Halliday, Resnick & Walker — Gravitation: Problem Problem_28

Assume a planet is a uniform sphere of radius \( R \) that (somehow) has a narrow radial tunnel through its center (Fig. 13.4.1). Also assume we can position an apple anywhere along the tunnel or outside the sphere. Let \( F_R \) be the magnitude of the gravitational force on the apple when it is located at the planet’s surface. How far from the surface is there a point where the magnitude is \( \frac{1}{2}F_R \) if we move the apple (a) away from the planet and (b) into the tunnel?