For　the　circular　restricted　three-body　problem　(CR3BP)　in　the　inertial　frame,　we　interpret　the　fact　that　there　is　no　non-trivial　2　pi-periodic　solution　of　the　problem＇s　homogeneous　system.　Furthermore,　based　on　Reissig＇s　theory,　the　existence　of　periodic　solutions　for　the　CR3BP　is　proved　rigorously　by　using　the　above　fact　in　conjunction　with　an　a　priori　estimate.　It　is　significant　that　the　existence　of　periodic　solutions　of　the　CR3BP　is　mainly　influenced　by　factors　such　as　initial　values,　primary　masses,　and　selection　of　the　problem＇s　control　function.　In　addition,　it　is　notable　that　the　analytic　proof　of　Poincare＇s　first　class　solutions　is　addressed　for　all　values　of　the　mass　parameter　in　the　interval　(0,　1),　the　value　of　which　must　be　sufficiently　small　according　to　previously　published　literature.