If a star's distance is doubled, assuming its tangential velocity stays the same, how does its proper motion change?

Answer

The proper motion halves

Because proper motion and distance are inversely related when speed is held constant, increasing the distance by a factor of two causes the resulting angular shift seen from Earth to decrease by a factor of two.

If a star's distance is doubled, assuming its tangential velocity stays the same, how does its proper motion change?
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