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what is the method of measuring the distance of star/planet /galaxy which are thousands light years away from us ? what is the accuracy?

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John McCann answered

Angular resolution/360 degrees = diameter/2(pi)r

A triangulation method using the apparent diameter of the object, the angular width of the triangular point, looking for r, the distance away from us.

Measuring red shift/blue shift is another method

sigma' - sigma/sigma = Vrel/c

Where sigma' = wavelength of measured radiation by us.

sigma = wavelength of radiation emitted by object.

Vrel = relative velocity of object, either towards or away from us.

c = speed of light.

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