5.
[tex]dane:\\M_{z} = 6\cdot10^{24} \ kg\\M_{k} = 7,35\cdot10^{22} \ kg\\r = 384 \ 000 \ m = 3,84\cdot10^{8} \ m\\G = 6,67\cdot10^{-11}\frac{Nm^{2}}{kg^{2}}\\szukane:\\F_{g} = ?\\\\F_{g} = g\cdot\frac{M_{z}\cdot M_{k}}{r^{2}}\\\\F_{g} = 6,67\cdot10^{-11}\frac{Nm^{2}}{kg^{2}}\cdot\frac{6\cdot10^{24} \ kg\cdot7,35\cdot10^{22} \ kg}{(3,84\cdot10^{8} \ m)^{2}}\\\\F_{g}\approx19,95\cdot10^{19} \ N \approx2\cdot10^{20} \ N[/tex]
6.
Stan nieważkości:
[tex]F_{g} = F_{b}\\\\mgh = \frac{mv^{2}}{R} \ \ /\cdot\frac{R}{m}\\\\v^{2} = gR\\\\v = \sqrt{gR}\\\\R = 64\cdot10^{5} \ m\\g = 10\frac{m}{s^{2}}\\\\v = \sqrt{10\frac{m}{s^{2}}\cdot64\cdot10^{5} \ m} =8\cdot10^{3}\frac{m}{s} = 8\frac{km}{s}[/tex]
Odp. Ziemia musiałaby się kręcić z prędkośćią v = 8 km/s.
