The sun's mass is about $$3.2$$ x $$105$$ times the earth's mass. The sun is about $$400$$ times as far from the earth as the earth is from the moon. Assume that the $$sun-moon$$ distance is constant and equal to $$sun-earth$$ distance. The ratio of the magnitudes of the gravitational pull of the sun on the moon Fms and of the earth on the moon Fem will be $$FmsFme=$$'n'. The value of n is $$____________$$

Question

The sun's mass is about $$3.2$$ x $$105$$ times the earth's mass. The sun is about $$400$$ times as far from the earth as the earth is from the moon. Assume that the $$sun-moon$$ distance is constant and equal to $$sun-earth$$ distance. The ratio of the magnitudes of the gravitational pull of the sun on the moon Fms and of the earth on the moon Fem will be $$FmsFme=$$'n'. The value of n is $$____________$$

Infinity Learn · Accepted Answer

Let m $$=$$ moon's mass, Ms $$=$$ sun's massMe $$=$$ earth's massrms $$=$$ the $$centre-to-centre$$ distance from the sun to the moonrme $$=$$ the $$centre-to-centre$$ distance from the earth to the moonFms $$=$$ gravitational force exerted on the moon by the sunFme $$=$$ gravitational force exerted on the moon by the earthThen $$FmsFme=MSrme2Merms2Putting$$ the values $$FmsFme=MSMermerms2$$                                      $$=3.2$$×$$10514002=3216=2$$

Gravitational force and laws

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