[tex]T=6h=21600s\\Fg=Fd\\\frac{GMm}{R^{2} } =m\omega^{2} R\\\frac{GM}{R^{2} } =\omega ^{2}R \\\frac{GM}{R^{2} } =(\frac{2\pi }{T} )^{2} *R\\\frac{6*10^{24}*6.67*10^{-11} }{R^{2} } =(\frac{2*3.14}{21600} )^{2} *R\\\frac{6*10^{24}*6.67*10^{-11} }{R^{2} } =8.45*10^{-8} *R\\4*10^{14} =8.45*10^{-8} *R^{3} \\R^{3} =4.73*10^{21} \\R=1.68*10^{7} m\\r=R-R_{Z} =1.68*10^{7} -6.4*10^{6} =1.04*10^{7} m[/tex]
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[tex]T=6h=21600s\\Fg=Fd\\\frac{GMm}{R^{2} } =m\omega^{2} R\\\frac{GM}{R^{2} } =\omega ^{2}R \\\frac{GM}{R^{2} } =(\frac{2\pi }{T} )^{2} *R\\\frac{6*10^{24}*6.67*10^{-11} }{R^{2} } =(\frac{2*3.14}{21600} )^{2} *R\\\frac{6*10^{24}*6.67*10^{-11} }{R^{2} } =8.45*10^{-8} *R\\4*10^{14} =8.45*10^{-8} *R^{3} \\R^{3} =4.73*10^{21} \\R=1.68*10^{7} m\\r=R-R_{Z} =1.68*10^{7} -6.4*10^{6} =1.04*10^{7} m[/tex]