Question

A geostationary satellite is at a height h above the surface of earth. If earth radius is R

• A. The minimum colatitude on earth upto which the satellite can be used for communication is $si{n}^{-1}$ (R/R + h).
• B. The maximum colatitudes on earth upon which the satellite can be used for communication is $si{n}^{-1}(R/R+h)$
• C. The area on earth escaped from this satellite is given as $2\pi R^2(1+sin\theta )$
• D. The area on earth escaped from this satellite is given as $2\pi R^2(1+cos\theta )$

Answer 1

The correct option is C The area on earth escaped from this satellite is given as $2\pi R^2(1+sin\theta )$

From diagram $\sin \theta =\frac{R}{R+h}$

minimum co altitude $={\sin }^{-1}\left(\frac{R}{R+h}\right)$

The curved area $AB$ on earth $=2\pi R^2\left(1-\sin \theta \right)$

Area on earth escaped from satellite $=4\pi R^2-2\pi R^2\left(1-\sin \theta \right)$

$=2\pi R^2\left(1+\sin \theta \right)$

Hence ,Option $C$ is correct.