1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

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


    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


    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook