The gravitation field strength is given as,
[tex]\begin{gathered} g=\frac{GM}{r^2} \\ g\propto\frac{1}{r^2} \end{gathered}[/tex]Here, G is the universal gravitational constant, M is the mass of the planet, and r is the separation between the center of the planet and the object.
Now, when the object is moved 1000 m away from the surface, so the new separation between the center of the planet and the object is,
[tex]r^{\prime}=r+1000\text{ m}[/tex]From the above equation, it is clear that r'>r.
The new gravitational field strength 1000 m away from the surface is,
[tex]\begin{gathered} g^{\prime}=\frac{GM}{(r+1000\text{ m})^2} \\ g^{\prime}=\frac{GM}{r^{\prime}^2} \\ g^{\prime}\propto\frac{1}{r^{\prime2}} \end{gathered}[/tex]Since, r'>r. Hence, g>g'. Therefore, the gravitational field strength of the planet is smaller at a distance of 1000 m away from the surface, than the gravitational field strength at the surface.
