Question

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.

Answer 1

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

$T=\sqrt{\frac{4\pi^2(R+h)^3}{GM}}=2\pi\sqrt{\frac{R+h}{g}}=2\pi\sqrt{\frac Rg. \sqrt{\frac{g_0}{g}}},$

$T\approx 90.2^m.$