Rz = 6,37 *10⁶ m h = 6,37 *10⁶ m R = Rz + h M = 6 *10²⁴ kg [latex] frac{mV_S^2}{R} = frac{GMm}{R^2} [/latex] [latex]V_S^2 = frac{GM}{R_Z + h} [/latex] [latex]V_S = sqrt{ frac{GM}{R_Z + h } } [/latex] [latex]V_S= sqrt{ frac{6,67 *10 ^{-11} frac{N*m^2}{kg^2}*6 *10 ^{24}kg }{6,7 *10^6 m + 6,7 *10^6 m} } = sqrt{ frac{40,02 *10 ^{13} frac{N*m^2}{kg} }{13,4 *10^6 m} } = 5,47 *10^3 frac{m}{s} [/latex] [latex]V_S = frac{2 pi r}{T} [/latex] [latex]V_S^2 = frac{4 pi ^2R^2}{T^2} [/latex] [latex] frac{4 pi ^2R^2}{T^2} = frac{GM}{R} [/latex] [latex]T^2 = frac{4 pi ^2 *R^3}{GM} / sqrt{} [/latex] [latex]GM = gR^2[/latex] [latex]T^2 = frac{4 pi ^2R^3}{gR^2} = frac{4 pi ^2 (2R)^3}{gR^2} = frac{32 pi ^2R^3}{gR^2} = 32 pi ^2 frac{R}{g} [/latex] [latex]T^2 = 32 * (3,14)^2 * frac{6,37 *10^6 m}{10 frac{m}{s^2} } = 200,98 *10^6 s^2 T = 14,2 *10^3s[/latex]
