# Question regarding the Milky Way when calculating galactic space velocities for galaxies

I have been calculating galaxy space velocities (where proper motions are known) in order to measure their orbits of the Milky Way using the method proposed in the appendix of http://www.aanda.org/articles/aa/pdf/2011/01/aa13415-09.pdf

The question I have is: Do we put the Milky Way through the same calculation process to get an initial velocity, or do we have that it's (0,0,0) as it is essentially our origin point (ie the U velocity component would mean that the Milky Way is moving in the direction away from its own galactic centre which doesn't really make sense to me as this could be any direction)?

I have put it through the process and found an initial space velocity of the Milky Way of (-11.1,232.24,7.25) (my method differs slightly from the link since I have used an updated velocity vector for the motion of the sun with respect to the Local standard of Rest) which essentially just comes from correction solar and galaxy rotation motions.

So, is this calculated vector correct for the Milky Way or should it be (0,0,0)?

Thanks

• Your velocity is surely the velocity of the Galactic centre wrt Local Standard of Rest.? – Rob Jeffries Apr 16 '16 at 21:56
• That's what I assumed when I saw that it was non zero. Is the one I calculated correct then? I just want my orbit simulations that I found to be on the right track! – R Thompson Apr 16 '16 at 21:59
• I understand it as, if the local standard of rest displays the motion of material around the Milky Way in the neighbourhood of the sun, then a non zero velocity of the galactic centre (which is material within the Milky Way) makes perfect sense – R Thompson Apr 16 '16 at 22:01
• Yes I think so, although am puzzled by the small, but non-zero $u$ and $w$ velocities.. – Rob Jeffries Apr 16 '16 at 22:34
• I simply just ran it through the method in that link and that's what was produced at the end :s – R Thompson Apr 16 '16 at 22:35

v$_r$ and μ are radial velocities and proper motion as seen from the Sun (ie heliocentric) and the equations in the appendix convert to v in the $S_o$ frame which is the center of the Galaxy. So, the motion of the MW is (0,0,0). If you want to, you can solve for v$_r$ and μ for the MW by plugging v=(0,0,0) into the equation, and find the heliocentric proper motion and radial velocity of the Galactic center. But it is not needed.