第76章 对火星轨道变化问题的最后解释（3 / 3）
inthesetwointegrations，therelativenumericalerrorinthetotalenergywas～10?6andthatofthetotalangularmomentumwas～10?10.
5.1resonancesintheneptune–plutosystem
kinoshitanakai(1996)integratedtheouterfiveplanetaryorbitsover±5.5x109yr.theyfoundthatfourmajorresonancesbetweenneptuneandplutoaremaintainedduringthewholeintegrationperiod，andthattheresonancesmaybethemaincausesofthestabilityoftheorbitofpluto.themajorfourresonancesfoundinpreviousresearchareasfollows.inthefollowingdescription，λdenotesthemeanlongitude，Ωisthelongitudeoftheascendingnodeand?isthelongitudeofperihelion.subscriptspandndenoteplutoandneptune.
meanmotionresonancebetweenneptuneandpluto(3:2).thecriticalargumentθ1=3λp?2λn??plibratesaround180°withanamplitudeofabout80°andalibrationperiodofabout2x104yr.
theargumentofperihelionofplutowp=θ2=?p?Ωplibratesaround90°withaperiodofabout3.8x106yr.thedominantperiodicvariationsoftheeccentricityandinclinationofplutoaresynchronizedwiththelibrationofitsargumentofperihelion.thisisanticipatedinthesecularperturbationtheoryconstructedbykozai(1962).
thelongitudeofthenodeofplutoreferredtothelongitudeofthenodeofneptune，θ3=Ωp?Ωn，circulatesandtheperiodofthiscirculationisequaltotheperiodofθ2libration.whenθ3becomeszero，i.e.thelongitudesofascendingnodesofneptuneandplutooverlap，theinclinationofplutobecomesmaximum，theeccentricitybecomesminimumandtheargumentofperihelionbecomes90°.whenθ3becomes180°，theinclinationofplutobecomesminimum，theeccentricitybecomesmaximumandtheargumentofperihelionbecomes90°again.williamsbenson(1971)anticipatedthistypeofresonance，laterconfirmedbymilani，nobilicarpino(1989).
anargumentθ4=?p??n+3(Ωp?Ωn)libratesaround180°withalongperiod，～5.7x108yr.
inournumericalintegrations，theresonances(i)–(iii)arewellmaintained，andvariationofthecriticalargumentsθ1，θ2，θ3remainsimilarduringthewholeintegrationperiod(figs14–16).however，thefourthresonance(iv)appearstobedifferent:thecriticalargumentθ4alternateslibrationandcirculationovera1010-yrtime-scale(fig.17).thisisaninterestingfactthatkinoshitanakai's(1995，1996)shorterintegrationswerenotabletodisclose.
6discussion
whatkindofdynamicalmechanismmaintainsthislong-termstabilityoftheplanetarysystem?wecanimmediatelythinkoftwomajorfeaturesthatmayberesponsibleforthelong-termstability.first，thereseemtobenosignificantlower-orderresonances(meanmotionandsecular)betweenanypairamongthenineplanets.jupiterandsaturnareclosetoa5:2meanmotionresonance(thefamous‘greatinequality’)，butnotjustintheresonancezone.higher-orderresonancesmaycausethechaoticnatureoftheplanetarydynamicalmotion，buttheyarenotsostrongastodestroythestableplanetarymotionwithinthelifetimeoftherealsolarsystem.thesecondfeature，whichwethinkismoreimportantforthelong-termstabilityofourplanetarysystem，isthedifferenceindynamicaldistancebetweenterrestrialandjovianplanetarysubsystems(itotanikawa1999，2001).whenwemeasureplanetaryseparationsbythemutualhillradii(r_)，separationsamongterrestrialplanetsaregreaterthan26rh，whereasthoseamongjovianplanetsarelessthan14rh.thisdifferenceisdirectlyrelatedtothedifferencebetweendynamicalfeaturesofterrestrialandjovianplanets.terrestrialplanetshavesmallermasses，shorterorbitalperiodsandwiderdynamicalseparation.theyarestronglyperturbedbyjovianplanetsthathavelargermasses，longerorbitalperiodsandnarrowerdynamicalseparation.jovianplanetsarenotperturbedbyanyothermassivebodies.
thepresentterrestrialplanetarysystemisstillbeingdisturbedbythemassivejovianplanets.however，thewideseparationandmutualinteractionamongtheterrestrialplanetsrendersthedisturbanceineffective;thedegreeofdisturbancebyjovianplanetsiso(ej)(orderofmagnitudeoftheeccentricityofjupiter)，sincethedisturbancecausedbyjovianplanetsisaforcedoscillationhavinganamplitudeofo(ej).heighteningofeccentricity，forexampleo(ej)～0.05，isfarfromsufficienttoprovokeinstabilityintheterrestrialplanetshavingsuchawideseparationas26rh.thusweassumethatthepresentwidedynamicalseparationamongterrestrialplanets(;26rh)isprobablyoneofthemostsignificantconditionsformaintainingthestabilityoftheplanetarysystemovera109-yrtime-span.ourdetailedanalysisoftherelationshipbetweendynamicaldistancebetweenplanetsandtheinstabilitytime-scaleofsolarsystemplanetarymotionisnowon-going.
althoughournumericalintegrationsspanthelifetimeofthesolarsystem，thenumberofintegrationsisfarfromsufficienttofilltheinitialphasespace.itisnecessarytoperformmoreandmorenumericalintegrationstoconfirmandexamineindetailthelong-termstabilityofourplanetarydynamics.
——以上文段引自ito，t.tanikawa，k.long-termintegrationsandstabilityofplanetaryorbitsinoursolarsystem.mon.not.r.astron.soc.336，483–500(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。 ↑返回顶部↑
5.1resonancesintheneptune–plutosystem
kinoshitanakai(1996)integratedtheouterfiveplanetaryorbitsover±5.5x109yr.theyfoundthatfourmajorresonancesbetweenneptuneandplutoaremaintainedduringthewholeintegrationperiod，andthattheresonancesmaybethemaincausesofthestabilityoftheorbitofpluto.themajorfourresonancesfoundinpreviousresearchareasfollows.inthefollowingdescription，λdenotesthemeanlongitude，Ωisthelongitudeoftheascendingnodeand?isthelongitudeofperihelion.subscriptspandndenoteplutoandneptune.
meanmotionresonancebetweenneptuneandpluto(3:2).thecriticalargumentθ1=3λp?2λn??plibratesaround180°withanamplitudeofabout80°andalibrationperiodofabout2x104yr.
theargumentofperihelionofplutowp=θ2=?p?Ωplibratesaround90°withaperiodofabout3.8x106yr.thedominantperiodicvariationsoftheeccentricityandinclinationofplutoaresynchronizedwiththelibrationofitsargumentofperihelion.thisisanticipatedinthesecularperturbationtheoryconstructedbykozai(1962).
thelongitudeofthenodeofplutoreferredtothelongitudeofthenodeofneptune，θ3=Ωp?Ωn，circulatesandtheperiodofthiscirculationisequaltotheperiodofθ2libration.whenθ3becomeszero，i.e.thelongitudesofascendingnodesofneptuneandplutooverlap，theinclinationofplutobecomesmaximum，theeccentricitybecomesminimumandtheargumentofperihelionbecomes90°.whenθ3becomes180°，theinclinationofplutobecomesminimum，theeccentricitybecomesmaximumandtheargumentofperihelionbecomes90°again.williamsbenson(1971)anticipatedthistypeofresonance，laterconfirmedbymilani，nobilicarpino(1989).
anargumentθ4=?p??n+3(Ωp?Ωn)libratesaround180°withalongperiod，～5.7x108yr.
inournumericalintegrations，theresonances(i)–(iii)arewellmaintained，andvariationofthecriticalargumentsθ1，θ2，θ3remainsimilarduringthewholeintegrationperiod(figs14–16).however，thefourthresonance(iv)appearstobedifferent:thecriticalargumentθ4alternateslibrationandcirculationovera1010-yrtime-scale(fig.17).thisisaninterestingfactthatkinoshitanakai's(1995，1996)shorterintegrationswerenotabletodisclose.
6discussion
whatkindofdynamicalmechanismmaintainsthislong-termstabilityoftheplanetarysystem?wecanimmediatelythinkoftwomajorfeaturesthatmayberesponsibleforthelong-termstability.first，thereseemtobenosignificantlower-orderresonances(meanmotionandsecular)betweenanypairamongthenineplanets.jupiterandsaturnareclosetoa5:2meanmotionresonance(thefamous‘greatinequality’)，butnotjustintheresonancezone.higher-orderresonancesmaycausethechaoticnatureoftheplanetarydynamicalmotion，buttheyarenotsostrongastodestroythestableplanetarymotionwithinthelifetimeoftherealsolarsystem.thesecondfeature，whichwethinkismoreimportantforthelong-termstabilityofourplanetarysystem，isthedifferenceindynamicaldistancebetweenterrestrialandjovianplanetarysubsystems(itotanikawa1999，2001).whenwemeasureplanetaryseparationsbythemutualhillradii(r_)，separationsamongterrestrialplanetsaregreaterthan26rh，whereasthoseamongjovianplanetsarelessthan14rh.thisdifferenceisdirectlyrelatedtothedifferencebetweendynamicalfeaturesofterrestrialandjovianplanets.terrestrialplanetshavesmallermasses，shorterorbitalperiodsandwiderdynamicalseparation.theyarestronglyperturbedbyjovianplanetsthathavelargermasses，longerorbitalperiodsandnarrowerdynamicalseparation.jovianplanetsarenotperturbedbyanyothermassivebodies.
thepresentterrestrialplanetarysystemisstillbeingdisturbedbythemassivejovianplanets.however，thewideseparationandmutualinteractionamongtheterrestrialplanetsrendersthedisturbanceineffective;thedegreeofdisturbancebyjovianplanetsiso(ej)(orderofmagnitudeoftheeccentricityofjupiter)，sincethedisturbancecausedbyjovianplanetsisaforcedoscillationhavinganamplitudeofo(ej).heighteningofeccentricity，forexampleo(ej)～0.05，isfarfromsufficienttoprovokeinstabilityintheterrestrialplanetshavingsuchawideseparationas26rh.thusweassumethatthepresentwidedynamicalseparationamongterrestrialplanets(;26rh)isprobablyoneofthemostsignificantconditionsformaintainingthestabilityoftheplanetarysystemovera109-yrtime-span.ourdetailedanalysisoftherelationshipbetweendynamicaldistancebetweenplanetsandtheinstabilitytime-scaleofsolarsystemplanetarymotionisnowon-going.
althoughournumericalintegrationsspanthelifetimeofthesolarsystem，thenumberofintegrationsisfarfromsufficienttofilltheinitialphasespace.itisnecessarytoperformmoreandmorenumericalintegrationstoconfirmandexamineindetailthelong-termstabilityofourplanetarydynamics.
——以上文段引自ito，t.tanikawa，k.long-termintegrationsandstabilityofplanetaryorbitsinoursolarsystem.mon.not.r.astron.soc.336，483–500(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。 ↑返回顶部↑