第76章 对火星轨道变化问题的最后解释 (第11/12页)

theorbitofpluto.themajorfourresonancesfoundinpreviousresearchareasfollows.inthefollowingdescriptioesthemeanlongitude，Ωisthelongitudeoftheasdingnodeand?isthelongitudeofperihelion.subscriptspaeplutoaune.

    meanmotionresoweeuneandpluto(3:2).thecriticalargumentθ1=3λp?2λn??plibratesaround180°litudeofabout80°andalibrationperiodofabout2x104yr.

    theargumentofperihelionofplutowp=θ2=?p?Ωplibratesaround90°eriodofabout3.8x106yr.thedominantperiodicvariationsoftheetricityandinationofplutoaresynizedwiththelibrationofitsargumentofperihelion.thisisanticipatedinthesecularperturbationtheorystructedbykozai(1962).

    thelongitudeofthenodeofplutoreferredtothelongitudeofthenodeofune，θ3=Ωp?Ωn，circulatesandtheperiodofthiscirculationisequaltotheperiodofθ2libration.whenθ3beeszero，i.e.thelongitudesofasdingnodesofuneandplutooverlap，theinationofplutobeaximum，theetricitybeinimumandtheargumentofperihelionbees90°.whenθ3bees180°，theinationofplutobeinimum，theetricitybeaximumandtheargumentofperihelionbees90°again.williamsbenson(1971)anticipatedthistypeofresoerfirmedbymilani，nobilicarpino(1989).

    anargumentθ4=?p??n 3(Ωp?Ωn)libratesaround180°withalongperiod，～5.7x108yr.

    inournumeritegrations，theresonances(i)–(iii)arewellmaintained，andvariationofthecriticalargumentsθ1，θ2，θ3remainsimilarduringthewholeiionperiod(figs14–16).however，thefourthresonance(iv)appearstobedifferent:thecriticalargumentθ4alternateslibrationandcirculationovera1010-yrtime-scale(fig.17).thisisaingfactthatkinoshitanakai's(1995，1996)shorteriionswerenotabletodisclose.

    6discussion

    whatkindofdynamicalmeismmaintainsthisloabilityoftheplaarysystem?weimmediatelythinkoftwomajorfeaturesthatmayberesponsiblefortheloability.first，thereseemtobenosignifitlower-orderresonances(meanmotionandsecular)betairamongthenineplas.jupiterandsaturnareclosetoa5:2meanmotionresohefamous‘greatinequality’)，butnotjustintheresonane.higher-orderresonancesmaycausethechaotiatureoftheplaarydynamic