Static n-Body Problem: Definition and Explanation

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A static n-body problem refers to a configuration where multiple bodies exert gravitational forces on each other without changing their positions over time. This concept often implies a balance of attractive and repulsive forces, leading to a dynamically stable state. In the context of general relativity, it relates to Einstein's early model of a static universe, which maintained gravitational equilibrium among celestial bodies. Understanding this configuration is crucial for studying gravitational interactions in astrophysics. The discussion highlights the need for clearer definitions and explanations of static n-body systems.
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What does it mean for an n-body problem to be static? I come from a mathematics background, so I don't know much about relativity, and I can't seem to find a clear, detailed definition of what a static n-body configuration is. If anyone can explain this to me, I would be very grateful. Thanks.
 
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maybe that there's a superposition of repulsive and attractive fields?
 
Most likely a "Static universe" (Einstein's first general relativistic cosmology, before modification by the cosmological constant) described at http://en.wikipedia.org/wiki/Static_universe" as "dynamically stable."

It maintains in theory a gravitational balance between galaxies, stars, gas and other astronomical objects.
 
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