I have one question:
Imagine a stone which is falling from space (from 500km). How long would it take to fall on earth? (I know that that kind of question has already been asked here but I want to know how to solve this using this way) So here's what I did:

According to Newton's universal law of gravity Force is:

$$
F=G\frac{Mm}{(r+x)^2}
$$
where $G$ is universal gravity constant, $r$ is an earth's radius and $x$ is distance from earth ($x_0$ is 500km)

and acceleration is:

$$
g(x)=\frac{GM}{(r+x)^2}\approx \frac{4\times10^{14}}{(64\times10^5+x)^2}