Course Physics1

The acceleration gravity g is calculated by using the previous equation (the gravitational force). If M represents the mass of the earth and m located at a distance 𝑟 from the center of the earth

$\overrightarrow{F_{M\to m}}=G\frac{\mathit{Mm}}{r^2}\vec{u}=m\vec{g}$

With

$\vec{g}=G\frac{M}{r^2}\vec{u}$

This vector represents the gravitational field of the earth it is always oriented towards the center of the earth.

$\overrightarrow{F_{M\to m}}=m\vec{g}$

Represents the weight of the body 𝑚, such that $\vec{P}=m\vec{g}$

On the surface of the earth (r = R) R is the ray of the earth (R = 6371 Km) and M is the mass of the earth $(M=5.9742\mathrm{.}{10}^{24}\mathit{kg})$

$g=G\frac{M}{r^2}=\frac{6.67384\mathrm{.}{10}^{-11}5.9742\mathrm{.}{10}^{24}}{{(6.371\mathrm{.}{10}^6)}^2}=9.80m\mathrm{.}{s}^{-2}$

For a body on earth the constant g is $g=9.80m\mathrm{.}{s}^{-2}$