地球的質(zhì)量M
mg=GMm/R^2
M=gR^2/G
地球同步衛(wèi)星周期T=24 H=86400 s
m*(2π(R+h)/T)^2/(R+h)=GMm/(R+h)^2
4π^2*(R+h)/T^2=GM/(R+h)^2
4π^2*(R+h)/T^2=gR^2/(R+h)^2
4π^2*(R+h)^3/T^2=gR^2
R+h=(g*R^2*T^2/(4π^2))^(1/3)
=(9.8*(6400*1000)^2*(86400)^2/(4*3.1416^2))^(1/3)≈4.23*10^7 (M)=4.23*10^4(km)
h≈4.23*10^4-6400=3.59*10^4 (km)
v=2π(R+h)/T=2*3.14*4.23*10^7/86400≈3079 (M/s)≈3.08 (km/s)
若發(fā)射一顆地球的同步衛(wèi)星,使它在赤道上空運(yùn)轉(zhuǎn),其高度應(yīng)為3.59*10^4km,線速度應(yīng)為3.08 km/s