GMm |
r2 |
m•4π2r |
T2 |
得:M=
4π2r3 |
GT2 |
(2)研究卫星绕行星做匀速圆周运动,根据圆周运动中向心加速度公式,得:
a=
4π2r |
T2 |
(3)对行星表面可以认为万有引力等于重力,
GMm |
R2 |
1 |
10 |
4π2r3 |
GT2 |
解得:g=
400π2r |
T2 |
答:(1)行星的质量为
4π2r3 |
GT2 |
(2)卫星的加速度为
4π2r |
T2 |
(3)那么行星表面的重力加速度是
400π2r |
T2 |
1 |
10 |
GMm |
r2 |
m•4π2r |
T2 |
4π2r3 |
GT2 |
4π2r |
T2 |
GMm |
R2 |
1 |
10 |
4π2r3 |
GT2 |
400π2r |
T2 |
4π2r3 |
GT2 |
4π2r |
T2 |
400π2r |
T2 |