How is the transverse velocity component, or proper motion, determined?
Answer
Comparing positional images over many years
Transverse velocity, or proper motion, requires observing the star's physical displacement across the celestial sphere over an extended period. Unlike the instantaneous Doppler measurement, this velocity must be determined by taking highly accurate positional images of the star across many years or even decades. By comparing the star's position in older records to its current location relative to fixed background objects, astronomers quantify the angular change over time, which is then converted into velocity using the star's known distance.
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How Fast Do Stars Move Due To Proper Motion? - Physics Frontier
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