Gravitational force on mass m outside a sphere with mass M is given by [tex]F=G\frac{mM}{r^2}[/tex], where r is the distance to the center of mass. Gravity inside the sphere surface because of the mass distribution, since only the portion of the sphere mass is inside r contributes to the attraction. If the Earth's density is constant (which it definitely is not), so given the mass inside r of [tex]M'=\frac{Mr^3}{R^3} [/tex], where R is Earth radius. Gravitational force in the earth's surface (r less than R) thus becomes: [tex]F=G\frac{mMr}{R^3}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

my question is how can we prove/shown formula [tex]M'=\frac{Mr^3}{R^3} [/tex]??

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# Homework Help: Gravitational force

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