<p>The Sun's velocity is known (with uncertainties) with respect to the Galactic centre (GC), as is the Sun's distance from the Galactic centre. These measurements have a long tortuous history, which I am not going to attempt to summarise here. However, the motion of the Sun with respect to the GC is established by measuring the proper motion of the Sgr A* source with respect to the assumed zero proper motions of distant radio quasars (see for example <a href="http://adsabs.harvard.edu/abs/1999ApJ...524..805B" rel="noreferrer">Backer &amp; Sramek 1999</a>; <a href="https://arxiv.org/abs/astro-ph/0408107" rel="noreferrer">Reid &amp; Brundthaler 2004</a>). </p>

<p>The astrometry frame of reference now is known as the <a href="https://en.wikipedia.org/wiki/International_Celestial_Reference_Frame" rel="noreferrer">International Celestial Reference Frame</a> and is defined by hundreds of compact, extragalactic radio sources.</p>

<p>If you then assume the Sun's orbit is circular and that Sgr A* is at the GC, then the job is done - the relative velocity divided by the distance to the GC gives the angular velocity $\Omega$, and the orbital period is $2\pi/\Omega$ . If you have a model for the Galactic potential then you can do a bit better. </p>

CC BY-SA 3.0
2016-11-11T10:53:17.790Z
2016-11-11T10:53:17.790Z
ProfRob
<p>When we say the sun takes 230M years to orbit the galaxy, what is this in relation to? We measure the earth's rotation relative to the distant stars. What is the reference for our Sun's motion around the galaxy?</p>

CC BY-SA 3.0
2016-11-01T10:09:30.620Z
Quite a good question!
Fattie
CC BY-SA 3.0
2016-11-01T13:38:04.343Z
See http://physics.stackexchange.com/q/25094/56299.
HDE 226868
CC BY-SA 3.0
2016-11-01T14:42:21.970Z
@HDE226868 Your comment on Skawang's answer is not true. The relative velocity of the GC with respect to the Sun, combined with a measurement of the distance to the GC does uniquely define an angular velocity $\omega = v/r$ and hence $P = 2\pi/\omega$ (for a circular orbit).
ProfRob
CC BY-SA 3.0
2016-11-01T16:51:11.260Z
Well yes and no - there's the solar year and the sidereal year.   I'd say to the extent that the sun's rotational axis is constant, one sun-galaxy year is the time it takes to return to the place in its orbit w/ same axial tilt.  Equivalently, for an elliptical orbit, time from apogee to apogee
Carl Witthoft
CC BY-SA 3.0
2016-11-01T17:02:50.010Z
@RobJeffries Ah, I see. I had considered defining $v$ with regards to the local standard of rest, and then dismissed that as a valid idea, but you're right, the relative velocity wrt the core is a possibility.
HDE 226868
CC BY-SA 3.0
2016-11-01T17:10:26.540Z
@RobJeffries I wouldn't necessarily say its not true. Technically he's right, you could generate any arbitrary reference frame. There might be one reference frame which is *preferred*, e.g., the one you cited, but it is by no means the "correct" frame.
zephyr
CC BY-SA 3.0
2016-11-01T18:03:18.033Z
@zephyr In what reference frame is the Sun not moving at $\sim 230$ km/s wrt the Galactic centre?
ProfRob
CC BY-SA 3.0
2016-11-01T18:15:59.720Z
@RobJeffries In a reference frame fixed on the galactic center and rotating with the Sun's orbit such that the Sun is fixed in that reference frame.
zephyr
CC BY-SA 3.0
2016-11-01T22:10:58.103Z
I like Rob Jeffries answer on angular momentum.  If the sun was still in relation to the galactic center, it would gradually fall to the center point, the lowest spot on the gravitational rubber sheet to quote a disliked analogy.   The angular momentum and orbital period can be calculated in relation to the gravitational field.   Not that those calculations are easy, and with galaxies, I'm not even sure they're all that consistent given local fluctuations, but there is a mostly direct relation between gravitational field strength of a galaxy and orbital period of objects within that galaxy.
userLTK
CC BY-SA 3.0
2016-11-01T22:13:44.407Z
@zephyr The GC has a proper motion corresponding to a tangential velocity of $\sim 230$ km/s  and an inward velocity of a few km/s. That is pretty much where the Galactic year estimate comes from.
ProfRob
CC BY-SA 3.0
2016-11-02T21:00:56.177Z
nobody has *actually answered the question:* **what is this in relation to?** It's a simple straightforward question.  You often hear the figure "230M" bandied about.  Is this in relation to the local group, or what?
Fattie
CC BY-SA 3.0
2016-11-02T23:39:38.023Z
Yes, the question has only been converted to, with respect to what reference do we say the galactic center has a proper motion of 230 km/s?  It's pretty hard to see through the whole galaxy to find background reference objects, I would assume, but if I had to guess, it would be distant radio quasars.
Ken G
CC BY-SA 3.0
2017-01-02T02:22:20.453Z
Thanks all for the discussion. I think I have the answer I was looking for: it is the ICRS based on distant quasars that are apparently stationary on account of their distance.
Arvind H
<the-sun><galaxy><galaxy-center>
When we say the sun takes 230M years to orbit the galaxy, what is this in relation to?
Arvind H
# When we say the sun takes 230M years to orbit the galaxy, what is this in relation to?

(Asked by: username_0 on 2016-11-01)

When we say the sun takes 230M years to orbit the galaxy, what is this in relation to? We measure the earth's rotation relative to the distant stars. What is the reference for our Sun's motion around the galaxy?

**Tags:** the-sun, galaxy, galaxy-center
> **Comments:**
> **username_1**: Quite a good question!  
> **username_2**: See http://physics.stackexchange.com/q/25094/56299.  
> **username_3**: @HDE226868 Your comment on Skawang's answer is not true. The relative velocity of the GC with respect to the Sun, combined with a measurement of the distance to the GC does uniquely define an angular velocity $\omega = v/r$ and hence $P = 2\pi/\omega$ (for a circular orbit).  
> **username_4**: Well yes and no - there's the solar year and the sidereal year.   I'd say to the extent that the sun's rotational axis is constant, one sun-galaxy year is the time it takes to return to the place in its orbit w/ same axial tilt.  Equivalently, for an elliptical orbit, time from apogee to apogee  
> **username_2**: @RobJeffries Ah, I see. I had considered defining $v$ with regards to the local standard of rest, and then dismissed that as a valid idea, but you're right, the relative velocity wrt the core is a possibility.  
> **username_5**: @RobJeffries I wouldn't necessarily say its not true. Technically he's right, you could generate any arbitrary reference frame. There might be one reference frame which is *preferred*, e.g., the one you cited, but it is by no means the "correct" frame.  
> **username_3**: @zephyr In what reference frame is the Sun not moving at $\sim 230$ km/s wrt the Galactic centre?  
> **username_5**: @RobJeffries In a reference frame fixed on the galactic center and rotating with the Sun's orbit such that the Sun is fixed in that reference frame.  
> **username_6**: I like Rob Jeffries answer on angular momentum.  If the sun was still in relation to the galactic center, it would gradually fall to the center point, the lowest spot on the gravitational rubber sheet to quote a disliked analogy.   The angular momentum and orbital period can be calculated in relation to the gravitational field.   Not that those calculations are easy, and with galaxies, I'm not even sure they're all that consistent given local fluctuations, but there is a mostly direct relation between gravitational field strength of a galaxy and orbital period of objects within that galaxy.  
> **username_3**: @zephyr The GC has a proper motion corresponding to a tangential velocity of $\sim 230$ km/s  and an inward velocity of a few km/s. That is pretty much where the Galactic year estimate comes from.  
> **username_1**: nobody has *actually answered the question:* **what is this in relation to?** It's a simple straightforward question.  You often hear the figure "230M" bandied about.  Is this in relation to the local group, or what?  
> **username_7**: Yes, the question has only been converted to, with respect to what reference do we say the galactic center has a proper motion of 230 km/s?  It's pretty hard to see through the whole galaxy to find background reference objects, I would assume, but if I had to guess, it would be distant radio quasars.  
> **username_0**: Thanks all for the discussion. I think I have the answer I was looking for: it is the ICRS based on distant quasars that are apparently stationary on account of their distance.  

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## 1 answers

### Answer by username_3 on 2016-11-11. Score: 7 | Accepted answer

The Sun's velocity is known (with uncertainties) with respect to the Galactic centre (GC), as is the Sun's distance from the Galactic centre. These measurements have a long tortuous history, which I am not going to attempt to summarise here. However, the motion of the Sun with respect to the GC is established by measuring the proper motion of the Sgr A\* source with respect to the assumed zero proper motions of distant radio quasars (see for example [Backer & Sramek 1999](http://adsabs.harvard.edu/abs/1999ApJ...524..805B); [Reid & Brundthaler 2004](https://arxiv.org/abs/astro-ph/0408107)).

The astrometry frame of reference now is known as the [International Celestial Reference Frame](https://en.wikipedia.org/wiki/International_Celestial_Reference_Frame) and is defined by hundreds of compact, extragalactic radio sources.

If you then assume the Sun's orbit is circular and that Sgr A\* is at the GC, then the job is done - the relative velocity divided by the distance to the GC gives the angular velocity $\Omega$, and the orbital period is $2\pi/\Omega$ . If you have a model for the Galactic potential then you can do a bit better.


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