ignifitextent.thisispartlybecausetheorbitaltime-scaleoftheplaheshortestofalltheplas，whichleadstoamorerapidorbitalevolutionthanotherplaheinnermostplamaybeoinstability.thisresultappearstobeinsomeagreementwithlaskar's(1994，1996)expectationsthatlargeandirregularvariationsappearintheetricitiesandinationsofmercuryonatime-scaleofseveral109yr.however，theeffectofthepossibleinstabilityoftheorbitofmercurymaynotfatallyaffecttheglobalstabilityofthewholeplaarysystemowingtothesmallmassofmercury.wewillmentiohelong-termorbitalevolutionofmercurylateriion4usinglow-passfilteredorbitalelements.
theorbitalmotionoftheouterfiveplasseemsrigorouslystableandquiteregularoverthistime-span(seealsose5).
3.2time–frequencyma
althoughtheplaarymotionexhibitsveryloabilitydefiheenceofcloseenterevents，thechaotiatureofplaarydynamigetheoscillatoryperiodandamplitudeofplaaryorbitalmotiongraduallyoversugtime-spans.evensuchslightfluctuationsoforbitalvariationinthefrequenain，particularlyinthecaseofearth，potentiallyhaveasignifiteffeitssurfaceclimatesystemthroughsolarinsolationvariation(cf.berger1988).
togiveanoverviewofthelong-termgeinperiodicityinplaaryorbitalmotion，weperformedmanyfastfouriertransformations(ffts)aloimeaxis，andsuperposedtheresultingperiodgramstodrawtwo-dimensionaltime–frequencymaps.thespecificapproachtodrawiime–frequencymapsinthispaperisverysimple–muchsimplerthanthewaveletanalysisorlaskar's(1990，1993)frequenalysis.
dividethelow-passfilteredorbitaldataintomanyfragmentsofthesamelenh.thelenhofeachdatasegmentshouldbeamultipleof2ioapplythefft.
eachfragmentofthedatahasalargeoverlappingpart:forexample，whehdatabeginsfromt=tiandendsatt=ti t，thedatasegmentrangesfromti δt≤ti δt t，whereδt?t.wetihisdivisionuntilwereachacertainnumbernbywhi treachesthetotaliionlenh.
lyanffttoeachofthedatafragments，andobtainnfrequencydiagrams.
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