Measuring Parallax Angle to the Method

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AlchemistK
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I have read the parallax method of determining large distances and i do understand it. I agree it is easy to find the distance of the basis(distance between two observation points) but how do they measure the parallax angle?
 
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Parallax is usually measured when Earth is at opposite sides of its orbit, so that the parallax has the largest angle, you then compare the position of the foreground star to those of distant stars which have a negligible parallax and you can then find out how far it has moved as an angular position. You also need to subtract the stars translational motion before finding the parallax.