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Gravitation (Potential Energy)

  1. Apr 13, 2009 #1
    1. The problem statement, all variables and given/known data
    How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1000 m/s?

    The radius of the asteroid is 565000 m, and the gravitational acceleration near the surface is 2.7 m/s^2


    2. Relevant equations



    3. The attempt at a solution
    I would have thought I could just see how much energy a particle of mass m has moving at 1000 m/s, and then see what radius r would be necessary to produce the gravitation potential energy of the asteroid-particle system equal to the initial kinetic energy. When I do this, solving for r gives me a very small number.
     
  2. jcsd
  3. Apr 13, 2009 #2

    Hootenanny

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    Note that the gravitation field is only valid near the surface of the asteroid. When you move away from the surface you need to use the full gravitational potential formula,

    [tex] U = \frac{GM}{r}[/tex]
     
    Last edited: Apr 13, 2009
  4. Apr 13, 2009 #3
    I know; isn't gravitational potential energy described by

    U = -(GMm)/r ?

    So can't I say that plus (1/2)mv^2 equals zero, and solve for r? When I do that, I get 1158815 meters, but that's not the right answer.
     
  5. Apr 13, 2009 #4
    Hi,
    "The radius of the asteroid is 565000 m, and the gravitational acceleration near the surface is 2.7 m/s^2"
    With this information You can find the mass of the asteroid.
    F=mg , F=GMm/R^2 --> g=GM/R^2 while g=2.7,R=565000.and G=6.67*10^-11 You can find M.

    now, the initial energy of the body is the kinetic energy+potential energy, when the potential energy as stated in the post above is U=-GMm/R.
    What happens in the highest point?
    The body's kinetic energy=0 and he has potential energy equal to -GMm/R+h(max).
    by the energy conservation------> Ei=Ef while i=initial and f=final.
    note:the little m, aka the mass of particle goes away.
    note 2:sometimes i wrote body instead of particle.
    Good luck! Tell me if You get the wrong answer
    note 3: I've seen Your message and You wrote that Ke+Up=0,seems logical, but I don't think its right...well what is the right answer?
     
  6. Apr 13, 2009 #5

    Hootenanny

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    The question asks for the distance from the surface, whereas r is the distance from the centre of the asteroid.
     
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