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Originally Posted by tel.lekatsas
Steven,
It depends on whether these extra dimensions are compact or not. If the extra dimensions are not compact then there are no stable orbits. On the other hand if the extra dimensions are compact there is no effect on the force law. KK and string theory assume compact extra dimensions.
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Tel,
You seem to be trying to reconcile Newtonian gravity into String Theory.
It doesn't work. Newtonian gravity is scale independent, the inverse square law applies to both small and large scales. Not so with gravity in String Theory.
In fact String Theory predicts the inverse square law is violated at small scales due to the existence of extra (compact) dimensions.
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The rotation curves of galaxies don't invalidate the inverse square law. The inverse square law can result in non-Keplerian orbits depending on the form of the gravitational potential and thus ultimately on the mass distribution within the galaxy.......
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A typical problem posed to maths and physics undergraduates is to prove that Keplarian elliptical orbits can only arise when the central force is based on the inverse square law.
As a corollary to this proof one can show that non Keplarian orbits can only arise if the central force is not a "pure" inverse square law.
Keplarian orbits arise under conditions such as spherical symmetry of the field and the absence of external forces.
If these conditions are not met the orbits are non Keplarian and can be derived through perturbation theory. In this case the perturbation results in additional central force terms that are smaller than the unperturbed inverse square term.
The central force is however no longer based on a simple inverse square law.
Regards
Steven