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.Murray@q

2、mw.ac.uk)Received18December1996/Accepted11June1997Abstract.Computeralgebraisusedtoderiveanalyticalexpres-AnattemptbyLaskar&Jacobson(1987)tofitthetheorysionsfortheelementsofasecularperturbationtheoryofthedescribedbyLaskar(1986)toVoyagerandEarth-basedobser-secondor

3、derinthemasses.Thelinearpartofthistheoryisin-vations,thelatterspanningapproximatelyoneorbitalperiodofcorporatedintothestandardLaplace-LagrangesolutionwhichUranus,necessitatedtheintroductionofempiricalcorrectionsisthenappliedtothemotionoftheuraniansatellites.This

4、en-totheirderivedseculareigenfrequencies,possiblyduetotheablestheeffectsofmeanmotionnear-resonancesinthissystemunmodelledeffectofthesenear-resonances.Thefirstanalyticaltobemodelled.TheresultsareinverygoodagreementwithtreatmentofthesephenomenawasperformedbyMalhotr

5、aetthefilteredoutputofanumericalintegrationbyMalhotraetalal(1989)(hereafterreferredtoasMFMN)inwhichtheeffects(1989).Theadditionalcomplexitiesofstudyingtheoutersolarofthe2:1Umbriel-Titaniaandthe3:2Titania-Oberonnear-systemusingasimilarapproacharediscussed.resonanc

6、esontheLaplace-Lagrangemodelwerequantified.Theresultwasfoundtobeinverygoodagreementwithanu-Keywords:celestialmechanics–satellites:satellitesofUranusmericalintegrationdescribedinthesamepaper.However,there–methods:analyticalstillremainedadiscrepancyexceedingthe1%le

7、vel(abench-marksetbytheirresultsfortheinclinationvariations)thatcanprobablybeattributedtotheeffectofweakernear-resonances.Thesubjectofthispaperisthedescriptionandrigorous1.Introductiontestingofamodelthatisbasedonageneraltheoryofthesec-ondorderinthemasses.Thiswas

8、describedindetailbyDuriezThesatellitesystemoftheplanetUranusisanidealtesting(1979)andwassubsequentlypresentedinamoresystematicgroundforsecularperturbationtheoriessinc