第76章 对火星轨道变化问题的最后解释(11/14)
geand'itivecorrelationinangularmomentumexchange.wemaypossiblyexplainthisthroughobservingthegeneralfactthattherearenoseculartermsinplanetarysemimajoraxesuptosecond-orderperturbationtheories(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,wetreatthejovianplanetarysystemasanindependentplanetarysystemintermsofthestudyofitsdynamicalstability.hence,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)integratedtheouterfiveplanetaryorbitsove
asfortheouterjovianplanetarysubsystem,jupiter–saturnanduranus–neptuneseemtomakedynamicalpairs.however,thestrenhoftheircouplingisnotasstrongcomparedwiththatofthevenus–earthpair.
5±5x1010-yrintegrationsofouterplanetaryorbits
sincethejovianplanetarymassesaremuchlargerthantheterrestrialplanetarymasses,wetreatthejovianplanetarysystemasanindependentplanetarysystemintermsofthestudyofitsdynamicalstability.hence,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)integratedtheouterfiveplanetaryorbitsove
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