382 Universal GravitationQ13.7Ten terms are needed in the potential energy:UUUUUUUUUUU=+++++++++12131415232425343545.With Nparticles, you need iNNiN−=−=∑1212afterms.Q13.8No, the escape speed does not depend on the mass of the rocket. If a rocket is launched at escapespeed, then the total energy of the rocket-Earth system will be zero. When the separation distancebecomes infinite U=0afthe rocket will stop K=0. In the expression 1202mvGM mrE, the massmof the rocket divides out.Q13.9It takes 100 times more energy for the 105kg spacecraft to reach the moon than the 103kgspacecraft. Ideally, each spacecraft can reach the moon with zero velocity, so the only term that needbe analyzed is the change in gravitational potential energy. Uis proportional to the mass of thespacecraft.Q13.10The escape speed from the Earth is 11.2 km/s and that from the Moon is 2.3 km/s, smaller by a factorof 5. The energy required—and fuel—would be proportional to v2, or 25 times more fuel is requiredto leave the Earth versus leaving the Moon.
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .