Assume a planet is a uniform sphere of radius R that (somehow) has a narrow radial tunnel through its center. Also assume we can position an apple anywhere along the tunnel or outside the sphere. Let FR be the magnitude of the gravitational force on the apple when it is located at the planet's surface. How far from the surface (in terms of R) is there a point where the magnitude of the gravitational force on the apple is 1/7FR if we move the apple (a) away from the planet and (b) into the tunnel?

Question

Assume a planet is a uniform sphere of radius R that (somehow) has a narrow radial tunnel through its center. Also assume we can position an apple anywhere along the tunnel or outside the sphere. Let FR  be the magnitude of the gravitational force on the apple when it is located at the planet's surface. How far from the surface (in terms of R) is there a point where the magnitude of the gravitational force on the apple is 1/7FR if we move the apple (a) away from the planet and (b) into the tunnel?

I have no idea how to start this question please help!

bobpursley · Answer

If the planet is uniform density, then the net gravity force is proportional to the volume enclosed by the radius.

1/7 (4/3 PI R^3)=4/3 PI r^3
so r/R= cuberoot 1/7

how far from the surface? H=R-r

H= R(1-cubroot 1/7) check that.