Question

22.一艘宇宙飞船绕着某行星作匀速圆周运动,已知运动的轨道半径为r,周期为T,引力常量为G,行星半径为R.求：

Answer 1

GMm/r^2=mr(2pai/T)^2得

M=4pai^2r^3/GT^2

GMm/R^2=mg

g=GM/R^2=4pai^2r^3/T^2R^2

GMm/R^2=mv^2/R

v=(GM/R)^(1/2)=(4pai^2r^3/RT^2)^(1/2)