The quantized model of Newtonian gravity indicates that the quantum effects of gravity become apparent when particles of sufficiently small mass are in the orbit of a gravitating body of mass. In particular, the stable orbital path of particles in such conditions are shown to be polygons. The stable circular path of classical mechanics emerges when the side counts of these polygons increase to infinity, as the quantum effects of gravity vanish due to the excessive mass of the orbiting particles. In this article, it is hypothesized that the particle mass in Saturn's North Pole jet stream is such that the quantum effects of gravity have become apparent. The hexagonal shape of Saturn's jet stream is therefore used to constrain the mass of its cloud particles to 7.4E-20 (kg). This in turn constrains the dimensions of ammonia ice crystals in the clouds to less than 100 nanometers. This theory also indicates that polygons of different side counts are also feasible at different latitudes, should the local particle mass permit the quantum effects of gravity to become visible. This aspect of the theory is also consistent with the presence of faint but still visible edges of some polygons at lower latitudes.