Estimate whether it takes more energy to get a satellite upto `1600 km` above the earth than to put in orbit there. Earth's radius is `6400 km`. Does your answer remain same for height `3200 km` or for height `4800 km`?

Explanation

Energy required to raise a satellite at height `h`
`E_(1)=-(GMm)/((R+h))(-(Gmm)/R)`
`=GMm(1/R-1/(R+h))=(GMmh)/(R(R+h))`
Energy required to put a satellite in orbit at that height `=KE` of satellite
`E_(2)=1/2mv^(2)=1/2m((GM)/r)=(GMm)/(2r)=(GMm)/(2(R+h))`
`(E_(1))/(E_(2))=(2(R+h))/(R(R+h))=(2h)/R=(2xx(1600km))/((6400km))`
`=(1)/(2)=0.5`
clearly, the answer depends on height if `h=3200km`
`(E_(1))/(E_(2))=(2h)/R=(2xx(3200km))/((6400km))=1.10`
for height `h=4800km`
`(E_(1))/(E_(2))=(2xx(4800km))/((6400km))=3/2=1.5`