第76章 对火星轨道变化问题的最后解释 (第4/12页)

rmvariationofplaaryorbitsusingalow-passfilterandincludesadiscussionofangularmomentumdeficit.iion5，wepreseofnumeritegrationsfortheouterfiveplahatspans±5x1010yr.iion6wealsodiscusstheloabilityoftheplaarymotionanditspossiblecause.

    2descriptionofthenumeritegrations

    （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。）

    2.3numericalmethod

    weutilizeased-orderwisdom–holmansymplecticmapasourmaiiohod(wisdomkinoshita，yoshidanakai1991)ecialstart-upproceduretoreducethetruncationerrorofanglevariables，‘warmstart’(sahatremaine1992，1994).

    thestepsizeforthenumeritegrationsis8dthroughoutalliionsofthenineplas(n±1，2，3)，whichisabout111oftheorbitalperiodoftheinnermostpla(mercury).asforthedeterminationofstepsize，wepartlyfollowthepreviousnumeritegrationofallnineplasinsussmanwisdom(1988，7.2d)andsahatremaine(1994，22532d).werouhedecimalpartofthetheirstepsizesto8tomakethestepsizeamultipleof2ioreducetheaccumulationofround-offerrorintheputationprocesses.iiontothis，wisdomholman(1991)performednumeritegrationsoftheouterfiveplaaryorbitsusingthesymplecticmapsizeof400d，110.83oftheorbitalperiodofjupiter.theirresultseemstobeaccurateenough，whichpartlyjustifiesourmethodofdeterminiepsize.however，siheetricityofjupiter(～0.05)ismuchsmallerthanthatofmercury(～0.2)，weneedsomecarewhenweparetheseiionssimplyintermsofstepsizes.

    iegrationoftheouterfiveplas(f±)，wefixedthestepsizeat400d.

    tgauss'fandgfunsinthesymplecticmaptogetherwiththethird-orderhalleymethod(danby1992)asasolverforkeplerequations.thenumberofmaximumiteratioinhalley'smethodis15，buttheyneverreachedthemaximuminanyofouriions.

    theintervalofthedataoutputis200000d(～547yr)forthecalculationsofallnineplas(n±1，2，3)，andabout8000000d(～21903yr)fortheiionoftheouterfiveplas(f±).

    althoughnooutputfilteringwasdohenumeritegrationswereinprocess，liedalow-passfiltertotheraworbitaldataafterwehadpletedallthecalculations.seese4.1formoredetail.

    2.4errorestimation

    2.4.1relativeerrorsint