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第76章 对火星轨道变化问题的最后解释


nplanetarylongitudes
  sincethesymplecticmapspreservetotalenergyandtotalangularmomentumofn-bodydynamicalsystemsinherentlywell,thedegreeoftheirpreservationmaynotbeagoodmeasureoftheaccuracyofnumericalintegrations,especiallyasameasureofthepositionalerrorofplanets,i.e.theerrorinplanetarylongitudes.toestimatethenumericalerrorintheplanetarylongitudes,weperformedthefollowingprocedures.wecomparedtheresultofourmainlong-termintegrationswithsometestintegrations,whichspanmuchshorterperiodsbutwithmuchhigheraccuracythanthemainintegrations.forthispurpose,weperformedamuchmoreaccurateintegrationwithastepsizeof0.125d(164ofthemainintegrations)spanning3x105yr,startingwiththesameinitialconditionsasinthen?1integration.weconsiderthatthistestintegrationprovidesuswitha‘pseudo-true’,wecomparethetestintegrationwiththemainintegration,n?1.fortheperiodof3x105yr,weseeadifferenceinmeananomaliesoftheearthbetweenthetwointegrationsof~0.52°(inthecaseofthen?1integration).thisdifferencecanbeextrapolatedtothevalue~8700°,about25rotationsofearthafter5gyr,sincetheerroroflongitudesincreaseslinearlywithtimeinthesymplecticmap.similarly,thelongitudeerrorofplutocanbeestimatedas~12°.thisvalueforplutoismuchbetterthantheresultinkinoshitanakai(1996)wherethedifferenceisestimatedas~60°.
  3numericalresults–i.glanceattherawdata
  inthissectionwebrieflyreviewthelong-termstabilityofplanetaryorbitalmotionthroughsomesnapshotsofrawnumericaldata.theorbitalmotionofplanetsindicateslong-termstabilityinallofournumericalintegrations:noorbitalcrossingsnorcloseencountersbetweenanypairofplanetstookplace.
  3.1generaldescriptionofthestabilityofplanetaryorbits
  first,webrieflylookatthegeneralcharacterofthelong-termstabilityofplanetaryorbits.ourinterestherefocusesparticularlyontheinnerfourterrestrialplanetsforwhichtheorbitaltime-scalesaremuchshorterthanthoseoftheouterfiveplanets.aswecanseeclearlyfromtheplanarorbitalconfigurationsshowninfigs2and3,orbitalpositionsoftheterrestrialplanetsdifferlittlebetweentheinitialandm.XiApE.COm
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