- A SKEPTIC's GUIDE - A SKEPTIC's GUIDE 
For instance, suppose that one day we assemble all the matter in the Solar System and build one gigantic spherical shell out of it. We arrange its radius so that the force of gravity at its surface (standing on the outside) is "Earth normal," i.e. 9.81 N/kg or g = 9.81 m/s2. This is all simple so far, and GAUSS' LAW tells us that as long as we are outside of the spherical shell enclosing the whole spherically symmetric mass distribution, the gravitational field we will see is indistinguishable from that produced by the entire mass concentrated at a point at the centre. The amazing prediction is that if we merely step inside the shell, there is still spherical symmetry, but the spherical surface touching our new radius does not enclose any mass and therefore sees no gravitational field at all! This is actually correct: inside the sphere we are weightless, and travel opportunities to other parts of the shell (across the inside) become quite interesting. There are many more examples of entertaining properties of spherically symmetric charge or mass distributions, all of which you can easily deduce from similar arguments to dazzle your friends. Let us now ask, however, if any less symmetric situations can also be treated easily with this technique.