[latex]5.\F = G * frac{m_1*m_2}{r^{2}}\\m_1 =M_{z}\m_2 = m_{K_}}\\F =G* frac{M_{z}M_{K}}{r^{2}}\\F_1 = G*frac{9M_{Z}M_{K}}{(3r)^{2}} = G*frac{M_{Z}M_K}{r^{2}}\\F_1 = F[/latex] Odp. Siła przyciągania nie zmieniłaby się. [latex]6.\dane:\m = 1 t = 1000 kg\F = 9 kN = 9000 N\M_{z} = 5,98*10^{24} kg\G = 6,67*10^{-11} frac{Nm^{2}}{kg^{2}}\szukane:\R = ?[/latex] [latex]F = G*frac{M_{z}m}{R^{2}} |*R^{2}\\F*R^{2} = G*M_{z}m /:F\\R^{2} = G*frac{M_{z}m}{F}\\R = sqrt{G*frac{M_{z}m}{F}} = sqrt{6,67*10^{-11}*frac{5,98*10^{24}*1000}{9000}}= sqrt{4,43*10^{13}} m\\=sqrt{44,3*10^{12}} = 6,6558245*10^{6} m\\R = 6655,8245 km[/latex] [latex]10.\dane:\M_{s} = 95M_{z}\R_{s} = 9,5R_{z}\v_{1z} = 7,9frac{km}{s}\szukane:\v_{s}= ?[/latex] [latex]v_{1z} = sqrt{G*frac{M_{z}}{R_{z}}} = 7,9frac{km}{s}\\v_{s} = sqrt{G*frac{M_{s}}{R_{s}}} = sqrt{G*frac{95M_{z}}{9,5R_{z}}} = sqrt{frac{95}{9,5}}*v_{1z} = sqrt{10}*7,9frac{km}{s}=24,98frac{km}{s}\\v_{s} approx 25frac{km}{s}\\Odp. d)[/latex] [latex]11.\dane:\R_{j} = 5,202 AU\R_{z} = 1 AU\T_{z} = 1 rok\szukane:\T_{j} = ?[/latex] [latex]frac{T_{z}^{2}}{R_{z}^{3}} = frac{T_{j}^{2}}{R_{j}^{3}}\\T_{j}^{2}*R_{z}^{3} = T_{z}^{2}*R_{j}^{3}} /:R_{z}^{3}\\T_{j}^{2} = T_{z}^{2}*frac{R_{j}^{3}}{R_{z}^{3}}\\T_{j} = sqrt{T_{z}^{2}*frac{R_{j}^{3}}{R_{z}^{3}}} = sqrt{1^{2}*frac{5,202^{3}}{1^{3}}}=sqrt{140,77} lat\\T_{j} = 11,86 lat\\Odp. c)[/latex]
