For μ=0, we study (generating) family i of symmetric periodic solutions of the plane circular restricted three-body problem. This family begins with the direct circular orbits of infinitely small radius around the primary P₁ of greater mass. We demonstrate how the generating family i is formed from the parts of families Id, E_N^±, B₁, and С_k,k+1. On the initial part of the generating family i, we computed (and plotted) all critical orbits, the period and both traces (the plane and the vertical ones), and characteristics of the family in various coordinate systems. It turned out that characteristics of the family have a rather complicated structure. We found cyclic regularities in this structure as well as in the structure of the whole family.

Mathematical problems and theory of numerical methods