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Dynamics Homework Help

  1. Feb 17, 2010 #1
    1. The problem statement, all variables and given/known data

    A Satellite is to be placed in an elliptic orbit about the earth. Knowing that the ration Va/Vp of the velocity at the apogee A to the velocity at perigee P is equal to the ration Rp/Ra of the distance to the center of the earth at P to that at A, and the distance between A and P is 80,000 km, determine the energy per unit mass required to place the satellite in its orbit by launching it from the surface of the earth.

    Pic:

    Va v-----Ra---------O----Rp----^ Vp

    |---------80,000km---------|

    2. Relevant equations
    Conservation of Momentum: T1 + V1 = T2 + V2
    T = .5mv^2
    V = - GMm/r


    3. The attempt at a solution
    Va/Vp = Rp/Ra
    Ra = 80,000 - Rp
    E = T + V
    E = 0.5mv^2 - GMm/r
    E/m = .5v^2 - GM/r

    I'm not sure where to go next. I know the final answer is 57.5 MJ/kg. How are all the 'r's and 'v's eliminated by just using the ratio? I'm generally able to solve these questions, but I've been working on this one for hours with no luck. Any help is greatly appreciated!
     
  2. jcsd
  3. Feb 18, 2010 #2

    tiny-tim

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    Homework Helper

    Hi kaos4! :smile:

    It's launched from the surface of the Earth …

    so where is the Earths's radius in your equations? :wink:
     
  4. Feb 18, 2010 #3
    hmm..I considered that. That would give me GM, but still Ra and Rb would be unknown. Unless I am missing something, but the earths radius would just add another number, not eliminate any variable (Earths radius is a part of Ra and Rb). Thanks for the advice though, I will try and see how else I can apply the earth's radius.
     
  5. Feb 18, 2010 #4
    Last edited by a moderator: Apr 24, 2017
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