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对火星轨道变化问题的最后解释（第1页）

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。

那么作者君在此列出相关参考文献中的一篇开源论文。

以下是文章内容：

LrationsandstabilityofplaaryorbitsinourSolarsystem

Abstract

&theresults-termegrationsofplaaryorbitalmotionsover109-yrtime-spansingalls。Aquispeericaldatasholaioinoursimpledynamistobequitestableevehisverylongtime-spathelowest-frequencyossusingalow-passfiltershowsusthepotentiallydiffusivecharacterofterrestrialplaiohatofMercury。ThebehaviouroftheetrierrationsisqualitativelysimilartotheresultsfromJacquesLaskarssecularperturbati。emax～yr）。However，therearesecreasesofetriinanyorbitalelemes，whichmayberevealedbystillloermegrations。erformedacouplerationsingmotioerfiveplahedurationof±5×1010yr。Theresultihethreemajorresoheosystemhavebeenmaihe1011-yrtime-span。

1Introdu

&ionoftheproblem

&ioyofourSolarsystemhasbeeedoverseveralhundredyears，siheeraofheproblemhasattrayfamousmathematisovertheyearsandhasplayedatralroleiofnon-lineardynamidchaostheory。However，wedohaveadefihequestioherourSolarsystemisstableornot。Thisispartlyaresultofthefactthatthedefinitioability’isvaguewhenitisusediotheproblemofplaionintheSolarsystem。Actuallyitisogiveaclear，rigorousandphysiiioyofourSolarsystem。

Amoionsofstability，herettheHilldefinition（Gladman1993）:actuallythisisionofstability，butofinstability。Wedefiemasbeingunstablewheeroewhereiem，startingfromaitialfiguratioherill&Boss1996;Ito&Tanikawa1999）。AsystemisdefinedasexperiengaterwhentwobodiesapproaotherwithihelargerHillradius。Otherwisethesystemisdefiable。HenceforwardwestatethatourplaemisdynamicallystableiferhappensduringtheageofourSolarsystem，about±5Gyr。Ihisdefinitionmaybereplaeinwhioybetweeherofapairofplaakesplace。Thisisbecauseweknowfromexperieanisverylikelytoleadtoaplaaryandprotoplaems（Yoshinaga，Kokubo&Makino1999）。Ofcoursethisstatementplyappliedtosystemswithstableorbitalresonancessuchastheosystem。

1。2Previousstudiesandaimsofthisresearch

Inadditiontothevagueheceptofstability，theplasinourSolarsystemshoiian&Wisdom1988，1992）。Thecauseofthischaoticbehaviourisnowpartlyuoodasbeiofresonance（Murray&Holman1999;Leklin&Holman2001）。However，itwouldrequireiingoveranensembleofplaemsingallsforaperiseveral10Gyrthlyuheloioaryorbits，siiamicalsystemsarecharacterizedbytheirstrongdepeials。

Fromthatpointofview，manyofthepreviouslong-termegratioheouterfiveplas（Sussman&Wisdom1988;Kinoshita&Nakai1996）。ThisisbecausetheorbitalperiodsoftheouterplasaresomugerthaheinnerfourplaitismucheasiertofollowthesystemfiveiopreseegrationspublishedinjourhoseofDun&Lissauer（1998）。Althoughtheirmaiheeffeain-sequenasslossoyofplaaryorbits，theyperformedmaiupto～1011yroftheorbitalmotionsofthefourjoviaheinitialorbitalelementsandmassesofplahesameasthoseofourSolarsysteminDun&Lissauerspaper，buttheydecreasethemassoftheSungraduallyintheirnumericalexperiments。Thisisbecausetheysidertheeffeain-sequenasslossinthepaper。tly，theyfoundthatthee-scaleofplaaryorbits，whibeatypidicatoroftheinstabilitytime-scale，isquiteseherateofmassdecreaseoftheSuhemassoftheSuspresehejoviasremainstableover1010yr，er。Dun&Lissaueralsoperformedfoursimilarexperimealmotios（Veune），whichcoveraspanof～109yr。Theirexperimentsosarepreheseemsthattheterrestrialplasalsoremaiheiionperiod，maintainingalmulaross。

Oherhand，inhisaccuratesemi-analyticalsecularperturbationtheory（Laskar1988），Laskarfindsthatlargeandirregularvariationsappeariiesandinsoftheterrestrialplas，espeerdMarsonatime-scaleofseveral109yr（Laskar1996）。TheresultsofLaskarssecularperturbationtheoryshouldbeedaedbyfullyegrations。

Inthispaperwepresentprelimisofsixlong-termegrationsoaryorbits，gaspanofseveral109yr，andoftwratiaspanof±5×1010yr。Thetotalelapsedtimeforalliiohan5yr，usingseveraldedicatedPdworkstatiohefuals-termiionsisthatSolarsystemplaioobestableiheHillstabilitymentioleastoveratime-spanof±4Gyr。Actually，iegratioemwasfarmorestablethanwhatisdefiability:notonlydiderhappenduriioalsoalltheplaaryorbitalelementshavebeenedinahintimeandfrequenain，thoughplaioicethepurposeofthispaperistoexhibitaheresults-termegratioypicalexamplefiguresasevideheveryloabilityofSolarsystemplaion。Forreaderswhohavemorespeddeeperisinournumericalresults，aredawebpage（access），raworbitalelements，theirlow-passfilteredresults，variationofDelausandangularmome，asofoursimpletime–frequenalysisonallrations。

&ion2webrieflyexplainourdynamiericalmethodandinitialsusediioiooadesofthequickresultsoftheegrati-termstabilityofSolarsystemplaionisapparentbothiarypositionsandorbitalelements。Aroughestimationofnumericalerrorsisalsogiveiooadisoftheloioaryorbitsusingalow-passfilterandincludesadisofangularmome。Iioasetofegratioerfiveplaspans±5×1010yr。Iion6wealsodiscusstheloabilityoftheplaionanditspossiblecause。

&ionoftheegrations

（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。）

2。3hod

&ilizeased-orderWisdom–Holmaiaiiohod（;amp;amp;Holman1991;Kinoshita，Yoshida&Nakai1991）ecialstart-upproceduretoreducethetrunerrlevariables，‘warmstart’（Saha&Tremaine1992，1994）。

&epsizefortheegrationsis8dthroughoutalliionsofthes（N±1，2，3），whichisabout111oftheorbitalperiodoftheipla（Mercury）。Asforthedeterminationofstepsize，wepartlyfollowthepreviousegrationofallsinSussman&Wisdom（1988，7。2d）andSaha&Tremaine（1994，22532d）。Werouhedecimalpartofthetheirstepsizesto8tomakethestepsizeamultipleof2ioreducetheacofrouheputationprorelationtothis，;amp;amp;Holman（1991）performedegratioerfiveplaaryorbitsusiicmapsizeof400d，110。83oftheorbitalperiodofJupiter。Theirresultseemsth，whichpartlyjustifiesourmethodthestepsize。However，siricityofJupiter（～0。05）ismuchsmallerthanthatofMercury（～0。2），weneedsomeweparetheseiionssimplyiepsizes。

Iioerfiveplas（F±），wefixedthestepsizeat400d。

&Gaussfandgfunthesymplecticmaptogetherwiththethird-orderHalleymethod（Danby1992）asasolverforKeplerequations。Thenumberofmaximumiteratioihodis15，buttheyhemaximuminanyrations。

&ervalofthedataoutputis200000d（～547yr）forthecalsofalls（N±1，2，3），andabout8000000d（～21903yr）fortheiioerfiveplas（F±）。

Althoughnooutputfilteringwasdoheegrationswereinprocess，liedalow-passfiltertotheraworbitaldataafterletedallthecals。SeeSe4。1formoredetail。

&imation

2。4。1Relativeerrorsintyandangularmomentum

Agtoohebasicpropertiesofsympletegrators，whiservethephysiservativequaalorbitalenergyandangularmomentum），-termegratioohavebeehverysmallerrors。Theaveragedrelativeerrorsofty（～10?9）andoftotalangularmomentum（～10?11）haveremainednearlytthroughouttheii。1）。Thespecialstartupprocedure，warmstart，wouldhavereducedtheaveragedrelativeerrorintybyaboutnitudeormore。

&ivenumericalerrorofthetotalangularmomentumδAA0aalenergyδEE0iegrationsN±1，2，3，whereδEaheabsolutegeofthetyandtotalangularmomeively，andE0aheirinitialvalues。ThehorizontalunitisGyr。

&differeingsystems，differeicallibraries，ahardwarearchitecturesresultinumericalerrhthevariationsinround-andnumeris。IntheupperpanelofFig。1，weizethissituationintheseumericalerrorialangularmomentum，whichshorouslypreserveduptomae-εpre。

2。4。2Erroriarylongitudes

&hesymplecticmapspreservetyandtotalangularmomentumofN-bodydynamicalsystemsilywell，thedegreeoftheirpreservationmaynotbeagoodmeasureoftheaeritegrations，especiallyasameasureofthepositionalerrorofplaheerroriaryloimatethenumericalerroriarylongitudes，weperformedthefollowingprocedures。Weparedtheresultofourmaiegrationswithsometestiions，whimuchshorterperiodsbutwithmuchhigheraccurathemaiions。Forthispurpose，weperformedamuchmrationsizeof0。125d（164ofthemaiions）spanning3×105yr，startingwiththesameinitialsasiegration。Wesiderthatthistestiioha‘pseudo-true’solutioaryorbitalevolutio，weparethetestiioegration，N?1。Fortheperiodof3×105yr，weseeadifferenaheEarthbetweeegrationsof～0。52°（iheion）。Thisdiffererapolatedtothevalue～8700°，about25rotatioer5Gyr，siheerritudesincreaseslihtimeiicmap。Similarly，thelongitudeerrorofPlutobeestimatedas～12°。ThisvalueforPlutoismuchbetterthainKinoshita&Nakai（1996）wherethediffereedas～60°。

3Numericalresults–I。Glaa

Iionwebrieflyreviewtheloabilityofplaaryorbitalmhsomesnapshotsofrawa。Theorbitalmotiosiermstabilityinallofouregrations:nosersbetairofplaookplace。

3。1Geioyofplaaryorbits

First，webrieflylookatthegeneralcharacteroftheloabilityofplaaryorbits。Ouriherefocusespartitheierrestrialplasforwhichtheorbitaltime-scalesaremuchshorterthaheouterfiveplas。AsweseeclearlyfromtheplanarorbitalfigurationsshowninFigs2and3，orbitalpositiorialplalebetweeialandfinalpartofeaumeritegration，whisseveralGyr。Thesolidlihepresentorbitsoftheplawithintheswarmofdotseveninthefinalpartofiions（b）and（d）。Thisihroughouttheeiohealmularvariationsofplaaryorbitalmotionremaihesameastheyareatpresent。

&icalviewofthefouriaryorbits（fromthez-axisdire）attheinitialandfinalpartsoftheiionsN±1。Theaxesuhexy-plaheinvariantplaneofSolarsystemtotalangularmomentum。（a）TheinitialpartofN+1（t=0to0。0547×109yr）。（b）ThefinalpartofN+1（t=4。9339×108to4。9886×109yr）。（itialpartofN?1（t=0to?0。0547×109yr）。（d）ThefinalpartofN?1（t=?3。9180×109to?3。9727×109yr）。Ineael，atotalof23684poiedwithanintervalofabout2190yrover5。47×107yr。SolidlinesineaeldeorbitsofthefourterrestrialplaakenfromDE245）。