Why do gravitational fields around point masses obey an inverse square law?

We can approach this question using the idea of flux lines. First we consider a sphere with a constant density of flux lines at its surface, as is the case for a point mass. These flux lines all point radially inwards to the surface and are evenly distributed. We know that the surface area of a sphere is proportional to its radius squared (A=4pi*r^2). So, as one moves outwards along a flux line, the area of a shell at that distance increases with the power 2. The idea of flux lines is that the strength of a field at any point is proportional to the density of the flux lines. Since the area over which the field lines are distributed increases with the power 2, the field lines per unit area decreases with the power 2 - thus the field obeys an inverse square law.