<p>v$_r$ and <strong>μ</strong> 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 <strong>μ</strong> 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.</p>

CC BY-SA 3.0
2016-04-26T16:57:37.347Z
Thank you, I shall alter my simulations and see how they differ
R Thompson
CC BY-SA 3.0
2016-04-26T16:22:25.877Z
2016-04-26T16:22:25.877Z
eshaya
<p>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 <a href="http://www.aanda.org/articles/aa/pdf/2011/01/aa13415-09.pdf" rel="nofollow">http://www.aanda.org/articles/aa/pdf/2011/01/aa13415-09.pdf</a></p>

<p>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)? </p>

<p>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.</p>

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

<p>Thanks </p>

CC BY-SA 3.0
2016-04-16T21:56:41.383Z
Your velocity is surely the velocity of the Galactic centre wrt Local Standard of Rest.?
ProfRob
CC BY-SA 3.0
2016-04-16T21:59:11.093Z
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
CC BY-SA 3.0
2016-04-16T22:01:47.247Z
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
CC BY-SA 3.0
2016-04-16T22:34:15.107Z
Yes I think so, although am puzzled by the small, but non-zero $u$ and $w$ velocities..
ProfRob
CC BY-SA 3.0
2016-04-16T22:35:51.793Z
I simply just ran it through the method in that link and that's what was produced at the end :s
R Thompson
CC BY-SA 3.0
2016-04-16T22:42:14.517Z
The V component is much larger due to the adding of the galactic rotation at the end
R Thompson
CC BY-SA 3.0
2016-04-16T22:46:41.943Z
So what did you use for the radial velocity, proper motions and distance to the centre of the Galaxy? In any case, what you've done sounds correct, but I would probably subtract the vector you have obtained fro all my velocities and make the Galactic centre the rest frame.
ProfRob
CC BY-SA 3.0
2016-04-16T23:09:27.737Z
I used the heliocentric radial velocities (I do have data for corrected velocities for the galactic rest frame but the method seems to want heliocentric). I used proper motions in as/yr for known galaxies and the distance to the galactic centre was 8.5 kpc (although the method asks for it in parsecs so I gave 8500 parsecs)
R Thompson
CC BY-SA 3.0
2016-04-16T23:17:03.503Z
But to get the space motion of the Galactic centre, you must have supplied a radial velocity and a proper motion no?
ProfRob
CC BY-SA 3.0
2016-04-16T23:18:08.253Z
No for that I had 0 proper motion and 0 radial velocity. I though this was strange but I could find values for these anywhere...
R Thompson
<galaxy><milky-way><velocity><galaxy-center>
Question regarding the Milky Way when calculating galactic space velocities for galaxies
R Thompson
# Question regarding the Milky Way when calculating galactic space velocities for galaxies

(Asked by: username_0 on 2016-04-16)

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

**Tags:** galaxy, milky-way, velocity, galaxy-center
> **Comments:**
> **username_1**: Your velocity is surely the velocity of the Galactic centre wrt Local Standard of Rest.?  
> **username_0**: 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!  
> **username_0**: 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  
> **username_1**: Yes I think so, although am puzzled by the small, but non-zero $u$ and $w$ velocities..  
> **username_0**: I simply just ran it through the method in that link and that's what was produced at the end :s  
> **username_0**: The V component is much larger due to the adding of the galactic rotation at the end  
> **username_1**: So what did you use for the radial velocity, proper motions and distance to the centre of the Galaxy? In any case, what you've done sounds correct, but I would probably subtract the vector you have obtained fro all my velocities and make the Galactic centre the rest frame.  
> **username_0**: I used the heliocentric radial velocities (I do have data for corrected velocities for the galactic rest frame but the method seems to want heliocentric). I used proper motions in as/yr for known galaxies and the distance to the galactic centre was 8.5 kpc (although the method asks for it in parsecs so I gave 8500 parsecs)  
> **username_1**: But to get the space motion of the Galactic centre, you must have supplied a radial velocity and a proper motion no?  
> **username_0**: No for that I had 0 proper motion and 0 radial velocity. I though this was strange but I could find values for these anywhere...  

---

## 1 answers

### Answer by username_2 on 2016-04-26. Score: 1 | Accepted answer

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.

> **Comments:**
> **username_0**: Thank you, I shall alter my simulations and see how they differ  

---

