6discussion
whatkindofdynamicalmechanismmaintainsthislong-termstabilityoftheplanetarysystem?wecanimmediatelythinkoftwomajorfeaturesthatmayberesponsibleforthelong-termstability.first，thereseemtobenosignificantlower-orderresonancesbetweenanypairamongthenineplanets.jupiterandsaturnareclosetoa5:2meanmotionresonance，butnotjustintheresonancezone.higher-orderresonancesmaycausethechaoticnatureoftheplanetarydynamicalmotion，buttheyarenotsostrongastodestroythestableplanetarymotionwithinthelifetimeoftherealsolarsystethesecondfeature，whichwethinkismoreimportantforthelong-termstabilityofourplanetarysystem，isthedifferenceindynamicaldistancebetweenterrestrialandjovianplanetarysubsystems.whenwemeasureplanetaryseparationsbythemutualhillradii，separationsamongterrestrialplanetsaregreaterthan26rh，whereasthoseamongjovianplanetsarelessthan14rh.thisdifferenceisdirectlyrelatedtothedifferencebetweendynamicalfeaturesofterrestrialandjovianplanets.terrestrialplanetshavesmallermasses，shorterorbitalperiodsandwiderdynamicalseparation.theyarestronglyperturbedbyjovianplanetsthathavelargermasses，longerorbitalperiodsandnarrowerdynamicalseparation.jovianplanetsarenotperturbedbyanyothermassivebodies.
thepresentterrestrialplanetarysystemisstillbeingdisturbedbythemassivejovianplanets.however，thewideseparationandmutualinteractionamongtheterrestrialplanetsrendersthedisturbanceineffective;thedegreeofdisturbancebyjovianplanetsiso，sincethedisturbancecausedbyjovianplanetsisaforcedoscillationhavinganamplitudeofo.heighteningofeccentricity，forexampleo～0.05，isfarfromsufficienttoprovokeinstabilityintheterrestrialplanetshavingsuchawideseparationas26rh.thusweassumethatthepresentwidedynamicalseparationamongterrestrialplanetsisprobablyoneofthemostsignificantconditionsformaintainingthestabilityoftheplanetarysystemovera109-yrtime-span.ourdetailedanalysisoftherelationshipbetweendynamicaldistancebetweenplanetsandtheinstabilitytime-scaleofsolarsystemplanetarymotionisnowon-going.
althoughournumericalintegrationsspanthelifetimeofthesolarsystem，thenumberofintegrationsisfarfromsufficienttofilltheinitialphasespace.itisnecessarytoperformmoreandmorenumericalintegrationstoconfirmandexamineindetailthelong-termstabilityofourplanetarydynamics.
——以上文段引自ito，t.&tanikawa，k.long-termintegrationsandstabilityofplanetaryorbitsinoursolarsystemon.not.r.astron.soc.336，483–500
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。