第76章 对火星轨道变化问题的最后解释 (第8/12页)

r)chart.

    weperformthereplat，andectallthegrey-scale(orcolour)chartsintoonegraphforeategration.thehorizontalaxisofthesenehsshouldbethetime，i.e.thestartingtimesofeachfragmentofdata(ti，wherei=1，…，n).theverticalaxisrepresentstheperiod(orfrequency)oftheoscillationoforbitalelements.

    wehaveadoptedanfftbecauseofitsoverwhelmingspeed，siheamountofnumericaldatatobedeposedintofrequenposisterriblyhuge(severaltensofgbytes).

    atypicalexampleofthetime–frequencymapcreatedbytheaboveproceduresisshowninagrey-scalediagramasfig.5，whichshowsthevariationofperiodicityintheetricityandinatiohinn 2iion.infig.5，thedarkareashowsthatatthetimeindicatedbythevalueontheabscissa，theperiodicityindicatedbytheordirohaninthelighterareaaroundit.wereizefromthismapthattheperiodicityoftheetricityandinatiohonlygesslightlyovertheentireperiodcoveredbythen 2iion.thisnearlyregulartrendisqualitativelythesameiegrationsandforotherplas，althoughtypicalfrequenciesdifferplabyplaabyelement.

    4.2long-termexgeoforbitalenergyandangularmomentum

    wecalculateverylong-periodicvariationandexgeofplaaryorbitalenergyandangularmomentumusingfiltereddelaunayelementsl，g，h.gandhareequivalenttotheplaaryorbitalangularmomentumanditsvertipoperunitmass.lisrelatedtotheplaaryorbitalenergyeperunitmassase=?μ22l2.ifthesystemispletelyliheorbitalenergyandtheangularmomentumineachfrequenmustbestant.non-liyintheplaarysystemcauseanexgeofenergyandangularmomentuminthefrequenain.theamplitudeofthelowest-frequencyoscillationshouldincreaseifthesystemisunstableandbreaksdowngradually.however，suchasymptomofinstabilityisnotpromiin-termiions.

    infig.7，thetotalorbitalenergyandangularmomentumofthefourinnerplasandallnineplasareshownforiionn 2.theupperthreepanelsshowthelong-periodicvariationoftotalenergy(denotedase-e0)，totalangularmomentum(g-g0)，aipo(h-h0)oftheinnerfourplascalculatedfromthelow-passfiltereddelaunayelements.e0，g0，h0deheinitialvaluesofeachquantity.theabsolutedifferentheinitialva