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Yes, that's the way it works. A parallax angle of 1" (arc-second) means that the object is at a distance of 1 parsec (that's how the parsec is defined); at a parallax angle of 1/10 of an arc-second, the object would be at a distance of 10 parsec, etc. A parsec is approximately 3.26 light-years.

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It doesn't just happen in space. Stick out your thumb and look at the background; as you move your hand toward you, the greater the parallax shift.

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Yes.

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Q: Is the larger a parallax shift the closer an object is?
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