J.J. Sylvester's two convex sets theorem and G.-L. Lesage's theory of gravity

Given two convex sets $K_1$ and $K_2$ in the plane, J.J. Sylvester computes the measure $m(K_1,K_2)$ of the family of straight lines which meet both $K_1$ and $K_2$. As their distance $d=d(K_1,K_2)$ increases to infinity $$displaystyle{m(K_1,K_2)=h(K_1)h(K_2)/d+O(1/d^2)}$$ for some $h(K_1)ge 0$ and $h(K_2)ge 0$, suggesting Newton's law of attraction in the plane. We discuss the analogy in the spirit of G. -L. Lesage.