Question

A是地球的同步卫星,另一卫星B也位于赤道平面内,离地高度为h,运行周期为T.已知地球半径为R,地球自转角速度

Answer 1

(1) VB=ωB(R+h)=(2π/T)(R+h)=2π(R+h)/T

(2) GMm/(R+h)²=mVB²/(R+h)

M=VB²(R+h)/G=4π²(R+h)³/GT²

(3) GMm/R²=mV1²/R

V1²=GM/R=4π²(R+h)³/RT²

V1=2π(R+h)[√(R+h)/R]/T

(4) 同步卫星角速度与地球自转角速度相同为ω0

GMmA/(R+H)²=mAω0²(R+H)

(R+H)³=GM/ω0²=4π²(R+h)³/ω0²T²

H=三次根号下4π²(R+h)³/ω0²T² -R