Finding general solutions to a mechanical system is often far too much to ask. Instead, we look for more tractable, special solutions, such as the equilibria. If the system is symmetric with respect to a group action then we can also look for the relative equilibria: these are solutions contained to a group orbit. Famous examples include the circular solutions of Euler and Lagrange in the 3-body problem. In this talk I will present a new formalism for finding relative equilibria by defining a 'web structure' on shape space, and demonstrate this by classifying the relative equilibria for the spherical 3-body problem.