Question

How does the gravitational field strength at the surface of a planet compare to the gravitational field strength 1000 m away from the surface?

Answer 1

The gravitation field strength is given as,

`\begin{gathered} g=(GM)/(r^2) \\ g\propto(1)/(r^2) \end{gathered}`

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,

`r^(\prime)=r+1000\text{ m}`

From the above equation, it is clear that r'>r.

The new gravitational field strength 1000 m away from the surface is,

`\begin{gathered} g^(\prime)=\frac{GM}{(r+1000\text{ m})^2} \\ g^(\prime)=(GM)/(r^(\prime)^2) \\ g^(\prime)\propto(1)/(r^(\prime2)) \end{gathered}`

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.