Question

The masses of the earth and moon are 6 × 10²⁴ kg and 7.4 × 10²² kg, respectively. The distance between them is 3.8 × 10⁵ km. Calculate the gravitational force of attraction between the two?
Use G = 6.7 × 10^–11 N m² kg^–2

Answer 1

the mass of the earth, M = 6 × 10²⁴ kg

the mass of the moon,

m = 7.4 × 10²² 

the distance between the earth and the moon,

d = 3.84 × 10⁵ km

= 3.84 × 10⁵ × 1000 m

= 3.84 × 10⁸ m

G = 6.7 × 10^-11 Nm²kg^-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 × 10²⁰ N.

Thus the force exerted by the earth on the moon is 2 × 10²⁰ N.