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

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SUMMARY

The discussion focuses on calculating the root mean square (r.m.s) radius of an N-body system, specifically in the context of globular clusters. Two methods are proposed: one involving the collection of multiple data points and the other utilizing waveform mapping. The first method's accuracy is contingent on the number of points measured, while the second method is deemed more accurate but lacks clarity on data collection techniques. The objective is to determine how much the radius of the cluster deviates from that of a circle with the same area.

PREREQUISITES
  • Understanding of root mean square (r.m.s) calculations
  • Familiarity with globular cluster dynamics
  • Basic knowledge of waveform analysis
  • Proficiency in calculus concepts
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  • Research methods for collecting data on globular clusters
  • Learn about advanced r.m.s calculations in astrophysics
  • Explore waveform mapping techniques for spatial data
  • Study the mathematical implications of N-body simulations
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Astronomers, astrophysicists, and students studying celestial mechanics or N-body simulations will benefit from this discussion.

luxiaolei
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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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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.
 

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