Question

A remote sensing satellite is revolving in an orbit of radius x over the equator of earth. If the area on each surface in which satellite can not send message is given as $(1-\frac{\sqrt{x^2-R^2}}{x})s\pi R^2$. Find $s$:

Answer 1

Area out of reach of the satellite includes the polar caps, twice the area covered by angle r.

$={\int }_0^{2\pi }{\int }_0^r{R}^2\sin rdrd\varphi$

$=2\pi R^2(1-\cos r)$

From figure, $\cos r=\frac{\sqrt{x^2-R^2}}{x}$

Hence area the satellite cannot send singal is

$2\times 2\pi R^2(1-\frac{\sqrt{x^2-R^2}}{x})$

$=4\pi R^2(1-\frac{\sqrt{x^2-R^2}}{x})$