Measuring Parallax Angle to the Method

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The parallax method for measuring large distances involves determining the parallax angle when Earth is at opposite sides of its orbit, maximizing the angle for accuracy. This angle is measured by comparing the position of a foreground star against distant stars, which exhibit negligible parallax. To accurately calculate the parallax, the translational motion of the star must be subtracted from the observed movement. Understanding these steps is crucial for effectively applying the parallax method in astronomy. This approach allows for precise distance measurements to celestial objects.
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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.
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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