How do you derive g=(Gm)/r^2 and V=-(Gm)/r?

Jan 28, 2018

Here you go....

Explanation:

Weight of an object on Earth = Gravitational force exerted on an object by the Earth.
Let us consider a body having mass "m".
$m g = G \cdot \frac{m M}{R} ^ 2$
where,
g=acceleration due to gravity,
G=Gravitational constant,
M=Mass of the Earth,
mass$\left(m\right) \cdot$gravitational acceleration$\left(g\right)$
Cancel out the $m$ on both sides to get:
$g = G \cdot \frac{M}{R} ^ 2 = \frac{G M}{R} ^ 2$