《天问》是屈原笔下的不朽诗篇,而“天问”行星探索系列代表着中国人对深空物理研究的不懈追求。如下图所示,半径均为R的两球形行星A、B的密度之比为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmtext%3E%CF%81%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3EA%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmn%3E%3A%3C%2Fmn%3E%3Cmsub%3E%3Cmrow%3E%3Cmtext%3E%CF%81%3C%2Fmtext%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3EB%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E%3A%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmath%3E)
, A、B各有一个近地卫星C、D,其绕行周期分别为:
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ET%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3EC%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
、
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ET%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3ED%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
。站在行星表面的宇航员从距A行星表面高为h处以
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ev%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
水平抛出一物体a,从距B行星表面高为2h处以
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ev%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
水平抛出另一物体b。下列说法正确的是( )
![](http://tikupic.21cnjy.com/2024/05/10/7e/ba/7eba8da45e837a364ef76f06acd998fd.jpeg)
- A、C、D绕A、B运行的速度之比为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E%3A%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmath%3E)
- B、B、D绕A、B运行的周期满足
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ET%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3EC%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3ET%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3ED%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
- C、由于不知道a与b的质量,所以无法求出二者落地时速度之比
- D、a、b两物体从抛出到落地的位移之比为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E%3A%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmath%3E)