PILNEEEE BARDZO NA TERAZ FIZYKA 2 ZADANIA

[latex]1.\dane:\r = 10 m\F = 1*10^{-3} N\G = 6,67*10^{-11}frac{Nm^{2}}{kg^{2}}\szukane:\m_1 = m2 = m = ?[/latex] [latex]F = G*frac{m_1*m_2}{r^{2}}\\m_1 = m_2 = m\\F = G*frac{m^{2}}{r^{2}} |*r^{2}\\G*m^{2}= F*r^{2} /:G\\m^{2} = frac{F*r{2}}{G}\\m = sqrt{frac{F*r^{2}}{G}} = sqrt{frac{1*10^{-3}*10^{2}}{6,67*10^{-11}}} kg =sqrt{14,9925*10^{8}} kg \\m = 3,87*10^{4} kg[/latex] [latex]4.\Z prawa Keplera:\\frac{mv^{2}}{r} = Gfrac{Mm}{r^{2}} /:m\\frac{v^{2}}{r} = G*frac{M}{r^{2}}\\G*M*r = v^{2}*r^{2} /:G*r\\M = frac{v^{2}*r}{G}\\v = frac{2 pi r}{T}\\M = frac{(frac{2 pi r}{T})^{2}*r}{G}[/latex] [latex]M = frac{4*pi ^{2}*r^{3}}{G*T^{2}}[/latex] [latex]Odp. B[/latex]