作者君在作品相关中已经解释过这个问题,并在此列出相关参考文献中的一篇开源论文。
以下是文章内容:
Long-termintegrationsandstabilityofplanetaryorbitsinourSolarsystem
Abstract
Wepresenttheresultsofverylong-termnumericalintegrationsofplanetaryorbitalmotionsover109-yrtime-spansincludingallnineplanets.Aquickinspectionofournumericaldatashowsthattheplanetarymotion,atleastinoursimpledynamicalmodel,seemstobequitestableevenoverthisverylongtime-span.Acloserlookatthelowest-frequencyoscillationsusingalow-passfiltershowsusthepotentiallydiffusivecharacterofterrestrialplanetarymotion,especiallythatofMercury.ThebehaviouroftheeccentricityofMercuryinourintegrationsisqualitativelysimilartotheresultsfromJacquesLaskar'ssecularperturbationtheory(e.g.emax∼0.35over∼±4Gyr).However,therearenoapparentsecularincreasesofeccentricityorinclinationinanyorbitalelementsoftheplanets,whichmayberevealedbystilllonger-termnumericalintegrations.Wehavealsoperformedacoupleoftrialintegrationsincludingmotionsoftheouterfiveplanetsoverthedurationof±5×1010yr.TheresultindicatesthatthethreemajorresonancesintheNeptune–Plutosystemhavebeenmaintainedoverthe1011-yrtime-span.
1Introduction
1.1Definitionoftheproblem
ThequestionofthestabilityofourSolarsystemhasbeendebatedoverseveralhundredyears,sincetheeraofNewton.Theproblemhasattractedmanyfamousmathematiciansovertheyearsandhasplayedacentralroleinthedevelopmentofnon-lineardynamicsandchaostheory.However,wedonotyethaveadefiniteanswertothequestionofwhetherourSolarsystemisstableornot.Thisispartlyaresultofthefactthatthedefinitionoftheterm‘stability’isvaguewhenitisusedinrelationtotheproblemofplanetarymotionintheSolarsystem.Actuallyitisnoteasytogiveaclear,rigorousandphysicallymeaningfuldefinitionofthestabilityofourSolarsystem.
Amongmanydefinitionsofstability,hereweadopttheHilldefinition(Gladman1993):actuallythisisnotadefinitionofstability,butofinstability.Wedefineasystemasbecomingunstablewhenacloseencounteroccurssomewhereinthesystem,startingfromacertaininitialconfiguration(Chambers,Wetherill&Ito&&Tanikawa1999).AsystemisdefinedasexperiencingacloseencounterwhentwobodiesapproachoneanotherwithinanareaofthelargerHillradius.Otherwisethesystemisdefinedasbeingstable.HenceforwardwestatethatourplanetarysystemisdynamicallystableifnocloseencounterhappensduringtheageofourSolarsystem,about±5Gyr.Incidentally,thisdefinitionmaybereplacedbyoneinwhichanoccurrenceofanyorbitalcrossingbetweeneitherofapairofplanetstakesplace.Thisisbecauseweknowfromexperiencethatanorbitalcrossingisverylikelytoleadtoacloseencounterinplanetaryandprotoplanetarysystems(Yoshinaga,Kokubo&&Makino1999).OfcoursethisstatementcannotbesimplyappliedtosystemswithstableorbitalresonancessuchastheNeptune–Plutosystem.
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