1、第三章第三章 兩體問題習題兩體問題習題22222222222221222222221cos221)0(221arccos2122arccos22222,0)1(2222)(2d0)(a 1.3LmamaLmErCmaLmErLmacmaLmEumaLLumaLmEdumaLLmaLEuLmamELdurLmamErLdrrLrVEmdrrLraVru 故起點使得選則合適的)12(221)0(221122222222,0)2(222222222222222LmashmaLmErCLmamErarshLmacLmamEuarshLmaLuLmamEduLmaLmaLEuLmamELdu，故起點使得

2、選則合適的)12(2210221122222222,0)3(222222222222222LmachmaLEmrCLmaEmrarchCLmacLmaEmuarchLmaLuLmaEmduLmaLmaLEuLmamELdu，故起點使得選則合適的；第一種情況為周期運動。種，粒子最終吸入力心第故第322,2yeechxyeeshxyxxxxuLmaEmuLmaEmtruletcuLmaEmuLmaEmLmamuLmaEmuduLmamrmLmaEmdrrmLraEmdrrmLVEmdrtma ,LE222222222222222222222222222)22(cso , 0,1 )22)22(2)

3、22(21)2(222 20 )2(mLamLarEmEtmLamLaErmEEmLmarLmaEmrLmaEmLmamuLmaEmuLmaEmuLmaEmuLmaEmLmamtur222132221)221221)22(2)22)22(22)22(22222222222222222222202lim）同理有（3.2,21)(2121,2222klrrmLmmrr拉相對運動0vr2020202020200000204242,42),(have we,0 mvkllmvLmvkllvmvkllrvrlrkrvmtwhenrrrrrrrrrrrrrmLlrkEmdrrmLrVEmdrtmk(r-l

4、)rLEmrLdrrLrVEmrLdk(r-l)V00002222222222222202)(212)(2)/2()(2 21初速度做拋體運動。以加速度質心在以重力加速度為021v3.3xadxxaxVxln)(100202)ln(2ln2ln2ln)ln(21,0lnlnln21aaxadxamxamadxtxamaxaaxaxmxaaaaExaxmL且能量守恒3. 5cossin22cossin22cossin221cossin221sinsincossin2121cos)cos(sin2121sinsin2222222222222222222222222222mglmlLEmldtmgl

5、mlLEmlmglmlLmlEmglmlLmlLLlmlPmglmlmlLmglmglVmlmlTelelererervzzzzzr守恒為循環坐標，所以xyZreeeNmgcossin2sin2cossin22sinsinsin,sinsin22222222222222mglmlLEdmlLmglmlLEmldmlLdtmlLmlLLlmlZZZzzzz3.622222323222212)()(rcrkmrLrmErcrkdrrcrkrVrcrkFr常數mcLkmmEmcLmkrmcLmcLLrmcLrkEmdrrmcLmcLLrmcLrkEmdrrLrLrVEmdrrL22222222222

6、2222222arccos22)(2d2222)(21,1cos1mkmcLEemkmcLPLmcaaepr3.7軌道穩定。代入，有把01)332(133210222222342432223232222drVdmLckrmrLrckrmrLrcrkdrVdmLckrmrLrcrkdrdVmrLrcrkVeffeffeffeff3.8cLamrmamarLtcmLrmamarmamLmLrmardrrmLramdrtrmLVEmdrtppryrpxryrxpreEmaELemaLpepr22222222222222222222223)()(23)(2222,sin,cos,cos1, 1, 021,cos13.10軌道穩定，圓軌道，,0,022221222drVdanmLrdrdVmrLarVarVeffneffneffn2, 003) 1(3) 1(3) 1(12222224naLanmLnanmLrnanmLrnanmmrnn，即考慮考慮勢能為周期，VdtrGMmdtrGMmdtrrGMrmTrrGMdtVdaVdrmTr rdr rrVVdrmrVdmrdVmdtVVmdtmVT21)(121)(21)(2121)0)(,(21)(21121121121111. 300303