Question

The height of a geostationary satellite is

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

Answer 1

Answer: (C)

36000 km

Answer 2

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 $h=\left(\frac{T^2R^2g}{4\pi^2}\right)^{1/3} -R$ But T = 24 h = 86400 s R = radius of earth = 6400 km $g=9.8 ms^{-2}=0.0098 kms^{-2}$ = $h=\left(\frac{(86400)^2\times(6400)^2\times0.0098}{4\times9.87}\right)^{1/3}$ d = 42330 - 6400 = 35930 km = 36000 km