Dimensionless value to differentiate between concentrated and dispersed

[independentphysics]

Homework Statement

Find a dimensionless value to differentiate between concentrated and dispersed mass systems

Relevant Equations

Newtonian mechanics

I want to find a dimensionless value that differentiates between concentrated mass systems such as the solar system and dispersed mass systems such as a galaxy. I assume spherical and radial symmetry, consider both the cases for point masses or smooth mass distributions.

The only value I can think of is the sum of multiplying each mass by its distance, but then I have to normalize this by some mass*distance to make it dimensionless.

Is there any other alternative?

 

[DaveC426913]

For what purpose? It is hard to define such a thing without knowing what it will be used for.
For example: in the absense of elaboration, I offer the following:
1 for localized objects such as stars, and 0 for diffuse objects such as gas clouds.
Fractional values can serve for in-between states, such as rock piles.

 

[independentphysics]

For what purpose? It is hard to define such a thing without knowing what it will be used for.
For example: in the absense of elaboration, I offer the following:
1 for localized objects such as stars, and 0 for diffuse objects such as gas clouds.
Fractional values can serve for in-between states, such as rock piles.

Hi Dave,

I need a dimensionless value based of physical parameters to differentiate between concentrated mass systems such as the solar system and dispersed mass systems such as a galaxy.

I do not understand your proposal. Although it is a dimensionless value, how can it be derived from physical parameters?