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Suppose that we have a body $B$ exerting action at a distance force on body $A$. Now if someone says that the dependence of force on distance between the bodies ($r$) is:

$f(r)=\dfrac{1}{r^2}+\dfrac{1}{r^3}$

Is there a way to refute this claim?

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    $\begingroup$ In physics : measurements of the system being modeled and comparison with the predictions/fit to the model. If the fit is bad, the model is bad. If the fit is good, the model is (probably) good. This is how things are decided in physics. BTW that's a polynomial function of $\frac 1 r$, not $r$. $\endgroup$ – StephenG Apr 21 '18 at 3:57
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Forces are mediated by fields. By Guass' law we have conservation of the field over any enclosing surface. As the surface area ~ r^2 we expect any azimuthally uniform field to do the inverse and if it doesn't it will break conservation laws.

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