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时间:2019-05-25
《A second order Laplace-Lagrange theory》由会员上传分享,免费在线阅读,更多相关内容在行业资料-天天文库。
1、Astron.Astrophys.327,416–427(1997)ASTRONOMYANDASTROPHYSICSAsecondorderLaplace-LagrangetheoryappliedtotheuraniansatellitesystemApostolosA.ChristouandCarlD.MurrayAstronomyUnit,QueenMaryandWestfieldCollege,MileEndRoad,LondonE14NS,UK(A.Christou@qmw.ac.uk,C.D.Murray@qmw.ac.u
2、k)Received18December1996/Accepted11June1997Abstract.Computeralgebraisusedtoderiveanalyticalexpres-AnattemptbyLaskar&Jacobson(1987)tofitthetheorysionsfortheelementsofasecularperturbationtheoryofthedescribedbyLaskar(1986)toVoyagerandEarth-basedobser-secondorderinthemasses
3、.Thelinearpartofthistheoryisin-vations,thelatterspanningapproximatelyoneorbitalperiodofcorporatedintothestandardLaplace-LagrangesolutionwhichUranus,necessitatedtheintroductionofempiricalcorrectionsisthenappliedtothemotionoftheuraniansatellites.Thisen-totheirderivedsecu
4、lareigenfrequencies,possiblyduetotheablestheeffectsofmeanmotionnear-resonancesinthissystemunmodelledeffectofthesenear-resonances.Thefirstanalyticaltobemodelled.TheresultsareinverygoodagreementwithtreatmentofthesephenomenawasperformedbyMalhotraetthefilteredoutputofanumeri
5、calintegrationbyMalhotraetalal(1989)(hereafterreferredtoasMFMN)inwhichtheeffects(1989).Theadditionalcomplexitiesofstudyingtheoutersolarofthe2:1Umbriel-Titaniaandthe3:2Titania-Oberonnear-systemusingasimilarapproacharediscussed.resonancesontheLaplace-Lagrangemodelwerequa
6、ntified.Theresultwasfoundtobeinverygoodagreementwithanu-Keywords:celestialmechanics–satellites:satellitesofUranusmericalintegrationdescribedinthesamepaper.However,there–methods:analyticalstillremainedadiscrepancyexceedingthe1%level(abench-marksetbytheirresultsfortheincl
7、inationvariations)thatcanprobablybeattributedtotheeffectofweakernear-resonances.Thesubjectofthispaperisthedescriptionandrigorous1.Introductiontestingofamodelthatisbasedonageneraltheoryofthesec-ondorderinthemasses.ThiswasdescribedindetailbyDuriezThesatellitesystemofthep
8、lanetUranusisanidealtesting(1979)andwassubsequentlypresentedinamoresystematicgroundforsecularperturbationtheoriessinc
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