Hi I am given two models for the gravity of earth, the first is with $x_3$ normal to the earth and is
$m\ddot{x}(t)=-mg(0,0,1)^T$
the other is with $x$ a distance vector from the centre of the earth and is
$m\ddot{x}=-GmM\frac{x}{|x|^3}$ with G being the gravitational constant.
I am asked to derive the first from the second by a formal expansion in $\frac{h_0}{R}$ and then show the expected accuracy is of the order $O(h_0/R)$
I have no idea how to start and have been looking at it for a while. I'm not even sure what it means by formally expanding by that. Any help would be appreciated.