Question

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

Answer 1

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".
`mg=G*(mM)/R^2`
where,
g=acceleration due to gravity,
G=Gravitational constant,
M=Mass of the Earth,
and R=radius of the Earth.
Weight of the body (on Earth)=
mass`(m)*`gravitational acceleration`(g)`
Cancel out the `m` on both sides to get:
`g=G*M/R^2=(GM)/R^2`