Calculate how much work is required to launch a spacecraft of mass m from the surface of the earth (mass mE, radius RE) and place it in a circular low earth orbit--that is, an orbit whose altitude above the earth's surface is much less than RE. (As an example, the International Space Station is in low earth orbit at an altitude of about 400 km, much less than RE

Work done to shift the spacecraft from Earth surface to low Earth radius is given as

Explanation:

As we know that spacecraft is at surface of Earth initially

So we will have

now when it is at low radius Earth Orbit then we have

now we know that work done to shift the spacecraft from Earth Surface to Low earth orbit is change in total energy

so we have

since we know h << Re

so work done is given as