean by the lookback time to a distant galaxy?

Answer
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Hint: As we know that light travel at finite speed so when light reaches us from a faraway object that light was emitted a long time ago so it brings us the old information so at that current time several more changed may have occurred to that object whose light reaches to earth so it becomes difficult to know the current scenario of the object.

Complete answer:
Light travels at a finite velocity of $3 \times {10^8}{\text{ m/s}}$ and it takes a definite amount of time to travel the given path for example light takes roughly 9.5 trillion kilometers to travel one year for measuring the stick astronomers frequently use this and this is known as a light- year.

For Example: If a star was one light year away from the earth light from that star will reach us one year late as travels through space for a whole one year and after then it reaches to as so gathers a light which was emitted one year ago and we do not see the star at that moment but as it was one year ago., Andromedia I is a galaxy that is 2.43 million light years from us. So the galaxy is based on light emitted 2.43 million years ago. the light is even more ancient for more distant objects. Therefore, in that way we look into the depths of the universe is a look back in time.

Note: It is interesting to note that we inhabitant of earth have been broadcasting electromagnetic signals for a century so that if there would be any alien receiving they are near us as information about us had travelled about 100 light years in our own milky way galaxy so anything in radius of hundred light year receives the signal