As shown in the figure, a particle of mass $$m = 10^{-10}\ \text{kg}$$ moving with velocity $$v_0 = 10^5\ \text{m}/\text{s}$$ approaches a stationary fixed target with impact parameter $$b$$ from a large distance. If the fixed rigid target has a core with repulsive central force $$F(r)=K/r^3$$, where constant $$K>0$$, and the particle scatters elastically, the closest distance of approach, if numerically $$K=b^2$$, is