对火星轨道变化问题的最后解释（1/4）

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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-termintegrationsandstabilityofplanetaryorbitsinoursolarsystem

abstract

wepresenttheresultsofverylong-termnumericalintegrationsofplanetaryorbitalmotionsover109-yrtime-，atleastinoursimpledynamicalmodel，seemstobequitestableevenoverthisverylongtime--frequencyoscillationsusingalow-passfiltershowsusthepotentiallydiffusivecharacterofterrestrialplanetarymotion，'ssecularperturbationtheory(∼∼±4gyr).however，therearenoapparentsecularincreasesofeccentricityorinclinationinanyorbitalelementsoftheplanets，whichmayberevealedbystilllonger-±–plutosystemhavebeenmaintainedoverthe1011-yrtime-

1introduction

thequestionofthestabilityofoursolarsystemhasbeendebatedoverseveralhundredyears，-，‘stability’，

amongmanydefinitionsofstability，hereweadoptthehilldefinition(gladman1993):actuallythisisnotadefinitionofstability，，startingfromacertaininitialconfiguration(chambers，wetherill&boss1996;ito&tanikawa1999).，about±，(yoshinaga，kokubo&makino1999).ofcoursethisstatementcannotbesimplyappliedtosystemswithstableorbitalresonancessuchastheneptune–

inadditiontothevaguenessoftheconceptofstability，theplanetsinoursolarsystemshowacharactertypicalofdynamicalchaos(sussman&wisdom1988，1992).thecauseofthischaoticbehaviourisnowpartlyunderstoodasbeingaresultofresonanceoverlapping(murray&holman1999;lecar，franklin&holman2001).however，itwouldrequireintegratingoveranensembleofplanetarysystemsincludingallnineplanetsforaperiodcoveringseveral10gyrtothoroughlyunderstandthelong-termevolutionofplanetaryorbits，

fromthatpointofview，manyofthepreviouslong-termnumericalintegrationsincludedonlytheouterfiveplanets(sussman&wisdom1988;kinoshita&nakai1996).，thelongestnumericalintegrationspublishedinjournalsarethoseofduncan&lissauer(1998).althoughtheirmaintargetwastheeffectofpost-main-sequencesolarmasslossonthestabilityofplanetaryorbits，theyperformedmanyintegrationscoveringupto∼&lissauer'spaper，-main-，theyfoundthatthecrossingtime-scaleofplanetaryorbits，whichcanbeatypicalindicatoroftheinstabilitytime-scale，，thejovianplanetsremainstableover1010yr，&lissaueralsoperformedfoursimilarexperimentsontheorbitalmotionofsevenplanets(venustoneptune)，whichcoveraspanof∼，butitseemsthattheterrestrialplanetsalsoremainstableduringtheintegrationperiod，

ontheotherhand，inhisaccuratesemi-analyticalsecularperturbationtheory(laskar1988)，laskarfindsthatlargeandirregularvariationscanappearintheeccentricitiesandinclinationsoftheterrestrialplanets，especiallyofmercuryandmarsonatime-scaleofseveral109yr(laskar1996).theresultsoflaskar'

inthispaperwepresentpreliminaryresultsofsixlong-termnumericalintegrationsonallnineplanetaryorbits，coveringaspanofseveral109yr，andoftwootherintegrationscoveringaspanof±，-termintegrationsisthatsolarsystemplanetarymotionseemstobestableintermsofthehillstabilitymentionedabove，atleastoveratime-spanof±，inournumericalintegrationsthesystemwasfarmorestablethanwhatisdefinedbythehillstabilitycriterion:notonlydidnocloseencounterhappenduringtheintegrationperiod，butalsoalltheplanetaryorbitalelementshavebeenconfinedinanarrowregionbothintimeandfrequencydomain，-termnumericalintegrations，weshowtypicalexamplefiguresasevidenceoftheverylong-，wehavepreparedawebpage(access)，whereweshowraworbitalelements，theirlow-passfilteredresults，variationofdelaunayelementsandangularmomentumdeficit，andresultsofoursimpletime–

insection2webrieflyexplainourdynamicalmodel，--termvariationofplanetaryorbitsusingalow-，wepresentasetofnumericalintegrationsfortheouterfiveplanetsthatspans±-

2descriptionofthenumericalintegrations