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一直有一个说法,三颗同步卫星能覆盖全球,事实上这只是一个以讹传讹的说法而已,下面我们来详细分析一下.假设地球半径为R,质量为M;同步卫星半径为r,质量为m,同步卫星绕地球公转周期与地球自转周期相同,设为T.由万有引力定律和向心力公式有:G(Mm)/(r~2)=m((2π)/T)~2r,由北极向下俯视地球,可作出图1,其中M=5.974×10~(24) kg,T=24×3600=86400 s,G=6.67×10~(-11)N·m~2/kg~2,计算得r=42.157×10~6 m.一颗卫星所覆盖的地球区域为地球球冠的表面,其赤道剖面图如图1,θ为经度角.
There has been a saying that three geostationary satellites can cover the whole world, in fact this is only a false assertion of false assertion, let’s analyze in detail below.If the earth radius is R, the mass is M, the radius of the satellite is r, the mass is m, The revolution period of the geostationary satellite around the Earth is the same as that of the Earth’s rotation, and is set as T. The law of gravitation and centripetal force is: G (Mm) / (r ~ 2) = m (2π) / T) ~ 2r, Looking down at the earth, we can make Figure 1, where M = 5.974 × 10 ~ (24) kg, T = 24 × 3600 = 86400 s, G = 6.67 × 10 ~ (-11) N · m ~ 2 / kg ~ R = 42.157 × 10 ~ 6 m. The earth area covered by a satellite is the surface of the Earth’s spherical crown. The equatorial cross section is shown in Figure 1, and θ is the longitude angle.