thedevelopmentofnon-lineardynamicsandchaostheory.However，wedonotyethaveadefiniteanswertothequestionofwhetherourSolarsystemisstableornot.Thisispartlyaresultofthefactthatthedefinitionoftheterm‘stability’isvaguewhenitisusedinrelationtotheproblemofplanetarymotionintheSolarsystem.Actuallyitisnoteasytogiveaclear，rigorousandphysicallymeaningfuldefinitionofthestabilityofourSolarsystem.

    Amongmanydefinitionsofstability，hereweadopttheHilldefinition(Gladman1993):actuallythisisnotadefinitionofstability，butofinstability.Wedefineasystemasbecomingunstablewhenacloseencounteroccurssomewhereinthesystem，startingfromacertaininitialconfiguration(Chambers，Wetherill&Boss1996;Ito&Tanikawa1999).AsystemisdefinedasexperiencingacloseencounterwhentwobodiesapproachoneanotherwithinanareaofthelargerHillradius.Otherwisethesystemisdefinedasbeingstable.HenceforwardwestatethatourplanetarysystemisdynamicallystableifnocloseencounterhappensduringtheageofourSolarsystem，about±5Gyr.Incidentally，thisdefinitionmaybereplacedbyoneinwhichanoccurrenceofanyorbitalcrossingbetweeneitherofapairofplanetstakesplace.Thisisbecauseweknowfromexperiencethatanorbitalcrossingisverylikelytoleadtoacloseencounterinplanetaryandprotoplanetarysystems(Yoshinaga，Kokubo&Makino1999).OfcoursethisstatementcannotbesimplyappliedtosystemswithstableorbitalresonancessuchastheNeptune–Plutosystem.

    1.2Previousstudiesandaimsofthisresearch

    Inadditiontothevaguenessoftheconceptofstability，theplanetsinourSolarsystems

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