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以下是文章内容：
longterionsandstabilityofaryorbitsoursorsyste
abstract
weresenttheresultsofverylongterbstegrationsofaryorbitalotionsover109yrtisanscdgallneicksectionofournubsdatashowsthatthearystoursibsodel，seestobeitestableevenoverthisverylongtisancloserlookatthelowestfreencyosciltionslowassfiltershowstheotentiallydiffivecharacterofterrestrialaryotion，eseciallythatofrcurythebehaviouroftheeentricityofrcuryourtegrationsisalitativelysirtotheresultsfror'ssecurerturbationtheory(egeax?035over?±gyr)however，therearenoaarentsecurcreasesofeentricityorclationanyorbitalelentsofthes，whichayberevealedbystilllongerterbstegrationswehavealsoerforduleoftrialtegrationscdgotionsoftheouterfiveoverthedurationof1010yrtheresultdicatesthatthethreebstheune–tosystehavebeenataedoverthe1011yrtisan
troduction
11defitionoftheroble
theestionofthestabilityofoursorsystehasbeendebatedoverseveralhundredyears，scetheeraofnewtontheroblehasattractedanyfasovertheyearsandhasyedcentralrolethedevelontofnonleardynabsandchaostheoryhowever，wedonotyethavedefiteanswertotheestionofwhetheroursorsysteisstableornotthisisartlyresultofthefactthatthedefitionoftheter‘stabilityisvaguewhenitisedretiontotheroblearyotionthesorsysteactuallyitisnoteasytogiveclear，rigoroandhysicallyangfuldefitionofthestabilityofoursorsyste
aonganydefitionsofstability，hereweadotthehilldefition(gdan1993):actuallythisisnotdefitionofstability，butofstabilitywedefesystegunstablewhencloseenunterourssowherethesyste，startgfrocertaitialnfiguration(chabers，wetherillboss1996itotanikawa1999)systeisdefedasexeriencgcloseenunterwhenbodiesaroachoneanotherwithanareaofthergerhillradiotherwisethesysteisdefedasbegstablehenceforwardwestatethatourarysysteisdynaicallystableifnocloseenunterhaensdurgtheageofoursorsyste，about±5gyrcidentally，thisdefitioncedbyonewhichanourrenceofanyorbitalcrossgbeeeneitherofairoftakescethisisbecaeweknowfrobsthatanorbitalcrossgisverylikelytoleadtocloseenunteraryandroarysystes(yoshaga，kokuboako1999)ofursethisstateotbesilyaliedtosysteswithstableorbitalresonancessuchastheune–tosyste
12reviostudiesandaisofthisresearch
additiontothevaguenessofthencetofstability，theoursorsysteshowcharactertyicalofdynabschaos(ssanwisdo1988，1992)thecaeofthischaoticbehaviourisnowartlyunderstoodasbegresultofresonanceoverg(n1999lecar，franklholan2001)however，itwouldreiretegratgoveranensearysystescdgallneforeriodvergseveral10gyrtothoroughlyunderstandthelongterevotionofaryorbits，scechaoticdynabssystesarecharacterizedbytheirstrongdeendenceonitialnditions
frothatotofview，anyofthereviolongterbstegrationscdedonlytheouterfive(ssanwisdo1988koshitanakai1996)thisisbecaetheorbitaleriodsoftheouteraresobslongerthanthoseofthenerfourthatitisbseasiertofollowthesysteforgiventegrationeriodatresent，thelongestnuionsublishedjournalsarethoseofduncanlissauer(1998)althoughtheirtargetwastheeffectofostrasslossonthestabilityofaryorbits，theyerforionsvergto?1011yroftheorbitalotionsofthefourjoviantheitialorbitalelentsandarethesaasthoseofoursorsystebslissauer'saer，buttheydecreasetheassofthesungraduallytheirnubsexerintsthisisbecaetheynsidertheeffectofostrasslosstheaernseently，theyfoundthatthecrossgtiscaleofaryorbits，whichcanbetyicaldicatorofthestabilitytiscale，isitesensitivetotherateofassdecreaseofthesunwhentheassofthesunisclosetoitsresentvae，thejovianreastableover1010yr，orerhaslongerduncanlissaueralsoerfordfoursirexerintsontheorbitalotionofseven(ventoune)，whichversanof?109yrtheirexerintsonthesevenarenotyetrehensive，butitseesthattheterrestrialalsoreastabledurgthetegrationeriod，atagalrosciltions
ontheotherhand，hisauratesebssecurerturbationtheory(skar1988)，skarfdsthatrgeandirregurvariationscanaeartheeentricitiesandclationsoftheterrestrials，eseciallyofrcuryandarsontiscaleofseveral109yr(skar1996)theresultsofskar'ssecurerturbationtheoryshouldbenfirigatedbyfullynuions
thisaerweresentreliaryresultsofsixlongterbstegrationsonallnearyorbits，vergsanofseveral109yr，andofothertegrationsvergsanof1010yrthetotalesedtiforalltegrationsisorethanyr，severaldedicatedcsandworkstationsoneofthefundasionsofourlongterionsisthatsorsystearyotionseestobestabletersofthehillstabilityntionedabove，atleastovertisanofgyractually，ournuionsthesystewasfarorestablethanwhatisdefedbythehillstabilitycriterion:notonlydidnocloseenunterhaendurgthetegrationeriod，butalsoallthearyorbitalelentshavebeennfednarrowregionbothtiandfreencydoa，thougharyotionsarestochasticscetheuroseofthisaeristoexhibitandoverviewtheresultsofourlongterbstegrations，weshowtyicalexalefiguresasevidenceoftheverylongterstabilityofsorsystearyotionforreaderswhohavebsanddeeerterestsournubsresults，wehaverearedwebage(aess)，whereweshowraworbitalelents，theirlowassfilteredresults，variationofdeunayelentsandangurontudeficit，andresultsofoursiletibsanalysisonallofourtegrations
sectionwe
ieflyexourdynabsbsthodanditialnditionsedourtegrationssectionisdevotedtodescritionoftheickresultsofthenuionsverylongterstabilityofsorsystearyotionisaarentbotharyositionsandorbitalelentsroughestiationofnubserrorsisalsogivensectiongoesontodiscsionofthelongesttervariationofaryorbitslowassfilterandcdesdiscsionofangurontudeficitsection5，weresentsetofnuionsfortheouterfivethatsans1010yrsectionwealsodiscsthelongterstabilityofthearyotionanditsossiblecae
descritionofthenuions
（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。）
23nubsthod
weutilizesendorderwisdoasourionthod(wisdon1991koshita，yoshidanakai1991)withsecialstarturoceduretoreducethetruncationerrorofanglevariables，‘warstart(sahatreae1992，1994)
thestesizeforthenuionsisthroughoutalltegrationsofthene(n±1，2，3)，whichisabout111oftheorbitaleriodofthener(rcury)asforthedeterationofstesize，weartlyfollowtherevionuionofallnessanwisdo(1988，72d)andsahatreae(1994，22532d)weroundedthedecialartofthetheirstesizestotoakethestesizeultileofordertoreducetheautionofroundofferrortheutationrocessesretiontothis，wisdon(1991)erforbstegrationsoftheouterfivearyorbitsthesybsawithstesizeof400d，11083oftheorbitaleriodofjuitertheirresultseestobeaurateenough，whichartlyjtifiesourthodofdetergthestesizehowever，scetheeentricityofjuiter(?005)isbssallerthanthatofrcury(?02)，weneedsocarewhenwearethesetegrationssilytersofstesizes
thetegrationoftheouterfive(f±)，wefixedthestesizeat400d
weadotgas'andfunctionsthesybsatogetherwiththethirdorderhalleythod(danby1992)assolverforkelereationsthenuberofaxiuiterationswesethalley'sthodis15，buttheyneverreachedtheaxiuanyofourtegrations
thetervalofthedataoututis200000(?547yr)forthecalcutionsofallne(n±1，2，3)，andabout8000000(?21903yr)forthetegrationoftheouterfive(f±)
althoughnooututfiltergwasdonewhenthenuionswererocess，wealiedlowassfiltertotheraworbitaldataafterwehadletedallthecalcutionsseesection41fororedetail
24errorestiation
241retiveerrorstotalenergyandangurontu
aordgtooneofthebasicroertiesofsyors，whichnservethehysicallynservativeantitieswell(totalorbitalenergyandangurontu)，ourlongterbstegrationsseetohavebeenerfordwithverysallerrorstheaveragedretiveerrorsoftotalenergy(?10?9)andoftotalangurontu(?10?11)havereaednearlynstantthroughoutthetegrationeriod(fig1)thesecialstarturocedure，warstart，wouldhavereducedtheaveragedretiveerrortotalenergybyaboutoneorderofagnitudeorore
retivenubserrorofthetotalangurontuδaa0andthetotalenergyδee0ournuionsn±1，2，3，whereδeandδaaretheabsotechangeofthetotalenergyandtotalangurontu，resectively，ande0anda0aretheiritialvaesthehorizontalunitisgyr
notethatdifferentoeratgsystes，differentries，anddifferenthardwarearchitecturesresultdifferentnubserrors，throughthevariationsroundofferrorhandlgandnubsalgorithstheueraneloffig1，wecanregnizethissituationthesecurnubserrorthetotalangurbsshouldberigorolyreservedtoeerecision
242errorarylongitudes
scethesybsasreservetotalenergyandtotalangurontuofnbodydynabssystelywell，thedegreeoftheirreservationaynotbegoodasureoftheauracyofnuions，eseciallyasasureoftheositionalerrorofs，ietheerrorarylongitudestoestiatethenubserrorthearylongitudes，weerfordthefollogrocedureswearedtheresultofourlongterionswithsoions，whichsanbsshortereriodsbutwithbshigherauracythantheionsforthisurose，weerforbsuratetegrationwithstesizeof0125(164oftheions)sanng105yr，startgwiththesaditionsasthen?1tegrationwensiderthatthistesttegrationrovideswith‘seudotruesotionofaryorbitalevotionnext，wearethetesttegrationwiththeion，n?1fortheeriodof105yr，weseedifferenceananoaliesoftheearthbeeenthetegrationsof?052°(thecaseofthen?1tegration)thisdifferencecanbeextraotedtothevae?8700°，about25rotationsofearthaftergyr，scetheerroroflongitudescreaseslearlywithtithesybsrly，thelongitudeerroroftocanbeestiatedas?12°thisvaefortoisbsbetterthantheresultkoshitanakai(1996)wherethedifferenceisestiatedas?60°
nubsresultsgnceattherawdata
thissectionwe
ieflyreviewthelongterstabilityofaryorbitalotionthroughsosnashotsofrawnubsdatatheorbitaldicateslongterstabilityallofournuions:noorbitalcrossgsnorcloseenuntersbeeenanyairoftookce
31generaldescritionofthestabilityofaryorbits
first，we
ieflylookatthegeneralcharacterofthelongterstabilityofaryorbitsourterestherefocesarticurlyonthenerfourterrestrialforwhichtheorbitaltiscalesarebsshorterthanthoseoftheouterfiveaswecanseeclearlyfrororbitalnfigurationsshownfigsand3，orbitalositionsoftheterrestrialdifferlittlebeeentheitialandfalartofeachnuion，whichsansseveralgyrthesolidlesdenotgtheresentorbitsoftheliealostwiththeswarofdotseventhefalartoftegrations(b)and(d)thisdicatesthatthroughouttheentiretegrationeriodthealrvariationsofaryorbitalotionreanearlythesaastheyareatresent
verticalviewofthefourneraryorbits(frotheaxisdirection)attheitialandfalartsofthetegrationsn±1theaxesunitsareauthexyneissettothevariantneofsorsystetotalangurontu(a)theitialartofn+10to0054710yr)(b)thefalartofn+14933910to4988610yr)(c)theitialartofn?1(t=to?00547109yr)(d)thefalartofn?1=?3918010to?3972710yr)eachanel，totalof23684otsarelottedwithantervalofabout2190yrover547107yrsolidleseachaneldenotetheresentorbitsofthefourterrestrial(takenfrode245)
thevariationofeentricitiesandorbitalclationsforthenerfourtheitialandfalartofthetegrationn+1isshownfigasexected，thecharacterofthevariationofaryorbitalelentsdoesnotdiffersignificantlybeeentheitialandfalartofeachtegration，atleastforven，earthandarsthe
对火星轨道变化问题的最后解释[1/2页]