No stable gravitationally or electrostatically bound atoms in n-space for n > 3

It is demonstrated in general that stable gravitational or electrostatic orbits are not possible for spatial dimensions n >=4, and in particular atoms cannot be bound by energy constraints in higher dimensions. Furthermore, angular momentum cannot be quantized in the usual manner in 4-space, leading to interesting constraints on mass. Thus Kaluza Klein and string theory may be impacted since it appears that the unfurled higher dimensions of string theory will not permit the existence of energetically stable atoms. This also has bearing on the search for deviations from 1/r2 of the gravitational force at sub-millimeter distances. The results here imply that such a deviation must occur at less than ~ 10-8 cm, since atoms would be unstable if the curled up dimensions were larger than this.