Answer to Question #159933 in Classical Mechanics for Yolande

Question #159933
Artificial satellite circles the Earth in a circulated orbit at a location where the accelaration due to gravity is 9 00m/s^2. Determine the orbital period of the satellite.
1
Expert's answer
2021-02-22T10:29:19-0500

g=g0(RR+h)2,R+h=Rg0g,g=GM(R+h)2,g=g_0(\frac{R}{R+h})^2,\\ R+h=R\sqrt{\frac{g_0}{g}},\\g=\frac{GM}{(R+h)^2},

T=4π2(R+h)3GM=2πR+hg=2πRg.g0g,T=\sqrt{\frac{4\pi^2(R+h)^3}{GM}}=2\pi\sqrt{\frac{R+h}{g}}=2\pi\sqrt{\frac Rg. \sqrt{\frac{g_0}{g}}},

T90.2m.T\approx 90.2^m.


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