The way to solve the problem of satellite constellation design was outlined in the 1960s on recognizing the importance of satellite coverage (continuous or periodic) function allowing interpreting the operation of different types of space systems. Due to the fact that Earth periodic coverage optimization is extremely complex, for many years the solutions of this problem have been searched for among a priori fixed constellation types successfully implemented before for continuous coverage, with continuous coverage seeming to be much easier than the periodic one. In this study, it is shown that the technological advance in satellite constellation design for periodic coverage could be achieved considering it as a unique and separate problem. The new research methodology for Earth periodic coverage aiming on creating methods for optimization arbitrary constellations, alternatively to traditional approach considering narrow classes of constellations to be analyzed, is described. The unknown before regularities in Earth periodic coverage and localization of optimal low-Earth-orbit satellite constellations parameters are presented and illustrated.