当人造卫星绕地球的圆形轨道运动时，其速率与轨道半径之间的关系
\u5728\u5706\u8f68\u9053\u4e0a\u8fd0\u52a8\u7684\u8d28\u91cf\u4e3am\u7684\u4eba\u9020\u5730\u7403\u536b\u661f\uff0c\u5b83\u5230\u5730\u7403\u7684\u8ddd\u79bb\u7b49\u4e8e\u5730\u7403\u534a\u5f84R\uff0c\u5730\u9762\u4e0a\u7684\u536b\u661f\u4f5c\u5706\u5468\u8fd0\u52a8\uff0c\u4e07\u6709\u5f15\u529b\u63d0\u4f9b\u5411\u5fc3\u529b
GmM/4R^2=mv^2/2R......\uff081\uff09
\u5728\u5730\u9762\u6709\uff1amg=GmM/R^2.....(2)
\u5f97\uff1av=\u6839\u53f7\u4e0bgR/2 A\u9519
GmM/4R^2=ma....(3)
\u5f97\uff1aa=g/4 B\u4e0d\u77e5\u9053\u5728\u5199\u4ec0\u4e48
GmM/4R^2=m4\u03c0^2*2R/T^2.....(4)
\u5f97\uff1aT=4\u03c0\u6839\u53f7\u4e0b2R/g C\u5bf9
\u536b\u661f\u7684\u52a8\u80fd\u4e3amv^2/2=1/4mRg D\u5bf9
\u6240\u4ee5\u7b54\u6848\u662fCD
\u5730\u9762,g=GM/R^2,G--\u4e07\u6709\u5f15\u529b\u6052\u91cf,M--\u5730\u7403\u8d28\u91cf,R--\u5730\u7403\u534a\u5f84
\u9ad8\u7a7a,g'=GM/(2R)^2=(1/4)GM/R^2=g/4
\u536b\u661f\u901f\u5ea6\u8bbe\u4e3aV
V^2/(2R)=\u5411\u5fc3\u52a0\u901f\u5ea6a=g'=g/4
V=\u6839\u53f7(Rg/2)...............................................A\u9519
\u5411\u5fc3\u52a0\u901f\u5ea6a=mg'/m=g'=g/4...................................B\u9519
\u52a8\u80fdEk=(1/2)mV^2=m[V^2/(2R)]*R=m(g/4)R=mgR/4...............C\u5bf9
可根据万有引力的公式推导
GMm/R^2=mv^2/R
GM/R=v^2
说明速度只与半径有关系(GM为定值)
R越小,速率越大
V=wR w是卫星环绕地球的角速度 V是线速度
半径越大,速度越小,所受的万有引力越小
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