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Atoms And Molecules

Question
CBSEENSC9006099

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

Solution

Mass of the earth, M = 6 x 1024 kg
Mass of the sun,   Ms = 2 x 1030 kg
Mass of the moon, Mm = 7.3 x 1022 kg
Distance of Earth from the sun, rs = 1.5 x 1011 m
Distance of Earth from the moon, rm = 3.84 x 108 m
Gravitational force exerted by the sun on the earth,
                        straight F subscript straight s space equals space straight G fraction numerator straight M subscript straight s straight M over denominator straight r subscript straight s superscript 2 end fraction 
Gravitational space force space exerted space by space the space moon space on space the space earth comma
straight F subscript straight m space equals space straight G fraction numerator straight M subscript straight m straight M over denominator straight r subscript straight m superscript 2 end fraction
therefore space space space space straight F subscript straight s over straight F subscript straight m space equals space fraction numerator GM subscript straight S straight M over denominator straight r subscript straight s superscript 2 end fraction cross times fraction numerator straight r subscript straight m superscript 2 over denominator GM subscript straight m straight M end fraction space equals space straight M subscript straight s over straight M subscript straight m cross times open parentheses straight r subscript straight m over straight r subscript straight s close parentheses squared
space space space space space equals space fraction numerator 2 space cross times 10 to the power of 30 over denominator 7.3 space cross times space 10 to the power of 22 end fraction cross times open parentheses fraction numerator 3.84 space cross times space 10 to the power of 8 over denominator 1.5 space cross times space 10 to the power of 11 end fraction close parentheses space equals space 179.55

Thus the sun exerts force, about 180 times the force exerted by the moon on the earth.