Two satellites are revolving round the earth at different heights. The ratio of their orbital speeds is 2: 1. If one of them is at a height of 100 km what is the height of the other satellite?

Explanation

Mass of earth, `m=6xx10^(20) kg`
`G=6.67xx10^(-11) N-m^2`/`kg^2`
Ratio of orbital velocities `V_(0_1): V_(0_2)=2:1`
Height of one satellite, h=100 km
But `V_(@)=sqrt((GM)/(R+h))`
By squaring on both sides `(Gm)/(R+h_1)=(1)/(4)(Gm)(R+h_2)`
` implies 4(R+h_2)=R+h_1`
`4R+4h_2=R+h_1 impliesh_1=3R+4h_2`.
Put `h_2=100 km`
`:. h_1=3xx6400+400=19600` km.