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How does Parallax work?

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Answer:

Did you ever sit in the passenger seat and look at the fuel gauge on the dash? You see the gauge from the side so it appears that the needle is pointing to Empty. The driver is looking straight at it so the driver sees the actual reading to be a quarter of a tank. That was a parallax error that your observation position created.

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Relevant answers:

How far out does parallax work?
According to this, about 100 parsec. http://hsc.csu.edu.au/physics/options/astrophysics/3035/PHY972net.html
Does parallax work for stars at any distance?
Stars at any distance will have a parallax, but when the distance becomes too large, the parallax becomes too small to measure.
Does the parallax method work for measuring the distance of all stars?
No it only works out to a certain distance. Beyond this you move in to the field of red shifting measurement.