3) (ex) W.E.T. for satellite orbit: Ignore air resistance and the rotation of the earth itself (which cannot\ be ignored in a real situation). A satellite of mass m begins at rest at the earths surface, and is then\ taken by a rocket up to a circular orbit at height h above the earths surface. As always, simplify all\ symbolic results, in terms of only m, h, and/or known constants.\ a) Find the following quantities:\ i) Speed of the satellite\ ii) Initial mechanical energy (KE + PE) of the satellite (while on the earths surface)\ iii) Final mechanical energy (KE + PE) of the satellite (while in orbit)\ iv) Work done by the rocket\ b) Calculate values for all of the above if m = 100 kg, and h = 5\ 1061.1 m (100 miles).\ c) When the satellite is gravitationally bound to earth, the total mechanical energy (KE + PE) is\ negative. Do your results agree with this, at both the initial and final situations?\ d) Use your symbolic results above to prove the following facts which are true for any satellite in\ circular orbit:\ i) The total mechanical energy is equal to the negative of the kinetic energy.\ ii) The total mechanical energy is equal to the half of the potential energy.\ e) How much additional work would a rocket need to do in order to free this satellite from earths1\ gravity? (Hint: To just barely escape, or be free from the earths gravity, as r , both KE\ 0 and PE 0 , and so the total mechanical energy 0 . If the satellite were gravitationally\ free then the total mechanical energy 0 .)