I explained this to my nephew when he was about 8 years old and his mind was completely blown. He thought I was making it up so he asked my bro in law, and when dad confirmed it he was hooked. Kid is 5 years older and way more into Physics than I ever was at his age. It was cool to spark that thing in his mind that made him start seeking out science.
Yes. Because the light leaving Earth would travel for 500 years before or reached the lense of your scope.
However… This magical telescope would be on the scale of the size of an entire solar system. And then you’d need a way to track the movement of the Earth, and tune out the insane amount of light noise from the sun.
Someone 500 light years away would see light that had spent 500 years travelling, so light generated in 1524.
That’s what a light year is — how far light travels (in a vacuum, if you’re being pedantic) in a year.
Now, chances are they wouldn’t be able to see people or cities, or detect any signs of civilization, because 500 years ago the human footprint was much less. However, they would probably be able to see oxygen in the atmosphere, which they would likely assume is a sign of life.
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