Question

A satellite revolves in the geostationary orbit but in a direction east to west. The time interval between its successive passing about a point on the equator is (in hrs)

Answer 1

Consider earth as shown in the figure. The satellite is moving in an east west direction.
We know that earth has rotation. Therefore, let ${\omega }_e$ be the angular velocity of earth.
And let ${\omega }_s$ be the angular velocity of the satellite.
Lets assume that $‘T^{\prime }$ to be the time period between successive passings about the equator.
We know that, when a satellite is moving in the geostationary orbit of earth, its angular velocity is the same as that of earth’s angular velocity.
So we can write,
${\omega }_e={\omega }_s$
Now $T=\frac{2\pi }{{\omega }_{rel}}=\frac{2\pi }{{\omega }_e+{\omega }_s}$

$T=\frac{2\pi }{2{\omega }_s}$
For Geostationary satellite $\frac{2\pi }{{\omega }_s}=24\text{hr}$

$T=\frac{2\pi \times 24\times hr.}{2\times 2\pi }$
$T=12\text{hr}$.