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What would happen if the force of gravitation suddenly starts varying as $1$$/$$r^3$ instead of $1/r^2$ ? Would the symmetry of universe now seen be disrupted?

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If you're asking physics questions to satisfy your own curiosity at 16 years old, you don't need to apologize for how it sounds. Good luck on your continuing education. – AdamRedwine Oct 18 '12 at 11:53

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It depends on what you mean by symmetry, But the force law 1/r^3 does not have stable orbits. Small perturbations will de stabilize your orbits to fall inward or outward.

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As addition to this answer: http://en.wikipedia.org/wiki/Bertrand%27s_theorem. – Nick Kidman Oct 18 '12 at 11:45
Also the iron sphere theorem would not hold as it relies on area of a sphere increasing with $r^2$. Relativity gets around this by changing the geometry. – SMeznaric Oct 18 '12 at 15:54

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