How to calculate r.m.s radius of a N-body system?

In summary, to calculate the root mean square radius of a globular cluster, one can use either a formula based on a set of points or by mapping the waveform. The first method may not be as accurate depending on the number of points measured, while the second method may be more accurate but requires complex data collection. The goal is to find the average deviation of the cluster's radius from that of a circle with the same area.
  • #1
luxiaolei
75
0
an example of a globular clusters, what method should be used to calculate the root mean square radius of it? thanks in advance!
 
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  • #2
I don't know how you would collect the data for something like that, but if you did the formula's are here:

http://en.wikipedia.org/wiki/Root_mean_square

The first one would be if you took a bunch of points, the second if you map the waveform. The first one would not be too accurate, or only as accurate as the amount of points you decide to measure I should say. The second one would be accurate but I really don't know how you would collect that data. Remember you are looking for the average of how much the radius of your cluster deviates from the radius of a circle of the same area. Sounds like mega-calculus to me, if you find an answer I'd be interested to see what it is.
 

1. What is the r.m.s radius of a N-body system?

The r.m.s radius, or root mean square radius, is a measure of the average distance of all the particles in a system from its center of mass.

2. How do you calculate the r.m.s radius of a N-body system?

The r.m.s radius can be calculated using the formula: rms = √(1/N * ∑(ri^2)), where N is the total number of particles in the system and ri is the distance of each particle from the center of mass.

3. Can the r.m.s radius be negative?

No, the r.m.s radius is always a positive value as it represents a distance.

4. Is the r.m.s radius affected by the mass of the particles in the system?

Yes, the r.m.s radius is directly proportional to the mass of the particles in the system. This means that as the mass increases, the r.m.s radius also increases.

5. What is the significance of calculating the r.m.s radius of a N-body system?

The r.m.s radius provides important information about the distribution and structure of a system. It can also be used to compare different systems and understand their overall size and density.

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