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tively，.
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，，–earthp
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