pargthevariationsofenergyandangularontuofthenerfourplasandallneplas，itisapparentthattheaplitudesofthoseofthenerplasareuchsallerthanthoseofallneplas:theaplitudesoftheouterfiveplasareuchlarrthanthoseofthenerplasthisdoesnotanthatthenerterrestrialplaarysubsysteisorestablethantheouterone:thisissiplyaresultoftherelativesallnessoftheassesofthefourterrestrialplasparedwiththoseoftheouterjovianplasanotherthgwenoticeisthatthenerplaarysubsysteaybeeunstableorerapidlythantheouteronebecaeofitsshorterorbitalti-scalesthiscanbeseenthepanelsdenotedasner4fig7wherethelonr-periodicandirregularoscillationsareoreapparentthanthepanelsdenotedastotal9actually，thefctuationsthener4panelsaretoalarextentasaresultoftheorbitalvariationofthercuryhowever，wecannotneglectthentributionfrootherterrestrialplas，aswewillseesubseentsections

44long-teruplgofseveralneighbourgplapairs

letseedividualvariationsofplaaryorbitalenergyandangularontuexpressedbythelow-passfiltereddelaunayelentsfigs10and11showlong-terevotionoftheorbitalenergyofeachplaandtheangularontun+1andn&;2tegrationswenoticethatplasforapparentpairstersoforbitalenergyandangularontuex插nparticular，venandearthakeatypicalpairthefigures，theyshownegativerrelationsex插nofenergyandpositiverrelationsex插nofangularontuthenegativerrelationex插noforbitalenergyansthattheoplasforacloseddynaicalsystetersoftheorbitalenergythepositiverrelationex插nofangularontuansthattheoplasaresiultaneolyundercertalong-terperturbationscandidatesforperturbersarejupiterandsaturnalfig11，wecanseethatarsshowsapositiverrelationtheangularontuvariationtotheven–earthsystercuryexhibitscertanegativerrelationstheangularontuverstheven–earthsyste，whichseestobeareactioncaedbythenservationofangularontutheterrestrialplaarysubsyste

itisnotclearattheontwhytheven–earthpairexhibitsanegativerrelationenergyex插nandapositiverrelationangularontuex插nweaypossiblyexpnthisthroughobservgtheneralfactthattherearenoseculartersplaaryseiajoraxesuptosend-orderperturbationtheories（cfbrouwer≈ap;clence1961;boaletti≈ap;pucao1998）thisansthattheplaaryorbitalenergy（whichisdirectlyrelatedtotheseiajoraxisa）ightbeuchlessaffectedbyperturbgplasthanistheangularontuex插n（whichrelatestoe）hence，theeentricitiesofvenandearthcanbedisturbedeasilybyjupiterandsaturn，whichresultsapositiverrelationtheangularontuex插nontheotherhand，theseiajoraxesofvenandeartharelesslikelytobedisturbedbythejovianplasththeenergyex插naybeliitedonlywiththeven–earthpair，whichresultsanegativerrelationtheex插noforbitalenergythepair

asfortheouterjovianplaarysubsyste，jupiter–saturnanduran–neptuneseetoakedynaicalpairshowever，thestrengthoftheiruplgisnotasstrongparedwiththatoftheven–earthpair

5&psn;5&tis;1010-yrtegrationsofouterplaaryorbits

scethejovianplaaryassesareuchlarrthantheterrestrialplaaryasses，wetreatthejovianplaarysysteasandependentplaarysystetersofthestudyofitsdynaicalstabilityhence，weaddedaupleoftrialtegrationsthatspan&psn;5&tis;1010yr，cdgonlytheouterfiveplas（thefourjovianplaspspto）theresultsexhibittherigorostabilityoftheouterplaarysysteoverthislongti-spanorbitalnfigurations（fig12），andvariationofeentricitiesandclations（fig13）showthisverylong-terstabilityoftheouterfiveplasboththetiandthefreencydoasalthoughwedonotshowapshere，thetypicalfreencyoftheorbitaloscillationofptoandtheotherouterplasisalostnstantdurgtheseverylong-tertegrationperiods，whichisdeonstratedtheti–freencyapsonourwebpa

theseotegrations，therelativenuricalerrorthetotalenergywas&si;10&;6andthatofthetotalangularontuwas&si;10&;10

51renancestheneptune–ptosyste

koshita≈ap;nakai（1996）tegratedtheouterfiveplaaryorbitsover&psn;55&tis;109yrtheyfoundthatfourajorrenancesbeeenneptuneandptoareataeddurgthewholetegrationperiod，andthattherenancesaybetheacaesofthestabilityoftheorbitofptotheajorfourrenancesfoundprevioresearchareasfollowsthefollogdescription，&labda;denotestheanlongitude，&oga;isthelongitudeoftheascendgnodeandϖisthelongitudeofperihelionsubscriptspandndenoteptoandneptune

anotionrenancebeeenneptuneandpto（3:2）thecriticalarguntθ1=3&labda;p&;2&labda;n&;ϖplibratesaround180°withanaplitudeofabout80°andalibrationperiodofabout2&tis;104yr

thearguntofperihelionofpto&oga;p=θ2=ϖp&;&oga;plibratesaround90°withaperiodofabout38&tis;106yrthedoantperiodicvariationsoftheeentricityandclationofptoaresynchronizedwiththelibrationofitsarguntofperihelionthisisanticipatedthesecularperturbationtheorynstructedbykozai（1962）