A 400 kg satellite is in a circular orbit of radius 2R_E about the Earth. How much energy is required to transfer it to a circular orbit of radius 4R_E?

A 400 kg satellite is in a circular orbit of radius 2R_E about the Ear

1.	A 400 kg satellite is in a circular orbit of radius 2R_E about the Earth. How much energy is required to transfer it to a circular orbit of radius 4R_E?
Answer» Solution :Initially `E_i=(GM_E m)/(4R_E)` While finally `E_f=-(GM_E m)/(8R_E)` The change in the TOTAL ENERGY is `DELTAE=E_f-E_i` `=(GM_E m)/(8R_R)=((GM_E)/R_E^2)=(mR_E)/8` `DeltaE=(GM R_E)/8=(9.81xx400xx6.37xx10^6)/8=3.13xx10^9` J