1. The problem statement, all variables and given/known data A satellite of mass M is in a circular orbit of radius R around the earth. (a) what is its total mechanical energy (where Ugrav is considered zero as R approaches infinity)? (b) How much work wouldbe required to move the satellite into a new orbit, with radius 2R? 2. Relevant equations (a) mv²/R=GMm/R² →→ mv²=GMm/R →→ K=1/2mv²=GMm/(2R), therefore, E=K+U=GMm/(2R)+(-GMm/R)=-GMm/(2R) (b) Here's where I got stuck : This is the correct answer on the book: From the equation Ki+Ui+W=Kf+Uf, W=(Kf+Uf)-(Ki+Ui) =Ef-Ei =-GMm/(2(2R))-(-GMm/(2R)) =GMm/(4R) Here's what I did, instead of using the equation above, Ki+Ui+W=Kf+Uf, I used the WORK-ENERGY THEOREM. But it came out the different answer. W=Kf-Ki=GMm/(4R)-GMm/(2R)=-GMm/(4R) , the same magnitude but different sign. What's wrong with using WORK-ENERGY THEOREM? 3. The attempt at a solution As above.