Gravity beetween planet Earth and another object

Question

The Earth is pulling on an object with gravity given by the formula $F=\frac{k}{r^2}$, $r$ is the distance from the object to the center of the Earth and $k$ is a konstant. If the object is such that $F$ is reduced by 1 $\frac {Newton}{kilometre}$ when $r=4000$ kilometer, then by which rate is $F$ reduced when $r=8000$ kilometer?

Answer 1

You are given the reducing rate of $F$ at $r=4000$ km: $$\frac{dF}{dr}\bigg|_{r=4000} = -1$$

If you differentiate the given formula $F=\frac{k}{r^2}$ and substitute the above given information, you will be able to solve konstant $k$. Then similarly, solve for the rate which $F$ is reduced when $r=8000$ km.