ies(cf.brouwerboccalettipucacco1998).thismeansthattheplanetaryorbitalenergy(whichisdirectlyrelatedtothesemimajoraxisa)mightbemuchlessaffectedbyperturbingplanetsthanistheangularmomentumexchange(whichrelatestoe).hence，theeccentricitiesofvenusandearthcanbedisturbedeasilybyjupiterandsaturn，whichresultsin'itivecorrelationintheangularmomentumexchange.ontheotherhand，thesemimajoraxesofvenusandeartharelesslikelytobedisturbedbythejovianplanets.thustheenergyexchangemaybelimitedonlywithinthevenus–earthpair，whichresultsinanegativecorrelationintheexchangeoforbitalenergyinthepair. asfortheouterjovianplanetarysubsystem，jupiter–saturnanduranus–neptuneseemtomakedynamicalpairs.however，thestrenhoftheircouplingisnotasstrongcomparedwiththatofthevenus–earthpair. 5±5x1010-yrintegrationsofouterplanetaryorbits sincethejovianplanetarymassesaremuchlargerthantheterrestrialplanetarymasses，，weaddedacoupleoftrialintegrationsthatspan±5x1010yr，includingonlytheouterfiveplanets(thefourjovianplanetspluspluto).theresultsexhibittherigorousstabilityoftheouterplanetarysystemoverthislongtime-span.orbitalconfigurations(fig.12)，andvariationofeccentricitiesandinclinations(fig.13)showthisverylong-termstabilityoftheouterfiveplanetsinboththetimeandthefrequencydomains.althoughwedonotshowmapshere，thetypicalfrequencyoftheorbitaloscillationofplutoandtheotherouterplanetsisalmostconstantduringtheseverylong-termintegrationperiods，whichisdemonstratedinthetime–frequencymapsonourwebpage. inthesetwointegrations，therelativenumericalerrorinthetotalenergywas～10?6andthatofthetotalangularmomentumwas～10?10. 5.1resonancesintheneptune–plutosystem kinoshitanakai(1996)integratedtheouterfiveplanetaryorbitsover±5.5x109yr.theyfoundthatfourmajorresonancesbetweenneptuneandplutoaremaintainedduringthewholeintegrationperiod，andthattheresonancesmaybethemaincausesofthestabilityoftheorbitofpluto.themajorfourresonancesfoundinpreviousresearchareasfollows.inthefollowingdescription，λdenotesthemeanlongitude，ΩisthelongiＭ.XＩAｐｅ.cＯＭ