The masses of the earth and moon are 6 × 10^{24} kg and 7.4 × 10^{22} kg, respectively. The distance between them is 3.8 × 10^{5} km. Calculate the gravitational force of attraction between the two? Use G = 6.7 × 10^{–11} N m^{2} kg^{–2}

#### Solution

the mass of the earth, M = 6 × 10^{24} kg

the mass of the moon,

m = 7.4 × 10^{22}

the distance between the earth and the moon,

d = 3.84 × 10^{5} km

= 3.84 × 10^{5} × 1000 m

= 3.84 × 10^{8} m

G = 6.7 × 10^{-11} Nm^{2}kg^{-2}

the force exerted by the earth on the moon is

F = `("G" "M" xx "m")/"d"^2`

`= (6.7 xx 10^-11 "Nm"^2"kg"^-2 xx 6 xx 10^24 "kg" xx 7.4 xx 10^22 "kg")/(3.84 xx 10^8 "m")^2`

`= ((6.7 xx 10^-11) xx (6 xx 10^24) xx (7.4 xx 10^22))/(3.84 xx 10^8)^2`

`= (6.7 xx 6 xx 7.4)/(3.84 xx 3.84) xx 10^19`

= **2 × 10 ^{20}^{ }N.**

Thus the force exerted by the earth on the moon is 2 × 10^{20}^{ }N.