Subtracting the proper motion resulting from movement of the Sun

AI Thread Summary
To compute a star's velocity relative to its local medium, proper motion measurements must be adjusted for the Sun's movement. The user has identified the solar peculiar motion components and the local standard of rest velocity but struggles with the conversion process. They attempted to convert proper motion from galactic to Cartesian coordinates, subtract the solar velocity, and then revert to galactic coordinates, yet the results are incorrect. A lack of clear guidance on this method is noted, with a reference to a potential resource in Astronomy and Astrophysics. Assistance in clarifying the calculation process is sought.
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Hello,
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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A brief cookbook can be found in Astronomy and Astrophysics, v.431, p.L1-L4 (2005) .
Just in a case someone might need it sometime :).
 
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