An Earth's satellite makes a circule around the Earth in `100` minutes. Calculate the height of the satellite above the Earth's surface. Given the radius of the Earth is `6400 km` `g = 10 ms^(-2)`. Use `pi^(2) = 10`.

Explanation

Here, `T = 100 minutes = 100 xx 60 = 6000 s`,
`R = 6400 km = 6.4 xx 10^(6) m , g = 10 ms^(-2)`
`h = ((T^(2) R^(2) g)/(4pi^(2)))^(1//3) - R`
`= [((600)^(2) xx (6.4 xx 10^(6))^(2) xx 10)/(4 xx 10)]^(1//3) - 6.4 xx 10^(6)`
`= 7.171 xx 10^(6) - 6.4 xx 10^(6) = 0.771 xx 10^(6)m`
`= 771 km`