# Why low precision of the radius of Sun's orbit in MW?

Gold Member
It seems that the value has only 1 1/2 significant digits. Why are values for the measurement of this radius not more precise? What prevents a greater precision?

I have recently been trying to learn about the sun's orbit in the Milky Way (MW) in order to calculate estimates re DM for another thread.. I have found that different sources give values for the radius of he sun's orbit that vary more than I expected.

Here are examples:
1. 25+ kly =7.7+ kpc
2. 26 kly = 7.97 kpc
3. 27.2 ± 1.1 kly = 8.33 +/- 0.35 kpc (= +/- 4%)
4. 27.7 kly = 8.5 kpc

I am using (3) in my calculations since that at least provides an error range.

## Answers and Replies

Mentor
Considering that only one of those references is to a paper in a peer-reviewed publication, I think it is pretty clear which of these numbers should be the best to use

Gold Member
I think it is pretty clear which of these numbers should be the best to use
Hi DrClaude:

Thank you for your post.

Can you perhaps suggest any reference that explains what makes a more precise measurement of the radius so difficult?

Regards,
Buzz

Staff Emeritus
Why is it hard? How do you measure distance? It's not like someone has put up signposts.

Staff Emeritus
Homework Helper
Hi DrClaude:

Thank you for your post.

Can you perhaps suggest any reference that explains what makes a more precise measurement of the radius so difficult?

Regards,
Buzz
Considering that the solar system is located approx. 27,000 LY from the galactic center, one or two digits of precision is pretty accurate. It's not like you're going to "ping" this distance to check it physically in less than 50,000 years or so.

https://en.wikipedia.org/wiki/Milky_Way

It's barely been outside of living memory that cosmic distances have been estimated to any degree of precision:

These measurements are being refined all the time. Even estimates of the size of the MW and some nearby galaxies (like Andromeda) tend to fluctuate as new methods of measuring cosmic distances are developed.

Gold Member
Why is it hard? How do you measure distance? It's not like someone has put up signposts.

Thank you for your post.

I suppose I was just naive and/or careless. I thought one of the standard candles that might be used to make this measurement had more precision than that, and that the problem was more specific, like maybe too much dust.

I just looked more closely at
The distance to Andromeda is given as 2.54 ± 0.11 Mly which is also about the same +/- 4% precision.

Regards,
Buzz

Gold Member
Hi SteamKing:

Thanks for you post.

Please see my post #6 responding to Vanadium.

Thanks especially for your citing the Wikipedia article on the cosmic distance ladder.

Regards,
Buzz

Also, you need to understand that the "orbit" of a star in a galaxy is not like the orbit of the Earth around the sun. The Earth is basically orbiting around a point mass, so the form of the orbit is quite simple - an ellipse with the sun at one focus. In the Milky Way, the sun is moving in a path determined by the combined pull from all of the other mass of the galaxy, and most of this mass is in motion as well. So, not only is the path much more complicated, the path is probably not even a closed curve. If you look at simulations of the paths of stars in a galaxy, the paths look more like a plate of spaghetti than like the orbits of the planets in the solar system. So before you can define the "radius" of the "orbit" with more precision, you would first have to define what you mean by these terms, and you would have to determine where is the center relative to which you are measuring this radius.

Gold Member
So, not only is the path much more complicated, the path is probably not even a closed curve.
Hi phyzguy:

Thanks for you post.

I gather from a Wikipedia source that the sun's orbit in the milky way seems to be close to a circle. Maybe this is also naive.

Regards,
Buzz

I gather from a Wikipedia source that the sun's orbit in the milky way seems to be close to a circle. Maybe this is also naive.
Regards,
Buzz

Yes, it is naive. This diagram is just a schematic, and the actual situation is much more complicated. Try running a simulation of the sun's path in a realistic model of the galaxy, and you will see that while the motion is approximately circular, the actual path is not a closed curve, and is probably chaotic. Try looking at this paper, where they tried to trace the path of the sun backwards in time. At the bottom of Figure 2, all of those red dots are possible initial locations of the sun which could have resulted in the sun being where it is today.

marcus
snorkack
It seems that the value has only 1 1/2 significant digits. Why are values for the measurement of this radius not more precise? What prevents a greater precision?
How come that even as much precision is claimed?

Gold Member
Try looking at this paper, where they tried to trace the path of the sun backwards in time.
Hi phyzguy:

Thanks for your post, and especially for the link for the Martınez-Barbosa et al article. The article seems to be quite interesting, and I plan to read it. From a quick scan and a look at Figure 2, I have to agree that the orbit simulation seems quite chaotic. I also find it particularly interesting that compared with the present distance from the MW center of 8.5 kpc, the birth distance could be anywhere from 6 kpc to 11 kpc. I have not yet found in the text why the authors seem to prefer the 11 kpc value.

Regards,
Buzz

Gold Member
Dearly Missed
Buzz I agree that the Martinez-Barbosa paper seems very interesting! AFAICS it was published online by MNRAS in November 2014 and in hard copy in January 2015. Going by that, the Sun has no such thing as an "orbit radius"---its path is chaotic---not a closed circle. As you point out they seem to prefer the idea that it was born around 11 kpc from center and has migrated inward to the present distance of about 8.5 kpc from center.
http://arxiv.org/abs/1410.2238
Radial Migration of the Sun in the Milky Way: a Statistical Study
C.A. Martínez-Barbosa, A.G.A Brown, S. Portegies Zwart
(Submitted on 8 Oct 2014)
The determination of the birth radius of the Sun is important to understand the evolution and consequent disruption of the Sun's birth cluster in the Galaxy. Motivated by this fact, we study the motion of the Sun in the Milky Way during the last 4.6 Gyr in order to find its birth radius. We carried out orbit integrations backward in time using an analytical model of the Galaxy which includes the contribution of spiral arms and a central bar. We took into account the uncertainty in the parameters of the Milky Way potential as well as the uncertainty in the present day position and velocity of the Sun. We find that in general the Sun has not migrated from its birth place to its current position in the Galaxy (R_\odot). However, significant radial migration of the Sun is possible when: 1) The 2:1 Outer Lindblad resonance of the bar is separated from the corrotation resonance of spiral arms by a distance ~1 kpc. 2) When these two resonances are at the same Galactocentric position and further than the solar radius. In both cases the migration of the Sun is from outer regions of the Galactic disk to R_\odot, placing the Sun's birth radius at around 11 kpc. We find that in general it is unlikely that the Sun has migrated significantly from the inner regions of the Galactic disk to R_\odot.
Comments: 19 pages, 13 figures, accepted for publication in MNRAS

http://arxiv.org/abs/0810.4674 says 8.33 +/- 0.35 kpc (= +/- 4%)
But this is not given as an "orbit radius" ---it is given as the current distance to the BH whose mass is insignificant compared with the mass of the galaxy (only a few million solar masses).
It is simply the current distance to that particular object.

But this is not given as an "orbit radius" ---it is given as the current distance to the BH whose mass is insignificant compared with the mass of the galaxy (only a few million solar masses). It is simply the current distance to that particular object.

Yes, exactly. I don't think we know very precisely the location of the center of mass of the galaxy in relation to the central black hole (Sgr A*). The location of SgrA* is a convenient marker because we can locate it very precisely, but the center of mass of the galaxy might be displaced from SgrA* by a significant amount. At least, that's what I think. Does anyone know of attempts to locate the center of mass of the Milky Way?

Gold Member
says 8.33 +/- 0.35 kpc (= +/- 4%)
But this is not given as an "orbit radius" ---it is given as the current distance to the BH whose mass is insignificant compared with the mass of the galaxy (only a few million solar masses).
It is simply the current distance to that particular object.
Hi marcus:

Thanks for your post, especially for the link you cited.

The number I have been using in calculations for another thread as the (current) distance of the sun from the MW center is 8.5 kpc. This is from
which says
r0 ~ 8.5 kpc is the distance of the Sun from the galactic center,​

I found the following quote in the article you cited.
Our current best estimate for the distance to the Galactic Center is R0 = 8.33 ± 0.35 kpc.​
Apparently the authors intended the BH which you mentioned to be the MW center.

Since this article is dated 2008, and the value also has error bounds, I will now use the 8.33 value in my calculations.

Regards,
Buzz

Gold Member
the center of mass of the galaxy might be displaced from SgrA* by a significant amount
Hi phyzguy:

As I pointed out in my previous post #15, the authors of the article marcus cited intended that SgrA* is the MW center.

Regards,
Buzz