Question

How much greater is the Sun’s gravitational force on Jupiter compared with the Sun’s gravitational force on the Earth? Use the following information: mass of the Sun = 2.0 x 1030 kg, mass of Jupiter = 1.9 x 1027 kg, mass of Earth = 6.0 x 1024 kg; G = 6.67 x 10-11 m3kg-1s-2; distance between Sun and Earth = 1.5 x 1011 m; distance between Sun and Jupiter = 7.8 x 1011 m. (Round your answer to one decimal place).

Answer 1

here we have given that

mass of the Sun = 2.0 x 10^30 kg,

mass of Jupiter = 1.9 x 10^27 kg,

mass of Earth = 6.0 x 10^24 kg;

G = 6.67 x 10^-11 m^3kg-1s-2;

distance between Sun and Earth = 1.5 x 10^11 m;

distance between Sun and Jupiter = 7.8 x 10^11 m.

now we have the gravitational force formula as here

F = Gm1m2/r2

so that for Jupiter

Fj = G * 1.9 x 10^27 kg * 2.0 x 10^30 kg/( 7.8 x 10^11 m.) ^2

AND for the earth here

Fe =  G * 6.0 x 10^24 kg * 2.0 x 10^30 kg/(1.5 x 10^11 m.) ^2'

so that when we take the ratio of there two forces here we will get

Fj/Fe = ( G * 1.9 x 10^27 kg * 2.0 x 10^30 kg/( 7.8 x 10^11 m.) ^2)/ (G * 6.0 x 10^24 kg * 2.0 x 10^30 kg/(1.5 x 10^11 m.) ^2)

Fj/Fe = 11.71104

hence here

Fj = Fe * 11.71104

which means  the Sun’s gravitational force on Jupiter is 11.71104 times the Sun’s gravitational force on the Earth