Question

A satellite rotating in the same sense as earth in equatorial orbit has a time period of $6hrs$ at a certain instant, it is directly overhead an observer on the equator of the earth. It is directly overhead the observer at a time ${}^{\prime }{t}^{\prime }$ again. The correct value of ${}^{\prime }{t}^{\prime }$ is :

• A. $8hrs$
• B. $4.8hrs$
• C. $12hrs$
• D. $24hrs$

Answer 1

The correct option is A $8hrs$

It is given that satellite and earth rotates in same sense.

$T_s=6hrs$

${\omega }_s=\frac{2\pi }{T_s}=\frac{2\pi }{6}rad/h$

$T_e=24hrs$

${\omega }_e=\frac{2\pi }{T_e}=\frac{2}{24}rad/h$

Angular velocity of satellite with respect to earth,

$\omega ={\omega }_s-{\omega }_e$

$\omega =\frac{2\pi }{6}-\frac{2\pi }{24}$

$\omega =\frac{2\pi }{8}rad/h$

Let the satellite be overhead again after at time $t$. When seen from the earth the satellite would rotate $2\pi$

$\omega =\frac{2\pi }{8}t=2\pi$

$t=8hrs$

The correct option is A.