<p>Is there any general formula to determine the total mass of a cluster of stars?</p>
<p>I have searched for one in Google, but most of them are for calculating mass of binary stars or single stars using Kepler's law. If the total mass can be found by multiplying the mass of a star by total number of stars, then how can the average mass of an individual star and the total number of stars in a cluster system be calculated? Will the equation vary for cluster system? Assume that the cluster is observable and  spectra are also attainable for the cluster.</p>

CC BY-SA 4.0
2021-05-14T02:11:31.063Z
I think you have an interesting question here, but it needs some more information. Are you asking about an *observed cluster?* If so, can the individual stars be resolved in an image? Can their spectra be measured and many if not all of their radial velocities be independently determined? If so, that might make an answer easier, though I'm no expert so not 100% sure. But I am sure that you should add some more of this kind of detail to your question. *Thanks!* and welcome to Astronomy Stack Exchange!
uhoh
CC BY-SA 4.0
2021-05-14T06:05:46.770Z
@uhoh yes, they are observable and their spectra can be determined.....how to do this calculation for a cluster then? will this vary for open and globular cluster?
Sudipto
CC BY-SA 4.0
2021-05-14T06:30:06.920Z
Okay great, thanks! You should edit your question directly https://i.sstatic.net/dVpHK.png and add that in and any other details like those I've mentioned. There are already 2 close votes for "Needs details or clarity; This question should include more details and clarify the problem." and it takes 5 to close a question. https://i.sstatic.net/BpK4k.png Some people don't bother to read the comments unfortunately, clarifications should always be implemented in the post itself. *Thanks!*
uhoh
CC BY-SA 4.0
2021-05-14T09:13:51.100Z
Can their proper motions be observed or 'just' their spectra and derived velocities? Can you provide / derive a velocity diagramme (wrt the centre of mass of the cluster)? Then you can derive the velocity dispersion. Will be interesting to see that plotted over central distance / radial distance on the (apparent) disc
planetmaker
CC BY-SA 4.0
2021-05-14T09:54:02.753Z
@planetmaker will a HR diagram be ok?
Sudipto
CC BY-SA 4.0
2021-05-14T10:34:24.213Z
@planetmaker if it's a statistical analysis of a large number of stars, then one can for example assume that the distribution in relative velocities along one direction represents it in the other two as well and obtain and report some answer based on that assumption. If later on proper motion is available for the other two dimensions with sufficient resolution, that assumption can be then tested and validated or refuted. This is Astronomy, one can't do controlled experiments, one has to make do with whatever data is available and always make at least some assumptions.
uhoh
CC BY-SA 4.0
2021-05-14T10:48:32.263Z
@planetmaker When the temperature of some gas thing is obtained from doppler broadening, one also gets a velocity distribution along only one axis and assumes it's the same in the other two. I'm sure there are some scenarios where this assumption is on shaky ground, but I can't think of any. So instead I'll ask [Any examples of a gas object temperature from Doppler broadening along one axis turning out to be wrong because velocity spread was not isotropic?](https://astronomy.stackexchange.com/q/43791/7982)
uhoh
CC BY-SA 4.0
2021-05-14T13:39:19.127Z
Could you use an IMF and constrain it with spectra for some certain system, and then sum over it? There would be model uncertainties of course...
Daddy Kropotkin
CC BY-SA 4.0
2021-05-14T16:12:24.143Z
is there any possibility to make this calculation using Virial theorem?
Sudipto
CC BY-SA 4.0
2021-05-16T15:36:30.327Z
@DaddyKropotkin Integrated Salpeter's IMF gives the total number of stars in cluster...then how to measure the average mass? just (lowest mas +highest mass)/2 or some other way?
Sudipto
CC BY-SA 4.0
2021-05-16T16:34:41.733Z
Have you seen here, using virial theorem? http://spiff.rit.edu/classes/phys440/lectures/glob_clus/glob_clus.html
Daddy Kropotkin
<star-cluster>
Mass of the stellar cluster (not the whole galaxy)
Sudipto
# Mass of the stellar cluster (not the whole galaxy)

(Asked by: username_0 on 2021-05-13)

Is there any general formula to determine the total mass of a cluster of stars?

I have searched for one in Google, but most of them are for calculating mass of binary stars or single stars using Kepler's law. If the total mass can be found by multiplying the mass of a star by total number of stars, then how can the average mass of an individual star and the total number of stars in a cluster system be calculated? Will the equation vary for cluster system? Assume that the cluster is observable and spectra are also attainable for the cluster.

**Tags:** star-cluster
> **Comments:**
> **username_1**: I think you have an interesting question here, but it needs some more information. Are you asking about an *observed cluster?* If so, can the individual stars be resolved in an image? Can their spectra be measured and many if not all of their radial velocities be independently determined? If so, that might make an answer easier, though I'm no expert so not 100% sure. But I am sure that you should add some more of this kind of detail to your question. *Thanks!* and welcome to Astronomy Stack Exchange!  
> **username_0**: @uhoh yes, they are observable and their spectra can be determined.....how to do this calculation for a cluster then? will this vary for open and globular cluster?  
> **username_1**: Okay great, thanks! You should edit your question directly https://i.sstatic.net/dVpHK.png and add that in and any other details like those I've mentioned. There are already 2 close votes for "Needs details or clarity; This question should include more details and clarify the problem." and it takes 5 to close a question. https://i.sstatic.net/BpK4k.png Some people don't bother to read the comments unfortunately, clarifications should always be implemented in the post itself. *Thanks!*  
> **username_2**: Can their proper motions be observed or 'just' their spectra and derived velocities? Can you provide / derive a velocity diagramme (wrt the centre of mass of the cluster)? Then you can derive the velocity dispersion. Will be interesting to see that plotted over central distance / radial distance on the (apparent) disc  
> **username_0**: @planetmaker will a HR diagram be ok?  
> **username_1**: @planetmaker if it's a statistical analysis of a large number of stars, then one can for example assume that the distribution in relative velocities along one direction represents it in the other two as well and obtain and report some answer based on that assumption. If later on proper motion is available for the other two dimensions with sufficient resolution, that assumption can be then tested and validated or refuted. This is Astronomy, one can't do controlled experiments, one has to make do with whatever data is available and always make at least some assumptions.  
> **username_1**: @planetmaker When the temperature of some gas thing is obtained from doppler broadening, one also gets a velocity distribution along only one axis and assumes it's the same in the other two. I'm sure there are some scenarios where this assumption is on shaky ground, but I can't think of any. So instead I'll ask [Any examples of a gas object temperature from Doppler broadening along one axis turning out to be wrong because velocity spread was not isotropic?](https://astronomy.stackexchange.com/q/43791/7982)  
> **username_3**: Could you use an IMF and constrain it with spectra for some certain system, and then sum over it? There would be model uncertainties of course...  
> **username_0**: is there any possibility to make this calculation using Virial theorem?  
> **username_0**: @DaddyKropotkin Integrated Salpeter's IMF gives the total number of stars in cluster...then how to measure the average mass? just (lowest mas +highest mass)/2 or some other way?  
> **username_3**: Have you seen here, using virial theorem? http://spiff.rit.edu/classes/phys440/lectures/glob_clus/glob_clus.html  

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## 0 answers

