Gravitational Motion of Masses on Polygons: n=8 to ∞

AI Thread Summary
In a system of point particles with mass "m" placed at the corners of an n-sided polygon, the particles will move radially inward due to gravitational attraction. Calculating the potential energy (PE) as a function of radius simplifies the analysis compared to adding individual gravitational forces. The discussion emphasizes finding a formula for the system as n approaches infinity. Participants suggest that this approach will yield insights into the collision time of the particles. Understanding the behavior of the system as n tends to infinity is crucial for predicting the dynamics of the particles.
Sakriya
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Suppose a n-sided polygon. Point particles of mass "m" each are placed in the corners of the polygon. How does the system of particles move if the only force anting between them is gravity? After how much time the bodies collide if n= 8 and n tends to infinity?


Any suggestions are welcome .
this is not homework question.
 
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Hi Sakriya! :wink:

It's symmetric, so they'll obviously move radially inwards.

Can't you just add all the individual forces?

If you don't fancy that, you could instead start by calculating the PE as a function of radius …

what do you get? :smile:​
 
Thanks
Adding individual forces would be very long, using PE it becomes easy...
how should i do it when n tends to infinity
 
Sakriya said:
… how should i do it when n tends to infinity

Can't you just find the formula for n, and let n -> ∞ ? :confused:
 

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