Question

A satellite close to the earth is in orbit above the equator with a period of revolution of $1.5hours$ in the same sense as that of the earth. If it is above a point $P$ on the equator at some time, it will be above $P$ again after a time.

• A. $1.5hours$
• B. $1.6hours$ if it is rotating from west to east
• C. $\frac{24}{27}$ hours if it is rotating from west to east
• D. none of these

Answer 1

Answer: (B)

$1.6hours$ if it is rotating from west to east

Given $T_s=1.5$ and $T_e=24$
So, ${\omega }_s=\frac{2\pi }{1.5}=\frac{4\pi }{3}radians/hr$
similarly ${\omega }_e=\frac{\pi }{12}radians/hr$
relative $\omega ={\omega }_s-{\omega }_e=\frac{4\pi }{3}-\frac{\pi }{12}=\frac{5\pi }{4}$
Relative $T=\frac{2\pi }{\frac{5\pi }{4}}=1.6hrs$
So, it will above point $P$ after $1.6hrs$.