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Work caused by gravity

  1. Oct 10, 2008 #1
    1. The problem statement, all variables and given/known data
    A 2500 kg space vehicle, initially at rest, falls vertically from a height of 3100 km above the Earth's surface.


    2. Relevant equations
    [tex]\frac{m_1m_2}{r^2}G=F_g[/tex]
    [tex]W=\int_a^b Fcos\theta dl[/tex]


    3. The attempt at a solution
    [tex]W=\int_a^b F_g dl[/tex]
    [tex]r=r_{Earth} + r_{ship}[/tex]
    [tex]W=\int_a^b \frac{m_1m_2}{r^2}G[/tex]
    [tex]W=m_1m_2G\int_a^b r^{-2} dl[/tex]
    [tex]W=m_1m_2G\bigg[-\tfrac{1}{r}\Big|_a^b\bigg][/tex]
    [tex]W=m_1m_2G\bigg[-\frac{1}{r_{Earth} + r_{ship}}\Big|_a^b\bigg][/tex]
    [tex]W=m_1m_2G\bigg[-\frac{1}{r_{Earth} + a}+\frac{1}{r_{Earth} + b}\bigg][/tex]
    [tex]a=3.1*10^6m; b=0[/tex]
    [tex]W=(2500)(5.98*10^{24})(6.67*10^{-11})\bigg[-\frac{1}{(6.38*10^6) + (3.1*10^6)}+\frac{1}{(6.38*10^6) + 0}\bigg][/tex]
    [tex]W=5.1*10^{10}[/tex]

    I believe this work is correct, can someone verify that my integral is correct please?
     
  2. jcsd
  3. Oct 11, 2008 #2

    D H

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    Staff Emeritus
    Science Advisor

    Looks good!
     
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