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Homework Help: Find minimum energy to escape an orbit

  1. Oct 21, 2011 #1
    1. The problem statement, all variables and given/known data
    When it orbited the Moon, the Apollo 11 spacecraft’s mass was 7170 kg, its period was 121 min, and its mean distance from the Moon’s center was 1.87167 × 106 m. Assume its orbit was circular and the Moon to be a uniform sphere of mass
    7.36 ×1022 kg. Its orbital speed was 1619.837645 m/s

    What is the minimum energy required for the craft to leave the orbit and escape the Moon’s
    gravitational field?
    Answer in units of J



    2. Relevant equations
    Don't know of any
    maybe UG=-Gm1m2/r


    3. The attempt at a solution
    UG=(6.67259*10−11*7.36*1022*7170)/1.87167*106

    But I do not think this is right
     
  2. jcsd
  3. Oct 21, 2011 #2

    Delphi51

    User Avatar
    Homework Helper

    It has to have energy zero to escape. How much energy does it have now?
    Notice the minus sign in your UG=-Gm1m2/r.
    Of course it has kinetic energy, too.
     
  4. Oct 21, 2011 #3

    gneill

    User Avatar

    Staff: Mentor

    You're on the right track, but you need one more piece of the puzzle. The total mechanical energy of a body in orbit is given by the sum of the kinetic and potential energies. In particular,
    [tex] E = m\left(\frac{v^2}{2} - \frac{GM}{r}\right) [/tex]
    The orbit becomes unbound (escape happens) when E ≥ 0.
     
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