Shell Theorem and Gravity Inside a Planet

Picture a point anywhere inside a hollow spherical shell of rock. Draw a thin double cone from that point out to the shell in both directions. The far wall of the shell it hits is bigger in area but farther away, the near wall is smaller but closer. Those two effects trade off exactly: more distant mass but more of it, less nearby mass but less distance to travel. The inverse-square law and the geometry of the cone cancel perfectly, so the pulls from both patches balance. Add up every such pair of patches over the whole shell and the net force at that interior point is zero, no matter where inside the shell the point sits.

This is why, once you tunnel into a uniform solid sphere like a simplified Earth, only the mass strictly closer to the center than you matters. Treat the planet as a stack of nested shells. Every shell farther out than you contributes nothing, by the result above. Every shell inside your radius acts as if it were a point mass at the center. So the gravity you feel only depends on the mass enclosed within radius r, not the mass beyond it.

For a uniform sphere, enclosed mass scales with r³ while the gravitational pull also divides by r², so the two effects combine to make g scale linearly with r: g(r) = g_surface x (r/R). This is the natural follow-up to treating planets as point masses from a distance: outside a uniform sphere gravity obeys the same inverse-square law as a point mass, but inside, the rules change completely.