Compare the gravitational forces exerted by the sun and the moon on the earth. Which exerts a greater force and by how many times?

Explanation

Mass of earth `M_(e)=6xx10^(24)kg`
Mass of moon `M_(m)=7.3xx10^(22)kg`
Mas of sun `M_(s)=2xx10^(30)kg`
Distance of moon from the earth `r_(m)=384000k m`
`=384000xx1000m`
`=3.84xx10^(8)m`
Distance of sun from the earth `r_(s)=1.5xx10^(11)m`
Let gravitational fore exerted by the moon on the earth `=F_(m)`
`:.` Using `F=(Gm_(1)m_(2))/(r^(2))` we have
`Fs=(GM_(e)M_(s))/(r_(s)^(2))`.........1
And `F_(m)=(GM_(e)M_(m))/(r_(m)^(2))` .......2
Dividing 1 by 2 we get
`(F_(s))/(F_(m))=(GM_(e)M_(s))/(rs^(2))xx(r_(m)^(2))/(GM_(e)M_(m))`
or `(F_(s))/(F_(m))=(M_(s))/(M_(m))((r_(m))/(r_(s)))^(2)`
`=(2xx10^(30))/(7.3xx10^(22))xx((3.84xx10^(8))/(1.5xx10^(11)))^(2)`
`=(2xx3.84xx3.84)/(7.3xx1.5xx1.5)xx10^(8)xx10^(-6)`
`=1.7955xx10^(2)`
`=179.55=180`
i.e. `(F_(s))/(F_(m))=180`
or `F_(s)=180F_(m)`
`:.` The sun exerts greater force by 180 times.