题目内容
(15分)我国发射的“嫦娥一号”卫星发射后首先进入绕地球运行的“停泊轨道”,通过加速再进入椭圆“过渡轨道”,该轨道离地心最近距离为L1,最远距离为L2,卫星快要到达月球时,依靠火箭的反向助推器减速,被月球引力“俘获”后,成为环月球卫星,最终在离月心距离L3的“绕月轨道”上飞行,如图所示.已知地球半径为R,月球半径为r,地球表面重力加速度为g,月球表面的重力加速度为
,求:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500371070811940.png)
(1)卫星在“停泊轨道”上运行的线速度大小;
(2)卫星在“绕月轨道”上运行的线速度大小;
(3)假定卫星在“绕月轨道”上运行的周期为T,卫星轨道平面与地月连心线共面,求在该一个周期内卫星发射的微波信号因月球遮挡而不能到达地球的时间(忽略月球绕地球转动对遮挡时间的影响).
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710677389.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/2014082500371070811940.png)
(1)卫星在“停泊轨道”上运行的线速度大小;
(2)卫星在“绕月轨道”上运行的线速度大小;
(3)假定卫星在“绕月轨道”上运行的周期为T,卫星轨道平面与地月连心线共面,求在该一个周期内卫星发射的微波信号因月球遮挡而不能到达地球的时间(忽略月球绕地球转动对遮挡时间的影响).
(1)v1=
(2)v2=
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250037107701211.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710786430.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710723635.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710739710.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250037107701211.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710786430.png)
(1)
=m![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710833477.png)
=mg,得v1=
.
(2)G
=m![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710911509.png)
G
=mg月,解得:v2=
.
(3)cos α=cos∠DOA=![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710973610.png)
cos β=cos∠CO′B=![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710989450.png)
t=
T=![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250037107701211.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710786430.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250037110989466.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710817871.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710833477.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710848857.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710723635.png)
(2)G
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710895764.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710911509.png)
G
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710926706.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710739710.png)
(3)cos α=cos∠DOA=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710973610.png)
cos β=cos∠CO′B=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710989450.png)
t=
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003711020581.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250037107701211.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003710786430.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250037110989466.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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