第三章两体问题习题

1、第三章第三章 两体问题（习题）两体问题（习题）22222222222221222222221cos221)0(221arccos2122arccos22222,0)1(2222)(2d0)(a 1.3lmamalmercmalmerlmacmalmeumallumalmedumallmaleulmameldurlmamerldrrlrvemdrrlravru 故起点使得选则合适的)12(221)0(221122222222,0)2(222222222222222lmashmalmerclmamerarshlmaclmameuarshlmalulmamedulmalmaleulmameldu，故

2、起点使得选则合适的)12(2210221122222222,0)3(222222222222222lmachmalemrclmaemrarchclmaclmaemuarchlmalulmaemdulmalmaleulmameldu，故起点使得选则合适的；第一种情况为周期运动。种，粒子最终吸入力心第故第322,2yeechxyeeshxyxxxxulmaemulmaemtruletculmaemulmaemlmamulmaemudulmamrmlmaemdrrmlraemdrrmlvemdrtma ,le222222222222222222222222222)22(cso , 0,1 )22)2

3、2(2)22(21)2(222 20 )2(mlamlaremetmlamlaermeemlmarlmaemrlmaemlmamulmaemulmaemulmaemulmaemlmamtur222132221)221221)22(2)22)22(22)22(22222222222222222222202lim）同理有（3.2,21)(2121,2222klrrmlmmrr拉相对运动0vr2020202020200000204242,42),(have we,0 mvkllmvlmvkllvmvkllrvrlrkrvmtwhenrrrrrrrrrrrrrmllrkemdrrmlrvemdrtmk

4、(r-l)rlemrldrrlrvemrldk(r-l)v00002222222222222202)(212)(2)/2()(2 21初速度做抛体运动。以加速度质心在以重力加速度为021v3.3xadxxaxvxln)(100202)ln(2ln2ln2ln)ln(21,0lnlnln21aaxadxamxamadxtxamaxaaxaxmxaaaaexaxml且能量守恒3. 5cossin22cossin22cossin221cossin221sinsincossin2121cos)cos(sin2121sinsin2222222222222222222222222222mglmllemld

5、tmglmllemlmglmllmlemglmllmllllmlpmglmlmllmglmglvmlmltelelererervzzzzzr守恒为循环坐标，所以xyzreeenmgcossin2sin2cossin22sinsinsin,sinsin22222222222222mglmlledmllmglmllemldmlldtmllmllllmlzzzzzzz3.622222323222212)()(rcrkmrlrmercrkdrrcrkrvrcrkfr常数mclkmmemclmkrmclmcllrmclrkemdrrmclmcllrmclrkemdrrlrlrvemdrrl2222222

6、22222222222arccos22)(2d2222)(21,1cos1mkmcleemkmclplmcaaepr3.7轨道稳定。代入，有把01)332(133210222222342432223232222drvdmlckrmrlrckrmrlrcrkdrvdmlckrmrlrcrkdrdvmrlrcrkveffeffeffeff3.8clamrmamarltcmlrmamarmamlmlrmardrrmlramdrtrmlvemdrtppryrpxryrxpreemaelemalpepr22222222222222222222223)()(23)(2222,sin,cos,cos1, 1, 021,cos13.10轨道稳定，圆轨道，,0,022221222drvdanmlrdrdvmrlarvarveffneffneffn2, 003) 1(3) 1(3) 1(12222224nalanmlnanmlrnanmlrnanmmrnn，即考虑考虑势能为周期，vdtrgmmdtrgmmdtrrgmrmtrrgmdtvdavdrmtr rdr rrvvdrmrvdmrdvmdtvvmdtmvt21)(121)(21)(2121)0)(,(21)(21121121121111. 300303