[tex]V=\frac{4\pi R^3}{3} \\\rho=\frac{m}{V} =\frac{m}{\frac{4\pi R^3}{3}}=\frac{3m}{4\pi R^3} \\g_o=k\frac{m}{R^2}=>m=\frac{R^2g_o}{k} \\\rho=\frac{3m}{4\pi R^3}=\frac{3\frac{R^2g_o}{k}}{4\pi R^3}=\frac{3g_o}{4\pi kR}=>k=\frac{3g_o}{4\rho\pi R}=\frac{3*9,8}{4*5,5*10^3*3,14*6,4*10^6}= \frac{29,4}{478,72*10^9}=0,061*10^{-9}=6,1*10^{-11} Nm^2/kg^2 \\k=6,1*10^{-11} Nm^2/kg^2[/tex]
