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Homework Help: Satllite Crashing into the Moon

  1. Dec 17, 2014 #1
    < Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

    An unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 50.0km . To the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 20.0m/s
    If nothing is done to correct its orbit, with what speed (in km/h) will the spacecraft crash into the lunar surface?

    What I've done is used the formula for circular orbit to find initial velocity. v=sqrt(GM/R). I got the velocity and subtracted 20 m/s to account for lost speed. I then used potential and kinetic energy to set up an equation such
    KEfinal=KEinitial+Uinitial using the formula U=GM/R. I got the wrong answer. I thought about it and decided that I had to account for Gravitational Potential energy at the surface of the moon. Thus KEfinal+Usurface=KEinitial+Uinital -> KEfinal=KEinitial+Uinitial-Usurface. My answer is 5785 km/h but the correct answer is 6060 km/hr. (if anyone wants to know I've disregarded mass of the satellite b/c it cancels out in the equation). I would appreciate any help. I've never posted here so please excuse my formatting.

    Constants are M=7.35X10^22 kg
    R=1.74X10^6 m
    Last edited by a moderator: Dec 17, 2014
  2. jcsd
  3. Dec 17, 2014 #2


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    Staff: Mentor

    You've almost got it. Find ##\xi = \frac{v^2}{2} - \frac{GM}{r} ## which is the specific mechanical energy of the new orbit. Note that it's the sum of the per-unit-mass KE and PE, where the zero reference for PE is at infinity. For any unperturbed orbit the specific mechanical energy is a constant over the whole orbit.

    Then you can find the the speed v at any distance along the orbit using the fact that ##\xi## is a constant.
  4. Dec 17, 2014 #3


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    Science Advisor
    Homework Helper
    Gold Member

    Your method is fine but I get the book answer. Please post your working.
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