elentsofrcury，eseciallyitseentricity，seegetosignificantextentthisisartlybecaetheorbitaltiscaleoftheistheshortestofallthes，whichleadstooreraidorbitalevotionthanotherthenertostabilitythisresultaearstobesoagreer's(1994，1996)exectationsthatrgeandirregurvariationsaeartheeentricitiesandclationsofrcuryontiscaleofseveral109yrhowever，theeffectoftheossiblestabilityoftheorbitofrcuryaynotfatallyaffecttheglobalstabilityofthewholearysysteogtothesallassofrcurywewillntion
ieflythelongterorbitalevotionoftersectionlowassfilteredorbitalelents
theorbitalotionoftheouterfiveseesrigorolystableanditereguroverthistisan(seealsosection5)
32tibsas
althoughthearyotionexhibitsverylongterstabilitydefedasthenonexistenceofcloseenunterevents，thechaoticnatureofarydynagetheosciltoryeriodandalitudeofaryorbitalotiongraduallyoversuchlongtisansevensuchslightfctuationsoforbitalvariationthefreencydorlythecaseofearth，canotentiallyhavesignificanteffectonitssurfacecliatesystethroughsorsotionvariation(cfberger1988)
togiveanoverviewofthelongtergeeriodicityaryorbitalotion，weerfordanyfastfouriertransforations(ffts)alongthetiaxis，andsuerosedtheresultgeriodgrastodrawodinsionaltibsasthesecificaroachtodragthesetibsasthisaerisverysibssilerthanthewaveletanalysisorskar's(1990，1993)freencyanalysis
dividethelowassfilteredorbitaldatatoanyfragntsofthesalengththelengthofeachdatasegntshouldbeultileofordertoalythefft
eachfragntofthedatahasrgeovergart:forexale，whentheithdatabegsfrot=tiandendsatt=ti+t，thenextdatasegntrangesfroti+δt≤ti+δt+t，whereδt?twentuethisdivisionuntilwereachcertanuberbywhichtn+treachesthetotaltegrationlength
wealyanffttoeachofthedatafragnts，andobtafreencydiagras
eachfreencydiagraobtaedabove，thestrengthoferiodicitycanberecedbygreyscale(orlour)chart
weerfort，andnnectallthegreyscale(orlour)chartstoonegrahforeachtegrationthehorizontalaxisofthesenewgrahsshouldbetheti，iethestartgtibsfragntofdata(ti，wherei=1，…，n)theverticalaxisreresentstheeriod(orfreency)oftheosciltionoforbitalelents
wehaveadotedanfftbecaeofitsoverwhelgseed，scetheaountofnubsdatatobedeosedtofreencyisterriblyhuge(severaltensofgbytes)
tyicalexaleofthetibsacreatedbytheaboveroceduresisshowngreyscalediagraasfig5，whichshowsthevariationoferiodicitytheeentricityandclationofearthn+2tegrationfig5，thedarkareashowsthatatthetidicatedbythevaeontheabscissa，theeriodicitydicatedbytheordateisstrongerthanthelighterareaarounditwecanregnizefrothisthattheeriodicityoftheeentricityandclationofearthonlychangesslightlyovertheentireeriodveredbythen+2tegrationthisnearlyregurtrendisalitativelythesaothertegrationsandforothers，althoughtyicalfreenciesdifferbyandelentbyelent
42longtergeoforbitalenergyandangurontu
wecalcuteverylongeriodicvariationandexchangeofaryorbitalenergyandangurontufiltereddeunayelentsl，g，andareeivalenttothearyorbitalangurontuanditsverticalerunitassisretedtothearyorbitalenergyerunitassase=?μ22l2ifthesysteletelylear，theorbitalenergyandtheangurontubsfreencystantnonlearitythearysystebscaeanexchangeofenergyandangurontuthefreencydoathealitudeofthelowestfreencyosciltionshouldcreaseifthesysteisunstableand
eaksdowngraduallyhowever，suchsytoofstabilityisnotroourlongterions
fig7，thetotalorbitalenergyandangurontuofthefournerandallneareshownfortegrationn+2theuerthreeanelsshowthelongeriodicvariationoftotalenergy(denotedasee0)，totalangurontugg0)，andtheverticalhh0)ofthenerfourcalcutedfrothelowassfiltereddeunayelentse0，g0，h0denotetheitialvaesofeachantitytheabsotedifferencefrotheitialvaesislottedtheanelsthelowerthreeanelseachfigureshowee0，gg0andhh0ofthetotalofnethefctuationshowntheloweranelsisvirtuallyentirelyresultoftheassivejovians
argthevariationsofenergyandangurontuofthenerfourandallnes，itisaarentthatthealitudesofthoseofthenerarebssallerthanthoseofallnes:thealitudesoftheouterfivearergerthanthoseofthenerthisdoesnotanthatthenerterrestrialarysubsysteisorestablethantheouterone:thisissilyresultoftheretivesallnessoftheassesofthefourterrestrialaredwiththoseoftheouterjoviananotherthgwenoticeisthatthenerarysubsysteeunstableoreraidlythantheouteronebecaeofitsshorterorbitaltiscalesthiscanbeseentheanelsdenotedasnerfigwherethelongereriodicandirregurosciltionsareoreaarentthantheanelsdenotedastotalactually，thefctuationstheneranelsaretorgeextentasresultoftheorbitalvariationofthercuryhowever，wecannotneglectthentributionfrootherterrestrials，aswewillseesubseentsections
44longterulgofseveralneighbourgairs
letseesodividualvariationsofaryorbitalenergyandangurontuexressedbythelowassfiltereddeunayelentsfigs10and11showlongterevotionoftheorbitalenergyofeachandtheangurontun+1andn?2tegrationswenoticethatsosforaarentairstersoforbitalenergyandangurgearticur，venandearthbsairthefigures，theyshownegativerretionsexchangeofenergyandositiverretionsexchangeofangurontuiverretionexchangeoforbitalenergyansthattheforcloseddynabssystetersoftheorbitalenergytheositiverretionexchangeofangurontuansthattheareseolyundercertalongtererturbationscandidatesforerturbersarejuiterandsaturnalsofig11，wecanseethatarsshowsositiverretiontheangurontuvariationtotheven–earthsystercuryexhibitscertanegativerretionstheangurontuverstheven–earthsystebsseestobereactioncaedbythenservationofangurontutheterrestrialarysubsyste
itisnotclearattheontwhytheven–earthairexhibitsnegativerretionenergyexchangeandositiverretionangurgeweayossiblyexthisthroughobservgthegeneralfactthattherearenosecurteraryseiajoraxestosendordererturbationtheories(cf
ouwerclebs1961boalettiucao1998)thisansthatthearyorbitalenergy(whichisdirectlyretedtotheseiajoraxisa)bslessaffectedbyerturbgthanistheangurge(whichretestoe)hence，theeentricitiesofvenandearthcanbedisturbedeasilybyjuiterandsaturn，whichresultsositiverretiontheangurgeontheotherhand，theseiajoraxesofvenandeartharelesslikelytobedisturbedbythejovianththeenergyexchangeaybeliitedonlywiththeven–earthair，whichresultsnegativerretiontheexchangeoforbitalenergytheair
asfortheouterjovianarysubsyste，juiter–saturnanduran–uneseetobsairshowever，thestrengthoftheirulgisnotasstrongaredwiththatoftheven–earthair
x1010yrtegrationsofouteraryorbits
scethejovianaryassesarergerthantheterrestrialaryasses，wetreatthejovianarysysteasandeendentarysystetersofthestudyofitsdynabsstabilityhence，weaddeduleoftrialtegrationsthatsan1010yr，cdgonlytheouterfive(thefourjovianto)theresultsexhibittherigorostabilityoftheouterarysysteoverthislongtisanorbitalnfigurations(fig12)，andvariationofeentricitiesandclations(fig13)showthisverylongterstabilityoftheouterfiveboththetiandthefreencydoasalthoughwedonotshowashere，thetyicalfreencyoftheorbitalosciltionoftoandtheotherouterisalstantdurgtheseverylongterioneriods，whichisdeonstratedthetibsasonourwebage
thesetegrations，theretivenubserrorthetotalenergywas?10?6andthatofthetotalangurontuwas?10?10
51resonancestheune–tosyste
koshitanakai(1996)tegratedtheouterfivearyorbitsover55109yrtheyfoundthatfourbsbeeenuneandtoareataeddurgthewholetegrationeriod，andthattheresonancesaybethecaesofthestabilityoftheorbitoftotheajorfourresonancesfoundrevioresearchareasfollowsthefollogdescrition，λdenotestheanlongitude，Ωisthelongitudeoftheascendgnodeandisthelongitudeoferihelionsubscritsanddenotetoandune
anbsbeeenuneandto(3:2)thecriticalarguntθ1=λ?λn??li
atesaround180°withanalitudeofabout80°andli
ationeriodofabout104yr
thearguntoferihelionoftow=θ2=??Ωli
atesaround90°witheriodofabout38106yrthedobsvariationsoftheeentricityandclationoftoaresynchronizedwiththeli
ationofitsarguntoferihelionthisisanticiatedthesecurerturbationtheorynstructedbykozai(1962)
thelongitudeofthenodeoftoreferredtothelongitudeofthenodeofune，θ3=Ω?Ωn，circutesandtheeriodofthiscircutionisealtotheeriodofθ2li
ationwhenθ3beeszero，iethelongitudesofascendgnodesofuneandtoover，theclationoftobeesaxitricitybeesiuandthearguntoferihelionbees90°whenθ3bees180°，theclationoftobeesitricitybeesaxiuandthearguntoferihelionbees90°agawilliasbenson(1971)anticiatedthistyeofresonance，ternfirni，nobilicaro(1989)
anarguntθ4=n+(Ω?Ωn)li
atesaround180°withlongeriod，?57108yr
ournuions，theresonances(i)–(iii)arewellataed，andvariationofthecriticalarguntsθ1，θ2，θ3rerdurgthewholetegrationeriod(figs14–16however，thefourthresonance(iv)aearstobedifferent:thecriticalarguntθ4alternatesli
ationandcircutionover1010yrtiscale(fig17)thisisanterestgfactthatkoshitanakai's(1995，1996)shortertegrationswerenotabletodisclose
discsion
whatkdofdynaisatasthislongterstabilityofthearysystebsidiatelythkofajorfeaturesthatayberesonsibleforthelongterstabilityfirst，thereseetobenosignificantlowerorderresonances(anotionandsecur)beeenanyairaongthenejuiterandsaturnarecloseto5:2anbs(thefao‘greateality)，butnotjttheresonancezonehigherorderresonancesaycaethechaoticnatureofthearydynabsotion，buttheyarenotsostrongastodestroythestablearyotionwiththelifetioftherealsorsystedfeature，whichwethkisoreiortantforthelongterstabilityofourarysyste，isthedifferencedynabsbeeenterrestrialandjovianarysubsystes(itotanikawa1999，2001)whenwearysearationsbytheutualhillradii(r_)，searationsaongterrestrialaregreaterthan26rh，whereasthoseaongjovianarelessthan14rhthisdifferenceisdirectlyretedtothedifferencebeeendynabsfeaturesofterrestrialandjovianterrestrialhavesallerasses，shorterorbitaleriodsandwiderdynabssearationtheyarestronglyerturbedbyjovianthathavergerasses，longerorbitaleriodsandnarrowerdynabssearationjovianarenoterturbedbyanyotherassivebodies
theresentterrestrialarysysteisstillbegdisturbedbytheassivejovianhowever，thewidesearationandaongtheterrestrialrendersthedisturbanceeffectivethedegreeofdisturbancebyjovianiso(ej)(orderofagnitudeoftheeentricityofjuiter)，scethedisturbancecaedbyjovianisforcedosciltionhavganalitudeofo(ej)heightengofeentricity，forexaleo(ej)?005，isfarfrottorovokestabilitytheterrestrialhavgsuchwidesearationas26rhthweassuthattheresentwidedynabssearationaongterrestrial26rh)isrobablyoneofthenditionsforatagthestabilityofthearysysteover109yrtisanourdetailedanalysisoftheretionshibeeendynabsbeeenandthestabilitytiscaleofsorsystearyotionisnowongog
althoughournuionssanthelifetiofthesorsyste，thenuionsisfarfrottofilltheitialhasesaceitisnecessarytoerfororeandbstegrationstonfirandexaedetailthelongterstabilityofourarydynaics
这只是作者君参考的一篇文章，关于太阳系的稳定性。
当然还有其他论文，不过其它论文下载一篇要九美元，作者君下不起，就不贴上来了。
对火星轨道变化问题的最后解释[2/2页]