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Find r'' and Theta''for the Spaceship

  1. Feb 19, 2013 #1
    1. The problem statement, all variables and given/known data
    The spacecraft P is in the elliptical orbit shown. At the instant represented, its speed is v = 13164 ft/sec. Determine the corresponding values of and . Use g = 32.23 ft/sec2 as the acceleration of gravity on the surface of the earth and R = 3959 mi as the radius of the earth.

    I have uploaded an image of the solution.

    2. Relevant equations

    3. The attempt at a solution

    r = 16388 miles

    I've found r' = 9050.85 ft/s and θ' = 0.00011047 rad/s

    But I cannot for the life of mt figure out why I can get θ'' or r''.

    For r''

    ƩFr = mar = m(r'' - rθ'2) = -GmmE/r2

    r'' = -GmE/r2 + rθ'2
    = -3.439x10-8ft4/lbfs4+ 4.095x1023 lbf=s2/lbf)/ 16388miles*5280) + (16388miles*5280)*0.00010472

    r'' = -.93236 ft/s2

    It says this is wrong and I've at a loss for where my mistake is.

    Likewise for θ''

    maθ = m(rθ''+2r'θ') = 0

    Mass cannot equal zero, therefore the summation in the brackets must be equal to zero

    θ'' = -2r'θ/r

    = _2*9050ft/s*(133.63°(π/180))

    θ'' = -.0004879

    This is also incorrect.

    Any help would be appreciated. Thanks.

    Attached Files:

  2. jcsd
  3. Feb 19, 2013 #2


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    Haven't you left out something on the left hand side?
    Last edited: Feb 19, 2013
  4. Feb 20, 2013 #3
    I'm sorry, but I don't see it. As far as I can tell the only force acting on the object is the force of the gravitational pull from the Earth.
  5. Feb 20, 2013 #4


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    Yes, but the left hand side is missing something.
  6. Feb 20, 2013 #5


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    You dropped a 1. Is that just a typo in the OP?
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