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Gravitation energy 4

  1. Jun 23, 2014 #1
    1. The problem statement, all variables and given/known data
    A satellite orbits at radius r1. What is the energy required to pass it to a greater radius r2. express in terms of m and g

    2. Relevant equations
    The total energy of a satellite: ##E=-\frac{GMm}{2r}##

    3. The attempt at a solution
    $$E=-\frac{GMm}{2r_2}+\frac{GMm}{2r_1}=-\frac{RGMm}{R2r_2}+\frac{RGMm}{R2r_1}=\frac{Rgm}{2}\left( \frac{1}{r_1}-\frac{1}{r_2}\right )$$
    The answer in the book:
    $$\frac{R^2gm}{2}\left( \frac{1}{r_1}-\frac{1}{r_2} \right)$$
     
  2. jcsd
  3. Jun 23, 2014 #2

    Orodruin

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    A good first check is to make sure that the physical dimensions are consistent in every step. Your answer has dimensions energy/length and is therefore wrong. I suggest controlling the intermediate steps.
     
  4. Jun 23, 2014 #3
    I found the mistake, Thanks, it helped
     
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