第76章 对火星轨道变化问题的最后解释（4/12）
esultsofsixlong-termnumericalintegrationsonallninelaaryorbits，coveringasanofseveral109yr，andoftootherintegrationscoveringasanof±51010yr.hetotalelasedtimeforallintegrationsismorethan5yr，usingseveraldedicatedsandorkstations.neofthefundamentalconclusionsofourlong-termintegrationsisthatolarsystemlaarymotionseemstobestableintermsoftheillstabilitymentionedabove，atleastoveratime-sanof±4yr.ctually，inournumericalintegrationsthesystemasfarmorestablethanhatisdefinedbytheillstabilitycriterion:notonlydidnocloseencounterhaenduringtheintegrationeriod，butalsoallthelaaryorbitalelementshavebeenconfinedinanarroregionbothintimeandfrequencydomain，thoughlaarymotionsarestochastic.incetheuroseofthisaeristoexhibitandovervietheresultsofourlong-termnumericalintegrations，eshotyicalexamlefiguresasevidenceoftheverylong-termstabilityofolarsystemlaarymotion.orreadershohavemoresecificanddeeerinterestsinournumericalresults，ehaverearedaebage(aess)，hereeshoraorbitalelements，theirlo-assfilteredresults，variationofelaunayelementsandangularmomentumdeficit，andresultsofoursimletime–frequencyanalysisonallofourintegrations.
nection2ebrieflyexlainourdynamicalmodel，numericalmethodandinitialconditionsusedinourintegrations.ection3isdevotedtoadescritionofthequickresultsofthenumericalintegrations.erylong-termstabilityofolarsystemlaarymotionisaarentbothinlaaryositionsandorbitalelements.roughestimationofnumericalerrorsisalsogiven.ection4goesontoadiscussionofthelongest-termvariationoflaaryorbitsusingalo-assfilterandincludesadiscussionofangularmomentumdeficit.nection5，eresentasetofnumericalintegrationsfortheouterfive
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