Answer to Question #271669 in Mechanics | Relativity for mia

Question

The earth exerts a gravitational force of 1,9 x 1020 N on the moon. The mass of the moon is 7,4 x 1022 kg and its radius is 1,74 x 106 m.

Calculate the distance between the centres of the earth and the moon.

(MEarth = 6 x 1024 kg)

Answer 1

$m_p = 6 \times 10^{24} \; kg \\ m_m = 7.4 \times 10^{22} \; kg \\ F_g = 1.9 \times 10^{20} \; N \\ G = 6.67 \times 10^{-11} \\ F_g = G \frac{m_pm_m}{r^2} \\ 1.9 \times 10^{20} = \frac{6.67 \times 10^{-11} \times 6 \times 10^{24} \times 7.4 \times 10^{22}}{r^2 } \\ 1.9 \times 10^{20} = \frac{296.148 \times 10^{35}}{r^2} \\ r^2 = \frac{296.148 \times 10^{35}}{1.9 \times 10^{20}} \\ r^2 = 155.86 \times 10^{15} \\ r = 3.94 \times 10^8 \; m$