<p>A commenter points out that accelerations in the galactic gravitational potential are extremely small:</p>

<blockquote>
  <p>The Sun's galactic orbital speed is roughly 200 km/s and its distance from the galactic centre is around 8 kpc. Using <span class="math-container">$a=v^2/r$</span> that gives an acceleration of roughly <span class="math-container">$1.6×10^{−10}\rm\,m/s^2$</span>.</p>
</blockquote>

<p>A century is only <span class="math-container">$\pi×10^9$</span> seconds, so in a hundred years the <span class="math-container">$\Delta\vec v$</span> for the Sun and its neighbors is only half a meter per second --- and that's mostly a difference of direction, not magnitude.  We can't measure three-dimensional stellar motions to a precision of a half-meter per second, and the career of a professional astronomer is usually shorter than a century.</p>

CC BY-SA 4.0
2019-12-02T18:45:04.063Z
2019-12-02T18:45:04.063Z
rob
<p>Many people concern themselves with understanding the Galactic potential. To me, the most obvious way is to measure the acceleration of a star, as this is directly related to the potential. So, one could measure a LOS velocity (or proper motion) at different years and measure its change. I understand that orbital timescales of stars are huge however, so can this be done? If not, how far (order of magnitude) away are we from having the required uncertainties for achieving this?</p>

CC BY-SA 4.0
2019-11-24T23:45:33.563Z
What is that "galactic potential"?
peterh
CC BY-SA 4.0
2019-11-25T00:09:08.380Z
Galactic potential = the gravitational potential of the Milky Way
user31040
CC BY-SA 4.0
2019-11-25T01:57:56.737Z
Not even with Gaia-level precision will we be able to measure accelerations to a meaningful level. However proper motions, translated into 3D velocities, paired with a bit of theory, i.e. the Virial theorem and such, will be able to achieve that to a degree.
AtmosphericPrisonEscape
CC BY-SA 4.0
2019-11-25T03:44:38.153Z
Those accelerations are pretty small, which makes them hard to measure accurately. Eg, the Sun's galactic orbital speed is roughly 200 km/s and its distance from the galactic centre is around  8 kpc. Using $a=v^2/r$ that gives an acceleration of roughly $\mathrm{1.6 \times 10^{-10} m/s^2}$
PM 2Ring
<galaxy><milky-way>
Can we measure stellar accelerations?
user31040
# Can we measure stellar accelerations?

(Asked by: username_0 on 2019-11-24)

Many people concern themselves with understanding the Galactic potential. To me, the most obvious way is to measure the acceleration of a star, as this is directly related to the potential. So, one could measure a LOS velocity (or proper motion) at different years and measure its change. I understand that orbital timescales of stars are huge however, so can this be done? If not, how far (order of magnitude) away are we from having the required uncertainties for achieving this?

**Tags:** galaxy, milky-way
> **Comments:**
> **username_1**: What is that "galactic potential"?  
> **username_0**: Galactic potential = the gravitational potential of the Milky Way  
> **username_2**: Not even with Gaia-level precision will we be able to measure accelerations to a meaningful level. However proper motions, translated into 3D velocities, paired with a bit of theory, i.e. the Virial theorem and such, will be able to achieve that to a degree.  
> **username_3**: Those accelerations are pretty small, which makes them hard to measure accurately. Eg, the Sun's galactic orbital speed is roughly 200 km/s and its distance from the galactic centre is around  8 kpc. Using $a=v^2/r$ that gives an acceleration of roughly $\mathrm{1.6 \times 10^{-10} m/s^2}$  

---

## 1 answers

### Answer by username_4 on 2019-12-02. Score: 1

A commenter points out that accelerations in the galactic gravitational potential are extremely small:

> The Sun's galactic orbital speed is roughly 200 km/s and its distance from the galactic centre is around 8 kpc. Using $a=v^2/r$ that gives an acceleration of roughly $1.6×10^{−10}\rm\,m/s^2$.

A century is only $\pi×10^9$ seconds, so in a hundred years the $\Delta\vec v$ for the Sun and its neighbors is only half a meter per second --- and that's mostly a difference of direction, not magnitude. We can't measure three-dimensional stellar motions to a precision of a half-meter per second, and the career of a professional astronomer is usually shorter than a century.


---

