Layman's glance at gravitation.

Recently watched popular science show which interestingly enough covered the idea of understanding gravity beyond the known large scale sense that we know of today (e.g., moons, planets, suns, and so forth) but covering something of the mysterious aspect upon approaching smaller and smaller distances. It seems ultimately having briefly glanced at the the classical equation something suspect if not problematic to the equation might appear...notice that like another classical force related equation gravitation is based upon the inverse square distance relation of two objects. Of course, holding that the big constant G is quite small implies for any significant enough length between two objects that sufficiently small mass regarding say the example of two objects would imply that gravitational force were very very small...hence why a cup doesn't automatically attract to my hand, or even if floating in space, the perceptively attractive force may be noticeably small in acting upon either my hand or the cup for that matter. But here is the catch, notice in the equation while say limiting mass and Gravitational constant are small, that as r < 1 approaches zero, in the equation surely gravitational force becomes more and more noticeable. Why doesn't gravitational force ultimately seem to prevail, or maybe it does? It seems in logic owing to any number of forces that do exist, other more exerting forces, may noticeably prevent in distance scaling thresholds say the two atoms from ultimately ever attracting to a zero space vanishing point...in fact these forces are so much stronger they are responsible for integrity of atomic structure and from gravity causing atomic decay?! It seems while potentially as distance between two mass objects (say atoms, quite small in mass) could attract owing to gravity, and that theoretically while classical equation neither prevents the two atoms for attracting from mass center to mass center towards a zero distance threshold, strong forces should at least prevail in so far as integral distances being maintained (through repulsive force interactions). But it seems inside the atom if a particle has any mass at all what prevents the same being true in so far classical gravitational mechanics? Hmm...at this point seems strange and odd, and something ultimately seems must be missing in so far as the classical mechanical picture here.