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第96章（第1页）

frothatpotofview，anyofthepreviolong-ternuricaltegrationscdedonlytheouterfiveplas（ssan≈ap;wisdo1988;koshita≈ap;nakai1996）thisisbecaetheorbitalperiodsoftheouterplasareuchlonrthanthoseofthenerfourplasthatitisucheasiertofollowthesysteforagiventegrationperiodatpresent，thelonstnuricaltegrationspubli射djournalsarethoseofduncan≈ap;lissauer（1998）althoughtheiratartwastheeffectofpost-a-seencelarasslossonthestabilityofplaaryorbits，theyperfordanytegrationsvergupto&si;1011yroftheorbitalotionsofthefourjovianplastheitialorbitalelentsandassesofplasarethesaasthoseofourlarsysteduncan≈ap;lissauer&39;spaper，buttheydecreasetheassofthesungraduallytheirnuricalexperintsthisisbecaetheynsidertheeffectofpost-a-seencelarasslossthepapernseently，theyfoundthatthecrossgti-scaleofplaaryorbits，whichcanbeatypicaldicatorofthestabilityti-scale，isitesensitivetotherateofassdecreaseofthesunwhentheassofthesunisclosetoitspresentvae，thejovianplasreastableover1010yr，orperhapslonrduncan≈ap;lissaueralperfordfoursiilarexperintsontheorbitalotionofsevenplas（ventoneptune），whichveraspanof&si;109yrtheirexperintsonthesevenplasarenotyetprehensive，butitseesthattheterrestrialplasalreastabledurgthetegrationperiod，atagalostregularoscillations

ontheotherhand，hisauratesei-analyticalsecularperturbationtheory（laskar1988），laskarfdsthatlarandirregularvariationscanappeartheeentricitiesandclationsoftheterrestrialplas，especiallyofrcuryandarsonati-scaleofseveral109yr（laskar1996）theresultsoflaskar&39;ssecularperturbationtheoryshouldbenfirdandvestigatedbyfullynuricaltegrations

thispaperwepresentpreliaryresultsofsixlong-ternuricaltegrationsonallneplaaryorbits，vergaspanofseveral109yr，andofoothertegrationsvergaspanof&psn;5&tis;1010yrthetotalelapsedtiforalltegrationsisorethan5yr，gseveraldedicatedpcsandworkstationsoneofthefundantalncsionsofourlong-tertegrationsisthatlarsysteplaaryotionseestobestabletersofthehillstabilityntionedabove，atleastoverati-spanof&psn;4gyractually，ournuricaltegrationsthesystewasfarorestablethanwhatisdefedbythehillstabilitycriterion:notonlydidnocloseenunterhappendurgthetegrationperiod，butalalltheplaaryorbitalelentshavebeennfedanarrowregionbothtiandfreencydoa，thoughplaaryotionsaresto插sticscethepurposeofthispaperistoexhibitandoverviewtheresultsofourlong-ternuricaltegrations，weshowtypicalexaplefiguresasevidenceoftheverylong-terstabilityoflarsysteplaaryotionforreaderswhohaveorespecificanddeeperterestsournuricalresults，wehavepreparedawebpa（aess），whereweshowraworbitalelents，theirlow-passfilteredresults，variationofdelaunayelentsandangularontudeficit，andresultsofoursipleti–freencyanalysisonallofourtegrations

section2webrieflyexpnourdynaicalodel，nuricalthodanditialnditionsedourtegrationssection3isdevotedtoadescriptionoftheickresultsofthenuricaltegrationsverylong-terstabilityoflarsysteplaaryotionisapparentbothplaarypositionsandorbitalelentsaroughestiationofnuricalerrorsisalgivensection4goesontoadiscsionofthelonst-tervariationofplaaryorbitsgalow-passfilterandcdesadiscsionofangularontudeficitsection5，wepresentasetofnuricaltegrationsfortheouterfiveplasthatspans&psn;5&tis;1010yrsection6wealdiscsthelong-terstabilityoftheplaaryotionanditspossiblecae

2descriptionofthenuricaltegrations

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

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23nuricalthod

weutilizeasend-orderwisdo–holansyplecticapasourategrationthod（wisdo≈ap;holan1991;koshita，yoshida≈ap;nakai1991）withaspecialstart-upproceduretoreducethetruncationerrorofanglevariables，&lso;warstart&rso;（saha≈ap;treae1992，1994）

thestepsizeforthenuricaltegrationsis8dthroughoutalltegrationsoftheneplas（n&psn;1，2，3），whichisabout111oftheorbitalperiodofthenerostpla（rcury）asforthedeterationofstepsize，wepartlyfollowtheprevionuricaltegrationofallneplasssan≈ap;wisdo（1988，72d）andsaha≈ap;treae（1994，22532d）weroundedthedecialpartofthetheirstepsizesto8toakethestepsizeaultipleof2ordertoreducetheauulationofround-offerrortheputationprocessesrelationtothis，wisdo≈ap;holan（1991）perfordnuricaltegrationsoftheouterfiveplaaryorbitsgthesyplecticapwithastepsizeof400d，11083oftheorbitalperiodofjupitertheirresultseestobeaurateenough，whichpartlyjtifiesourthodofdetergthestepsizehowever，scetheeentricityofjupiter（&si;005）isuchsallerthanthatofrcury（&si;02），weneedcarewhenweparethesetegrationssiplytersofstepsizes

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