The gravitational force between the spheres is
[tex]F_{\rm g}=\dfrac{G(188\,\mathrm{kg})(0.93\,\mathrm{kg})}{(0.27\,\mathrm m)^2}\approx1.6\times10^{-7}\,\mathrm N[/tex]
where G = 6.674 x 10⁻¹¹ N m²/kg².
The weight of the lighter sphere is
[tex]F_{\rm w}=(0.93\,\mathrm{kg})g\approx9.1\,\mathrm N[/tex]
where g = 9.80 m/s².
The ratio between the two forces is then
[tex]\dfrac{F_{\rm g}}{F_{\rm w}}\approx1.8\times10^{-8}[/tex]