A second order Laplace-Lagrange theory

《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