问题 问答题

在半径为R=1.6×106m某星球上,宇航员在离地面5m高处自由释放一个物体,物体落地时速度大小为9m/s.不计空气阻力和星球自转,求:

(1)求该星球表面的重力加加速度;

(2)若宇航员乘坐的宇宙飞船在离该星球表面高度为H=3R处绕该星球做匀速圆周运动,求飞船的速率.

答案

(1)由v2=2gh

可知:g=

v2
2h
=8.1m/s2

(2)设该星球质量为M,宇宙飞船的质量为m,则:

宇宙飞船在该星球表面时有:G

Mm
R2
=mg

宇宙飞船做匀速圆周运动时有:G

Mm
(R+H)2
=m
v12
R+H

H=3R   

由以上三式可知:v1=1.8×103m/s

答:(1)该星球表面的重力加加速度为8.1m/s2

(2)飞船的速率为1.8×103m/s.

单项选择题
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