A satellite orbiting the earth in a circular orbit of radius R completes one revolution in 3h. If orbital radius of geostationary satellite is 36000 km , orbital radius of earth is

Step-by-step solution

Time period of satellite T^2= 4 ^2 G M r^3 or T^2= 4 ^2 g R^2 r^3 [ G M=g R^2 ] or T= 2 R r^3 g or T r^ 3 / 2 T₁ T₂ = ( r₁ r₂ )^ 3 / 2 Given, T₁=3 ~h , T₂=24 ~h (geostationary satellite) r₁=R, r₂=36000 ~km 3 24 = ( R 36000 )^ 3 / 2 or R= ( 1 8 )^ 2 / 3 36000 or R= 1 4 36000=9000 ~km