Using the data given below, find the height at which a communication satellite can reside. ( (G=6.67 10⁻¹¹ ~N - m ^2 ~kg ⁻², M=5.98 10²⁴ . ) ( kg , R=6.4 10^6 ~m ) )

Step-by-step solution

Given, (G=6.67 10⁻¹¹ ~N - m ^2 ~kg ⁻² ) (M=5.98 10²⁴ ~kg , R=6.4 10^6 ~m ) For communication satellite, (T=24 ~h =24 60 60 ~s =8.64 10^4 ~s ) We know that, time period of communication satellite is given as ( aligned T & = 2 (R+h) G M R_e+h =2 (R_e+h )^3 G M T^2 & =4 ^2 (R_e+h )^3 G M R_e+h= ( T^2 G M 4 ^2 )^ 1 / 3 h & = ( T^2 G M 4 ^2 )^ 1 / 3 -R & = [ 8.64 10^4 6.67 10⁻¹¹ 5.98 10²⁴ 4 (3.14)^2 ]^ 1 / 3 -6.4 10^6 & =42.25 10^6-6.4 10^6=35.85 10^6 ~m & =35850 10^3 ~m =35850 ~km aligned )