对火星轨道变化问题的最后解释

    作者君在作品相关中其实已经解释过这个问题。

    不过仍然有人质疑——“你说得太含糊了”，“火星轨道的变化比你想象要大得多！”

    那好吧，既然作者君的简单解释不够有力，那咱们就看看严肃的东西，反正这本书写到现在，嚷嚷着本书bug一大堆，用初高中物理在书中挑刺的人也不少。

    以下是文章内容：

    long-teraryorbitsinoursolarsystem

    abstract

    ，atleastinoursis，±5x–plutosystemhavebeenmaintainedoverthe1011-yrtime-span.

    1introduction

    thequestionofthestabilityofoursolarsystersystem.

    admp;amp;boss1996;itoamp;amp;tanikawa1999).，about±，(yoshinaga，kokuboamp;amp;makino1999).ofcoursethisstatementcannotbesimplyappliedtosystemswithstableorbitalresonancessuchastheneptune–plutosystem.

    inadditiontothevaguenessoftheconceptofstability，theplanetsinoursolarsystearysystesforaperiodcoveringseveral10gyrtothoroughlyunderstandthelong-teraryorbits，sincechaoticdynamicalsystemsarecharacterizedbytheirstrongdependenceoninitialconditions.

    fros(sussaryorbits，theyperforaryorbits，whichcanbeatypicalindicatoroftheinstabilitytisres(venustoneptune)，whichcoveraspanof～，butitseesalsoreroscillations.

    ontheotherhand，inhisaccurateses，especiallyofskar1996).theresultsoflaskarssecularperturbationtheoryshouldbeconfirmedandinvestigatedbyfullynumericalintegrations.

    inthispaperwepresentpreliaryorbits，coveringaspanofseveral109yr，andoftwootherintegrationscoveringaspanof±5x，，atleastoveratiaryorbitaleleunayelermomentumdeficit，andresultsofoursimpletime–frequencyanalysisonallofourintegrations.

    insection2webrieflyexplainourdynasthatspans±5x.

    2descriptionofthenumericalintegrations

    （本部分涉及比较复杂的积分计算，作者君就不贴上来了，贴上来了起点也不一定能成功显示。）

    weutilizeasecond-orderwisdom–holmansymplecticmapasourmainintegrationmethod(wisdomamp;amp;holman1991;kinoshita，yoshidaamp;amp;nakai1991)withaspecialstart-upproceduretoreducethetruncationerrorofanglevariables，‘warmstart’(sahaamp;amp;tremaine1992，1994).

    thestepsizeforthenuparetheseintegrationssimplyintermsofstepsizes.

    intheintegrationoftheouterfiveplanets(f±)，wefixedthestepsizeat400d.

    weadoptgaussfandgfunctionsinthesymplecticmaptogetherwiththethird-orderhalleymethod(danby1992)smethodis15，buttheyneverreachedthemaximuminanyofourintegrations.

    theintervalofthedataoutputisd(～547yr)forthecalculationsofallnineplanets(n±1，2，3)，andaboutd(～yr)fortheintegrationoftheouterfiveplanets(f±).

    althoughnooutputfilteringwasdonewhenthenumericalintegrationswereinprocess，.

    accordingtooneofthebasicpropertiesofsyrngulartiveerrorintotalenergybyaboutoneorderofmagnitudeormore.

    relativenungularngularmomentum，respectively，.

    notethatdifferentoperatingsysternungularmomentum，whichshouldberigorouslypreserveduptomachine-eprecision.

    sincethesyparethetestintegrationwiththetedtothevalue～8700°，about25rotationsofearthafter5gyr，，thelongitudeerrorofplutocanbeestimatedas～12°.thisvalueforplutoismuchbetterthantheresultinkinoshitaamp;amp;nakai(1996)wherethedifferenceisestimatedas～60°.

    3numericalresults–

    :noorbitalcrossingsnorcloseencountersbetweenanypairofplanetstookplace.

    first，，orbitalpositionsoftheterrestrialplanetsdifferlittlebetweentheinitialandfinalpartofeachnuaryorbitalmotionremainnearlythesameastheyareatpresent.

    verticalviewofthefourinnerplanetaryorbits(frondfinalpartsoftheintegrationsn±.(a)theinitialpartofn+1(t=x109yr).(b)thefinalpartofn+1(t=xx109yr).(c)theinitialpartofn?1(t=0to?x109yr).(d)thefinalpartofn?1(t=?x109to?x109yr).ineachpanel，x(takenfromde245).

    thevariationofeccentricitiesandorbitalinclinationsfortheinnerfourplanetsintheinitialandfinalpartoftheintegrationn+，thecharacterofthevariationofplanetaryorbitaleles;s(1994，1996)，.

    theorbitalsseeroverthistime-span(seealsosection5).

    –frequencymaps

    althoughtheplanetaryrlyinthecaseofearth，canpotentiallyhaveasignificanteffectonitssurfaceclirinsolationvariation().

    togiveanoverviewofthelong-teraryorbitalskars(1990，1993)frequencyanalysis.

    .

    eachfragrgeoverlappingpart:forexample，whentheithdatabeginsfromt=tiandendsatt=ti+t，thenextdatasegmentrangesfromti+δt≤ti+δt+t，whereδt?+treachesthetotalintegrationlenh.

    weapplyanffttoeachofthedatafragments，andobtainnfrequencydiagrams.

    ineachfrequencydiagracedbyagrey-scale(orcolour)chart.

    weperforcexisrepresentstheperiod(orfrequency)oftheoscillationoforbitalelements.

    wehaveadoptedanfftbecauseofitsoverwhelposedintofrequencyponentsisterriblyhuge(severaltensofgbytes).

    atypicalexabyplanetandelementbyelement.

    wecalculateverylong-periodicvariationandexchangeofplanetaryorbitalenergyandangularunayelementsl，g，=?，，suchasymptomofinstabilityisnotprominentinourlong-termintegrations.

    ，thetotalorbitalenergyandangularponent(h-h0)，g0，，.

    cosandallnineplanets，itisapparentthattheasares::，，wecannotneglectthecontributionfros，aswewillseeinsubsequentsections.

    +1andn?，，，wecanseethatarysubsystem.

    itisnotclearatthearyorbitalenergy(whichisdirectlyrelatedtothesesthanistheangulartestoe).hence，theeccentricitiesofvenusandearthcanbedisturbedeasilybyjupiterandsaturn，，–earthpair，whichresultsinanegativecorrelationintheexchangeoforbitalenergyinthepair.

    asfortheouterjovianplanetarysubsysteparedwiththatofthevenus–earthpair.

    5±5x1010-yrintegrationsofouterplanetaryorbits

    sincethejovianplanetaryarys(thefourjovianplanetspluspluto).()，andvariationofeccentricitiesandinclinations()，thetypicalfrequencyoftheorbitaloscillationofplutoandtheotherouterplanetsisalmostconstantduringtheseverylong-termintegrationperiods，whichisdemonstratedinthetime–frequencymapsonourwebpage.

    inthesetwointegrations，therelativenungularmomentumwas～10?10.

    –plutosystem

    kinoshitaaaryorbitsover±x，，λdenotesthemeanlongitude，Ωisthelongitudeoftheascendingnodeand?.

    rgumentθ1=3λp?2λn??plibratesaround180°withanamplitudeofabout80°andalibrationperiodofabout2x104yr.

    theargumentofperihelionofplutowp=θ2=?p?Ωplibratesaround90°x(1962).

    thelongitudeofthenodeofplutoreferredtothelongitudeofthenodeofneptune，θ3=Ωp?Ωn，，，theinclinationofplutobecoeses90°.whenθ3becoeseses90°;aterconfirni，nobiliamp;amp;carpino(1989).

    anargumentθ4=?p??n+3(Ωp?Ωn)libratesaround180°withalongperiod，～x108yr.

    inournurgurduringthewholeintegrationperiod(figs14–16).however，thefourthresonance(iv)appearstobedifferent:thecriticalargutionovera1010-yrtime-scale().thisisaninterestingfactthatkinoshitaamp;amp;nakais(1995，1996)shorterintegrationswerenotabletodisclose.

    6discussion

    whatkindofdynaarysystearysystearysubsystearyseparationsbythesaregreaterthan26rh，，，.

    ，thewideseparationandsrendersthedisturbanceineffective;thedegreeofdisturbancebyjovianplanetsiso(ej)(orderofsisaforcedoscillationhavinganamplitudeofo(ej).heighteningofeccentricity，forexampleo(ej)～，(amp;;26rh).

    althoughournursystem，.

    ——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。