oblicz mase ziemi przyjmujac wartosc przyspieszena ziemskiego g=10 m s2

[latex] R_z = 6378 km = 6,4 *10^3 km = 6,4 *10^6 m g = 10 m/s^2 G = 6,67 *10 ^{-11} frac{N*m^2}{kg^2} M_z = ? g = GM_z /R_z^2 gR_z^2 = GM_z M_z = gR_z^2/G M_z = frac{10 frac{m}{s^2} * (6,4 *10^6 m)^2}{6,67 *10 ^{-11} frac{N*m^2}{kg^2} } M_z = frac{409,6 *10 ^{12} frac{m^3}{s^2} }{6,67 *10 ^{-11} frac{N*m^2}{kg^2} } M_z = 61,4 *10 ^{23} kg M_z = 6 *10 ^{24} kg[/latex]

[latex]dane:\Rz = 6,4 * 10^{6} m\g = 10 m/s^{2}\G = 6,67 * 10^{-11} Nm^{2}?kg^{2}\szukane:\Mz = ?[/latex] Rozwiązanie. [latex]Fg = G * frac{Mzm}{r^{2}}\\mg = G * frac{Mzm}{r^{2}} /:m\\g = G * frac{Mz}{r^{2}}\\G * Mz = g * r^{2}\\Mz = frac{g*r^{2}}{G} = frac{10m/s^{2} ^ (6,4 * 10^{6}m)^{2}}{6,67 * 10^{-11}Nm^{2}/kg^{2}}\\Mz = 6 * 10^{24} kg[/latex]