<p>Yes indeed, the Sun (and other stars) has an oscillatory velocity perpendicular to the galactic plane. According to <a href="http://www.nature.com/nature/journal/v316/n6030/abs/316706a0.html" rel="nofollow">this Nature article</a>, the Sun crosses the galactic plane roughly every 30 million years, reaching a max height of 150-300 lightyears.</p>

<p>Depending on how you measure it, a more recent analysis by <a href="http://arxiv.org/abs/0704.0950" rel="nofollow">Joshi (2007)</a> finds that we are currently somewhere between 20 and 90 lightyears above the plane.</p>

CC BY-SA 3.0
2015-03-26T13:50:27.140Z
2015-03-26T14:05:24.150Z
2015-03-26T14:05:24.150Z
pela
<p>I think your question is answered by the duplicate mentioned: but here are the relevant highlights.</p>

<p><a href="http://adsabs.harvard.edu/full/1995AJ....110.2183H" rel="nofollow noreferrer">Humphreys &amp; Larsen (1995)</a> suggest, using star count information, a distance of $20.5 \pm 3.5$ pc <strong>above the Galactic plane</strong>; consistent with, but more precise than the Bahcall paper referred to by Schleis. <a href="http://adsabs.harvard.edu/abs/2007MNRAS.378..768J" rel="nofollow noreferrer">Joshi (2007)</a> is more guarded, investigating some systematic uncertainties in the estimation techniques and ends up with distances between <strong>13 and 20 pc above the plane</strong>.</p>

<p>The Sun moves at about 15-20 km/s with respect to a local standard of rest defined by the general motion of stars in our vicinity around the Galaxy. In three-dimensions, this "peculiar velocity" is $U=10.00 \pm 0.36$ km/s (radially inwards), $V=5.25 \pm 0.62$ km/s (in the direction of Galactic rotation) and <strong>$W=7.17 \pm 0.38$ km/s</strong> (<strong>up and out of the plane</strong>).  <a href="http://adsabs.harvard.edu/abs/1998MNRAS.298..387D" rel="nofollow noreferrer">(Dehnen &amp; Binney 1998)</a>. Different authors arrive at velocities that differ by $\sim 1-2$ km/s from these values and so this would probably be a more conservative estimate of the uncertainties.</p>

<p>The Sun executes oscillations around its mean orbit in the Galaxy, periodically crossing the Galactic plane. I borrowed this illustration (not to scale!) from <a href="http://www.visioninconsciousness.org/Science_B08.htm" rel="nofollow noreferrer">http://www.visioninconsciousness.org/Science_B08.htm</a> to show this oscillatory motion. The oscillations will not be exactly sinusoidal because the restoring force towards the plane does not very linearly with height above the plane.
As the Sun is currently above the plane and moving upwards, and each cycle takes about 70 million years with an amplitude of 100pc (<a href="http://adsabs.harvard.edu/abs/1995Icar..116..255M" rel="nofollow noreferrer">Matese et al. 1995</a>), it will be roughly 30 million years before we cross the plane again.</p>

<p>EDIT: Actually I'm glad I revisited this question because I think the picture is not very good at all. As the Sun takes ~230 million years to go around the Gaaxy, it should only execute 3 complete vertical oscillations in our Galactic year, whereas the picture implies many more. Secondly, the Sun executes a radial oscillation with a period of around 160 million years, which is not even indicated!</p>

<p><img src="https://i.sstatic.net/Dv1Ii.jpg" alt="Sun&#39;s motion around the Galaxy"></p>

CC BY-SA 3.0
2015-03-27T14:33:07.170Z
Thanks for the great answer. I had already accepted the other answer (which also answers my question) so I can't mark you. And if I had voting up privileges you'd certainly had my vote up, but I have too few points.
TomCho
CC BY-SA 3.0
2015-03-30T20:43:44.180Z
@TomCho: I think it's possible to change your acceptance of an answer. Feel free to do that; I think Rob's answer is great and more elaborate than mine.
pela
CC BY-SA 3.0
2015-12-13T23:38:24.913Z
How does the relative attitude of our ecliptic plane progress through this ? Does it stay at 63% ? In other words, in addition to revolving around center of galaxy, does it also rotate about itself somehow ?
kert
CC BY-SA 3.0
2015-12-13T23:53:04.913Z
@kert I would think that it will stay the same unless some torque forces it to do otherwise. i.e. The angular momentum vectors of the planets around the Sun are independent of the Sun's motion through the Galaxy in much the same way as the tilt of the Earth's rotation axis to the ecliptic is not changed by the motion of the Earth around the Sun.
ProfRob
CC BY-SA 3.0
2015-03-26T23:39:00.320Z
2015-03-26T23:47:42.860Z
2015-03-26T23:47:42.860Z
ProfRob
<p>I got from <a href="https://astronomy.stackexchange.com/questions/546/why-is-our-solar-system-tipped-about-63%c2%b0-with-respect-to-the-plane-of-our-gala">this answer</a> that the axis of the solar system is tilted of about 63 degrees in relation to that of our galaxy, so I can assume that we move through space (at least locally) roughly in a direction that is 63° tilted in relation to our solar system's plane, is that correct?</p>
<p>If so, then: is there also some net velocity of our solar system (probably small) in a direction that is perpendicular to the galaxy's plane, as opposed to the main direction that is &quot;parallel&quot; to the galaxy's plane?</p>
<hr />
<p>EDIT</p>
<p>I think my question is different from <a href="https://astronomy.stackexchange.com/questions/822/how-far-is-the-earth-sun-above-below-the-galactic-plane-and-is-it-heading-towar">this one</a> in that the latter asks about the distance from the solar system to the galactic plane, with no regards as to the speed with which this distance is changing. On the other hand, I'm interested not on the distance, but on the speed with which this distance is changing, which can promptly be approximated with respect to time with a sine function from pela's answer, which was my main intention.</p>

CC BY-SA 3.0
2015-03-26T19:14:01.280Z
possible duplicate of [How far is the Earth/Sun above/below the galactic plane, and is it heading toward/away from it?](http://astronomy.stackexchange.com/questions/822/how-far-is-the-earth-sun-above-below-the-galactic-plane-and-is-it-heading-towar)
ProfRob
CC BY-SA 4.0
2019-10-29T21:18:52.657Z
The angle between the Galactic and ecliptic planes is 60 degrees.
ProfRob
<solar-system><galaxy><galactic-dynamics>
What is the direction of the movement of the solar system in relation to the galaxy's plane
TomCho
# What is the direction of the movement of the solar system in relation to the galaxy's plane

(Asked by: username_0 on 2015-03-26)

I got from [this answer](https://astronomy.stackexchange.com/questions/546/why-is-our-solar-system-tipped-about-63%c2%b0-with-respect-to-the-plane-of-our-gala) that the axis of the solar system is tilted of about 63 degrees in relation to that of our galaxy, so I can assume that we move through space (at least locally) roughly in a direction that is 63° tilted in relation to our solar system's plane, is that correct?

If so, then: is there also some net velocity of our solar system (probably small) in a direction that is perpendicular to the galaxy's plane, as opposed to the main direction that is "parallel" to the galaxy's plane?

---

EDIT

I think my question is different from [this one](https://astronomy.stackexchange.com/questions/822/how-far-is-the-earth-sun-above-below-the-galactic-plane-and-is-it-heading-towar) in that the latter asks about the distance from the solar system to the galactic plane, with no regards as to the speed with which this distance is changing. On the other hand, I'm interested not on the distance, but on the speed with which this distance is changing, which can promptly be approximated with respect to time with a sine function from pela's answer, which was my main intention.

**Tags:** solar-system, galaxy, galactic-dynamics
> **Comments:**
> **username_1**: possible duplicate of [How far is the Earth/Sun above/below the galactic plane, and is it heading toward/away from it?](http://astronomy.stackexchange.com/questions/822/how-far-is-the-earth-sun-above-below-the-galactic-plane-and-is-it-heading-towar)  
> **username_1**: The angle between the Galactic and ecliptic planes is 60 degrees.  

---

## 2 answers

### Answer by username_2 on 2015-03-26. Score: 2 | Accepted answer

Yes indeed, the Sun (and other stars) has an oscillatory velocity perpendicular to the galactic plane. According to [this Nature article](http://www.nature.com/nature/journal/v316/n6030/abs/316706a0.html), the Sun crosses the galactic plane roughly every 30 million years, reaching a max height of 150-300 lightyears.

Depending on how you measure it, a more recent analysis by [Joshi (2007)](http://arxiv.org/abs/0704.0950) finds that we are currently somewhere between 20 and 90 lightyears above the plane.


---

### Answer by username_1 on 2015-03-26. Score: 4

I think your question is answered by the duplicate mentioned: but here are the relevant highlights.

[Humphreys & Larsen (1995)](http://adsabs.harvard.edu/full/1995AJ....110.2183H) suggest, using star count information, a distance of $20.5 \pm 3.5$ pc **above the Galactic plane**; consistent with, but more precise than the Bahcall paper referred to by Schleis. [Joshi (2007)](http://adsabs.harvard.edu/abs/2007MNRAS.378..768J) is more guarded, investigating some systematic uncertainties in the estimation techniques and ends up with distances between **13 and 20 pc above the plane**.

The Sun moves at about 15-20 km/s with respect to a local standard of rest defined by the general motion of stars in our vicinity around the Galaxy. In three-dimensions, this "peculiar velocity" is $U=10.00 \pm 0.36$ km/s (radially inwards), $V=5.25 \pm 0.62$ km/s (in the direction of Galactic rotation) and **$W=7.17 \pm 0.38$ km/s** (**up and out of the plane**). [(Dehnen & Binney 1998)](http://adsabs.harvard.edu/abs/1998MNRAS.298..387D). Different authors arrive at velocities that differ by $\sim 1-2$ km/s from these values and so this would probably be a more conservative estimate of the uncertainties.

The Sun executes oscillations around its mean orbit in the Galaxy, periodically crossing the Galactic plane. I borrowed this illustration (not to scale!) from <http://www.visioninconsciousness.org/Science_B08.htm> to show this oscillatory motion. The oscillations will not be exactly sinusoidal because the restoring force towards the plane does not very linearly with height above the plane.
As the Sun is currently above the plane and moving upwards, and each cycle takes about 70 million years with an amplitude of 100pc ([Matese et al. 1995](http://adsabs.harvard.edu/abs/1995Icar..116..255M)), it will be roughly 30 million years before we cross the plane again.

EDIT: Actually I'm glad I revisited this question because I think the picture is not very good at all. As the Sun takes ~230 million years to go around the Gaaxy, it should only execute 3 complete vertical oscillations in our Galactic year, whereas the picture implies many more. Secondly, the Sun executes a radial oscillation with a period of around 160 million years, which is not even indicated!

![Sun's motion around the Galaxy](https://i.sstatic.net/Dv1Ii.jpg)

> **Comments:**
> **username_0**: Thanks for the great answer. I had already accepted the other answer (which also answers my question) so I can't mark you. And if I had voting up privileges you'd certainly had my vote up, but I have too few points.  
> **username_2**: @TomCho: I think it's possible to change your acceptance of an answer. Feel free to do that; I think Rob's answer is great and more elaborate than mine.  
> **username_3**: How does the relative attitude of our ecliptic plane progress through this ? Does it stay at 63% ? In other words, in addition to revolving around center of galaxy, does it also rotate about itself somehow ?  
> **username_1**: @kert I would think that it will stay the same unless some torque forces it to do otherwise. i.e. The angular momentum vectors of the planets around the Sun are independent of the Sun's motion through the Galaxy in much the same way as the tilt of the Earth's rotation axis to the ecliptic is not changed by the motion of the Earth around the Sun.  

---

