Deflection and spin in a distant sphere encounter ($\delta Y_{\max }=27a^2/(32b),\Delta \vartheta =-9\pi a^2/(32b^2)$)

In a planar force-driven encounter with a fixed equal sphere and positive impact parameter $b\gg a$, the mobility correction from a fixed distant sphere gives $Y-b=27a^{2}b/[32(X^2+b^2)]+O(a^4/b^3)$. The moving sphere reaches maximum deflection $27a^2/(32b)$ and rotates clockwise through $9\pi a^2/(32b^2)$ to leading order. The spin is obtained by integrating half the reflected Stokeslet vorticity, as prescribed by Faxén rotation law. These numerical formulas require a distant encounter.