对火星轨道变化问题的最后解释（4/4）

asfortheouterjovianplanetarysubsystem，jupiter–saturnanduranus–，thestrengthoftheircouplingisnotasstrongcomparedwiththatofthevenus–

5±5×1010-yrintegrationsofouterplanetaryorbits

sincethejovianplanetarymassesaremuchlargerthantheterrestrialplanetarymasses，，weaddedacoupleoftrialintegrationsthatspan±5×1010yr，includingonlytheouterfiveplanets(thefourjovianplanetspluspluto).theresultsexhibittherigorousstabilityoftheouterplanetarysystemoverthislongtime-()，andvariationofeccentricitiesandinclinations()showthisverylong-，thetypicalfrequencyoftheorbitaloscillationofplutoandtheotherouterplanetsisalmostconstantduringtheseverylong-termintegrationperiods，whichisdemonstratedinthetime–

inthesetwointegrations，therelativenumericalerrorinthetotalenergywas～10?6andthatofthetotalangularmomentumwas～10?

–plutosystem

kinoshita&nakai(1996)integratedtheouterfiveplanetaryorbitsover±×，，λdenotesthemeanlongitude，Ωisthelongitudeoftheascendingnodeand?

meanmotionresonancebetweenneptuneandpluto(3:2).thecriticalargumentθ1=3λp?2λn??plibratesaround180°withanamplitudeofabout80°andalibrationperiodofabout2×

theargumentofperihelionofplutoωp=θ2=?p?Ωplibratesaround90°×(1962).

thelongitudeofthenodeofplutoreferredtothelongitudeofthenodeofneptune，θ3=Ωp?Ωn，circulatesandtheperiodofthiscirculationisequaltotheperiodofθθ3becomeszero，，theinclinationofplutobecomesmaximum，theeccentricitybecomesminimumandtheargumentofperihelionbecomes90°.whenθ3becomes180°，theinclinationofplutobecomesminimum，theeccentricitybecomesmaximumandtheargumentofperihelionbecomes90°&benson(1971)anticipatedthistypeofresonance，laterconfirmedbymilani，nobili&carpino(1989).

anargumentθ4=?p??n+3(Ωp?Ωn)libratesaround180°withalongperiod，～×

inournumericalintegrations，theresonances(i)–(iii)arewellmaintained，andvariationofthecriticalargumentsθ1，θ2，θ3remainsimilarduringthewholeintegrationperiod(figs14–16).however，thefourthresonance(iv)appearstobedifferent:thecriticalargumentθ4alternateslibrationandcirculationovera1010-yrtime-scale().thisisaninterestingfactthatkinoshita&nakai's(1995，1996)

6discussion

whatkindofdynamicalmechanismmaintainsthislong-termstabilityoftheplanetarysystem?wecanimmediatelythinkoftwomajorfeaturesthatmayberesponsibleforthelong-，thereseemtobenosignificantlower-orderresonances(meanmotionandsecular):2meanmotionresonance(thefamous‘greatinequality’)，-orderresonancesmaycausethechaoticnatureoftheplanetarydynamicalmotion，，whichwethinkismoreimportantforthelong-termstabilityofourplanetarysystem，isthedifferenceindynamicaldistancebetweenterrestrialandjovianplanetarysubsystems(ito&tanikawa1999，2001).whenwemeasureplanetaryseparationsbythemutualhillradii(r_)，separationsamongterrestrialplanetsaregreaterthan26rh，，，

，thewideseparationandmutualinteractionamongtheterrestrialplanetsrendersthedisturbanceineffective;thedegreeofdisturbancebyjovianplanetsiso(ej)(orderofmagnitudeoftheeccentricityofjupiter)，sincethedisturbancecausedbyjovianplanetsisaforcedoscillationhavinganamplitudeofo(ej).heighteningofeccentricity，forexampleo(ej)～，(>26rh)isprobablyoneofthemostsignificantconditionsformaintainingthestabilityoftheplanetarysystemovera109-yrtime--scaleofsolarsystemplanetarymotionisnowon-

althoughournumericalintegrationsspanthelifetimeofthesolarsystem，-

——以上文段引自ito，&tanikawa，-，483–500(2002)

这只是作者君参考的一篇文章，关于太阳系的稳定性。

还有其他论文，不过也都是英文的，相关课题的中文文献很少，那些论文下载一篇要九美元（《nature》真是暴利），作者君写这篇文章的时候已经回家，不在检测中心，所以没有数据库的使用权，下不起，就不贴上来了。