Question

Calculate the force of gravity that Earth (mass 7.4 x 1022 kg) exert on each other. The average Earth-Moon distance is 3.8 x 108 m.

Answer 1

Gravitational force for Earth and Moon system:

$F_G = \frac{GMm}{R^2}$

G = gravitational constant

M = mass of Earth

m = mass of Moon

R = distance between them

$G = 6.674 \times 10^{-11} \\ M = 5.97 \times 10^{24} \;kg \\ m = 7.36 \times 10^{22} \;kg \\ R = 3.84 \times 10^8 \;m \\ F_G = \frac{6.674 \times 10^{-11}\times 5.97 \times 10^{24} \times 7.36 \times 10^{22}}{(3.84 \times 10^8)^2} \\ F_G = 1.986 \times 10^{20} \;N$