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I have been trying to compute the velocity of the star with respect to its local medium from the proper motion measurements. Sure, you can calculate the corresponding velocities by v = 4.74*(proper motion)*distance (in suitable units), but this resulting velocity is now with respect to Sun.

I have been searching for a method to compute that. So far I have found the velocity components of the solar peculiar motion (U, V, W) = (10, 11, 7.2) km/s and velocity of the local standard of rest v_lsr = 240 km/s. I have tried to convert the proper motion (in galactic coordinates) into velocity in cartesian coordinates, then subtract the solar velocity given as (10, 11 - 240, 7.2) and convert the resulting velocity back into galactic coordinates but I keep getting the wrong values...

I must be doing something wrong. I have not been able to found any comprehensible guide on how to do this. If someone know of something that can help me, I will be grateful.

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# Subtracting the proper motion resulting from movement of the Sun

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