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Changing orbits

  1. Jan 14, 2009 #1
    1. The problem statement, all variables and given/known data

    A shuttle orbiting the earth at 400km deploys a satellite of mass 800kg into orbit a further 200km from earth. Calculate the work that must be done by the shuttle to deploy the sattelite.

    2. Relevant equations

    [tex]E_{k} = \frac{GMm}{2r}[/tex], [tex]U = -\frac{GMm}{r}[/tex]

    3. The attempt at a solution

    I tried using [tex]W = \Delta E_{k}[/tex] to solve the problem:

    [tex]800GM\left(\frac{1}{2 \times 600000} - \frac{1}{2 \times 400000}\right)=-1.334 \times 10^{11} J[/tex]

    But the solutions gives [tex]1.4 \times 10^9 J[/tex]

    Moreover, using the following method gives a different answer:

    [tex]\int_{400000}^{600000} \frac{GM(800)}{r^2}dr=2.658 \times 10^{11} J[/tex]

    But I thought [tex]E_{tot} = E_{k} + U[/tex], so [tex]\Delta E_{k} = -\Delta U[/tex] ??

    Could someone tell me why my methods do not work and what the correct method is for dealing with this? Thankyou
  2. jcsd
  3. Jan 14, 2009 #2


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    a case of mistaken Identity …

    Hi Identity! :smile:
    They do work …

    but you need to measure r from … ? :wink:
  4. Jan 14, 2009 #3
    Oh right I need to measure r from the centre of mass XD thanks tiny-tim


    [tex]800GM\left(\frac{1}{2(6.4 \times 10^6 + 600000)} - \frac{1}{2(6.4 \times 10^6 + 400000)}\right)=-6.7 \times 10^8 J[/tex]

    which is still different!

    Also, when the satellite moves from 400km to 600km, is the total energy of the satellite constant? If so, why do I get different answers when working with GPE as opposed to Kinetic energy?
  5. Jan 14, 2009 #4


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    WIhtout seeing the details of your calculation, I can't check it …

    but it would be a lot easier to use the formula 1/r - 1/(r + ∆) ~ ∆/r2 :wink:

    anyway, going to bed now … :zzz:
  6. Jan 14, 2009 #5
    lol I just plugged the whole calculation into my calculator...

    Sorry i'm having some trouble understanding. Can you show me how you would do it?
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