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.uk)Re

2、ceived18December1996/Accepted11June1997Abstract.Computeralgebraisusedtoderiveanalyticalexpres-AnattemptbyLaskar&Jacobson(1987)tofitthetheorysionsfortheelementsofasecularperturbationtheoryofthedescribedbyLaskar(1986)toVoyagerandEarth-basedobser-secondorderinthemasses.Theline

3、arpartofthistheoryisin-vations,thelatterspanningapproximatelyoneorbitalperiodofcorporatedintothestandardLaplace-LagrangesolutionwhichUranus,necessitatedtheintroductionofempiricalcorrectionsisthenappliedtothemotionoftheuraniansatellites.Thisen-totheirderivedseculareigenfreq

4、uencies,possiblyduetotheablestheeffectsofmeanmotionnear-resonancesinthissystemunmodelledeffectofthesenear-resonances.Thefirstanalyticaltobemodelled.TheresultsareinverygoodagreementwithtreatmentofthesephenomenawasperformedbyMalhotraetthefilteredoutputofanumericalintegrationby

5、Malhotraetalal(1989)(hereafterreferredtoasMFMN)inwhichtheeffects(1989).Theadditionalcomplexitiesofstudyingtheoutersolarofthe2:1Umbriel-Titaniaandthe3:2Titania-Oberonnear-systemusingasimilarapproacharediscussed.resonancesontheLaplace-Lagrangemodelwerequantified.Theresultwasf

6、oundtobeinverygoodagreementwithanu-Keywords:celestialmechanics–satellites:satellitesofUranusmericalintegrationdescribedinthesamepaper.However,there–methods:analyticalstillremainedadiscrepancyexceedingthe1%level(abench-marksetbytheirresultsfortheinclinationvariations)thatca

7、nprobablybeattributedtotheeffectofweakernear-resonances.Thesubjectofthispaperisthedescriptionandrigorous1.Introductiontestingofamodelthatisbasedonageneraltheoryofthesec-ondorderinthemasses.ThiswasdescribedindetailbyDuriezThesatellitesystemoftheplanetUranusisanidealtesting(

8、1979)andwassubsequentlypresentedinamoresystematicgroundforsecularperturbationtheoriessinc