Libration　points　are　the　five　equilibrium　solutions　in　the　circular　restricted　three-body　problem　(i.e.　CRTBP)　,　and　there　are　many　periodic　orbits　around　them.　Studies　on　the　probes　moving　around　orbits　in　the　vicinity　of　the　libration　points　have　theoretical　significance　and　important　applications　for　deep　space　explorations.　From　the　view　of　modal　motion,　the　periodic　orbits　are　analyzed,　and　the　polynomial　series　are　used　to　derive　the　approximate　relationships　in　different　directions　during　periodic　motions,　which　provides　a　new　point　of　view　to　investigate　the　dynamics　and　analyze　the　overall　characteristics　of　the　whole　system　with　general　rules.　Meanwhile　,　it　also　provides　the　theoretical　basis　for　analyzing　the　orbits　characteristics　and　the　references　of　the　spacecraft　orbits　under　the　actual　dynamic　models.　The　methodology　of　deriving　topological　relationships　has　the　potential　to　be　extended　to　Elliptical　R3BP　in　three　dimensional　cases　or　orbits　around　the　collinear　libration　points.　©　2018　Journal　of　Dynamics　and　Control.　All　rights　reserved.