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Orbiting Satellite Homework Help

  1. Apr 7, 2009 #1
    1. The problem statement, all variables and given/known data
    A satellite of mass m is in a circular orbit of radius R_2 around a spherical planet of radius R_1 made of a material with density rho. ( R_2 is measured from the center of the planet, not its surface.) Use G for the universal gravitational constant.

    Find the kinetic energy of this satellite, K.
    Express the satellite's kinetic energy in terms of G, m, pi, R_1, R_2, and p.


    2. Relevant equations

    I have found the mass of the planet to be

    5Cfrac%7B4%7D%7B3%7D%5Cleft%28R_%7B1%7D%5Cright%29%5E%7B3%7D%7B%5Cpi%7D%7B%5Ccdot%7D%7B%5Crho%7D.gif

    The magnitude of the gravitational force on the satellite

    7D%7B%5Ccdot%7D%7B%5Cpi%7D%7B%5Ccdot%7D%7B%5Crho%7D%5Cright%29%7D%7BR_%7B2%7D%7B%5E%7B2%7D%7D%7D.gif

    and the velocity of the satellite to be

    render?infix=sqrt%28G%2A4%2Api%2AR_1%5E3%2Arho%2F%283%2AR_2%29%29.gif





    3. The attempt at a solution

    I thought I could just plug in the velocity of the satellite and the mass of the planet into the equation

    K = 1/2MV^2

    When I did that I did not get the correct answer. Can anyone please point me in the right direction I probably skipped a step along the way somewhere
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 7, 2009 #2

    LowlyPion

    User Avatar
    Homework Helper

    For orbit isn't the condition that

    mv2/r = GMm/r2

    mv2 = GMm/r

    1/2*mv2 = 1/2*GMm/R2

    Plug in M from p*volume
     
  4. Jan 3, 2012 #3
    Your reasoning is valid, just did this problem myself. The most likely error is plugging in the wrong mass in the equation for kinetic energy. Notice that the required mass is listed as m, the mass of the satellite, and not M, the mass of the earth. Use your speed in the formula K = 1/2 m_s v_s^2
     
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