Hold your finger out at arms length and close one eye. Now switch eyes. Your finger appears to move a little. Switch eyes back and forth quickly. That’s parallax. Now, since we know the distance between your eyes, and the distance your finger appears to move, we can use that to math out how far your finger is.
So you can take a picture of a distant star, then wait 6 months for the Earth to be on the other side of our orbit and take the picture again. Now we can compare how much that star appears to move on the picture. Since we know how far apart the Earth was at each point in orbit we can math out how far away the star is.
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