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# Derive the formula for the universal law of gravitation.

**Newton's law of universal gravitation:**

Newton's law of gravitation, states that every particle of matter in the universe attracts every other particle in the universe with a force varying directly as the product of their masses and inversely as the square of the distance between the particles.

$F\propto m_1.m_2$

And $F\propto \frac{1}{r^2}$

Therefore, $F\propto\frac{m_1.m_2}{r^2}$

Or $F=G\frac{m_1.m_2}{r^2}$, Where $G$ is constant whose value is $6.67\times10^{-11}$.

Let $m$ be the mass of an object and $M$ be the mass of the earth and $g$ be the gravity.

Then weight$=mg$

$mg=G\frac{mM}{r^2}

Or $g=G\frac{M}{r^2}$.

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