Question #104643
At which height from the surface of the earth a satellite has to revolve around the earth if it is a geosynchronous satellite? It is given that R" = 6.4 × 10* m, g. = 9.8 m s2 ⁄ .
1
Expert's answer
2020-03-05T09:42:20-0500

The Kepler's third law says


T2=4π2r3GM=4π2r3gR2T^2=\frac{4\pi^2 r^3}{GM}=\frac{4\pi^2 r^3}{gR^2}

Hence, the radius of the satellite's orbit


r=gR2T2/4π23r=\sqrt[3]{gR^2T^2/4\pi^2}=9.8×(6.4×106)2×(24×3600)24π23=4.23×107m.=\sqrt[3]{\frac{9.8\times (6.4\times10^6)^2\times(24\times 3600)^2}{4\pi^2}}=4.23\times 10^7\:\rm m.

Finally, the height from the surface of the earth to the satellite


h=rR=4.23×1076.4×106=3.6×107m=36000km.h=r-R=4.23\times 10^7-6.4\times 10^6=3.6\times 10^7\:\rm m=36\:000\:\rm km.

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