If the height of a satellite completing one revolution around the earth in T seconds is `h_1` meter, then what would be the height of a satellite taking 2 `sqrt2`T seconds for one revolution?

Explanation

1st case `T_1`=T and `r_1 = h_1`
2nd case `T_2 =2sqrt2T` and `r_2=h_2`=?
`T^2 prop r^3`
`T^2 = kr^3 ` (1st case)
`T_1^2 = kr_1^3`
`T_1^2 = kh_1^3` …(i)
`T_2^2=Kr_2^3` (2nd case )
`[2sqrt2T]^2 = kh_2^3`
`8T^2 = kh_2^2`
`8kh_1^3 = kh_2^2`...(i)
`8h_1^3 = h_2^3`
`h_2=2h_1`