A second order Laplace-Lagrange theory

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1、Astron.Astrophys.327,416–427(1997)ASTRONOMYANDASTROPHYSICSAsecondorderLaplace-LagrangetheoryappliedtotheuraniansatellitesystemApostolosA.ChristouandCarlD.MurrayAstronomyUnit,QueenMaryandWestfieldCollege,MileEndRoad,LondonE14NS,UK(A.Christou@qmw.ac.uk,C.D.M

2、urray@qmw.ac.uk)Received18December1996/Accepted11June1997Abstract.Computeralgebraisusedtoderiveanalyticalexpres-AnattemptbyLaskar&Jacobson(1987)tofitthetheorysionsfortheelementsofasecularperturbationtheoryofthedescribedbyLaskar(1986)toVoyagerandEarth-based

3、obser-secondorderinthemasses.Thelinearpartofthistheoryisin-vations,thelatterspanningapproximatelyoneorbitalperiodofcorporatedintothestandardLaplace-LagrangesolutionwhichUranus,necessitatedtheintroductionofempiricalcorrectionsisthenappliedtothemotionoftheu

4、raniansatellites.Thisen-totheirderivedseculareigenfrequencies,possiblyduetotheablestheeffectsofmeanmotionnear-resonancesinthissystemunmodelledeffectofthesenear-resonances.Thefirstanalyticaltobemodelled.Theresultsareinverygoodagreementwithtreatmentoftheseph

5、enomenawasperformedbyMalhotraetthefilteredoutputofanumericalintegrationbyMalhotraetalal(1989)(hereafterreferredtoasMFMN)inwhichtheeffects(1989).Theadditionalcomplexitiesofstudyingtheoutersolarofthe2:1Umbriel-Titaniaandthe3:2Titania-Oberonnear-systemusingas

6、imilarapproacharediscussed.resonancesontheLaplace-Lagrangemodelwerequantified.Theresultwasfoundtobeinverygoodagreementwithanu-Keywords:celestialmechanics–satellites:satellitesofUranusmericalintegrationdescribedinthesamepaper.However,there–methods:analytica

7、lstillremainedadiscrepancyexceedingthe1%level(abench-marksetbytheirresultsfortheinclinationvariations)thatcanprobablybeattributedtotheeffectofweakernear-resonances.Thesubjectofthispaperisthedescriptionandrigorous1.Introductiontestingofamodelthatisbasedona

8、generaltheoryofthesec-ondorderinthemasses.ThiswasdescribedindetailbyDuriezThesatellitesystemoftheplanetUranusisanidealtesting(1979)andwassubsequentlypresentedinamoresystematicgroundforsecularperturbationtheoriessinc