Summary: In this paper we create a theory of central measures for celestial mechanics. This theory generalizes central configurations to include continuum mass distributions. Roughly speaking, if \(V\) is the Newtonian potential generated by a unit point mass, a central measure \(\mu\) for \(V\) is a mass distribution in space characterized by the property that gravitational acceleration vector of any \(x\) in the support of \(\mu\) is a constant multiple of the vector from the mass center of \(\mu\) to \(x\). This formulation includes central configurations as special cases for which central measures are discrete. We show that concentric spherical shells can be properly arranged so that their mass distributions are central measures for \(V\). For any pair of adjacent shells, the ratio of outer and inner radii is between \((\root{3}\of{2},\infty)\) and this bound is sharp. This provides a bound for outer and inner radii of concentric spheres if the system explodes or collapses homothetically. We also extend our definition of central measure to mollified potential \(V\) generated by solid balls, and that allows us to include one-dimensional mass distributions such as circular rings. In this case, we study existence of central measures for concentric circular rings and show a one-dimensional model for which \(V\) can be properly chosen so as to make the Lebesgue measure on an interval a central measure.