For a satellite to orbit around the earth, which of the following must be true ?
a) It must be above the equator at some time
b) It cannot pass over the poles at any time
c) Its height above the surface cannot exceed 36,000 km
d) Its period of rotation must be > 2√( R / g)

Plane of orbit of the satellite may not lie in the equatorial plane , but its centre must coincide with the centre of earth. Radius of radius (r) must be greater than the radius of earth (R) . Hence r = R +h .Here h is the height above the surface of earth. Time period of rotation of the satellite is given by$m{\omega }^{2}r=\frac{GMm}{r^2}\Rightarrow {\left(\frac{2\pi }{T}\right)}^{2}r=\frac{GM}{r^2}$

$T^2=\left(\frac{4{\pi }^2}{GM}\right)r^3\Rightarrow \Rightarrow T^2=\frac{4{\pi }^2}{R^2\left({\displaystyle \frac{GM}{R^2}}\right)}{r}^3$

$T=2\pi \sqrt{\frac{r^3}{g{R}^2}}$

$\sin ce r>R, T>2\pi \sqrt{\frac{R}{g}}$