Question

The height of a geostationary satellite is

• A. 1000 km
• B. 32000 km
• C. 36000 km
• D. 850 km

Answer 1

Answer: (C)

A satellite which revalues around the earth in its equatorial plane with the same angular speed and in the same direction as the earth rotates about its own axis is called a geostationary or synchronous satellite.
The height of a satellite above the earth's surface is given by
$h={\left(\frac{T^2{R}^{2}g}{4{\pi }^2}\right)}^{1/3}-R$
But T = 24 h = 86400 s
R = radius of earth = 6400 km
$g=9.8m{s}^{-2}=0.0098km{s}^{-2}$
= $h={\left(\frac{(86400{)}^2\times (6400{)}^2\times 0.0098}{4\times 9.87}\right)}^{1/3}$
d = 42330 - 6400 = 35930 km
= 36000 km