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Homework Help: Energy of Planetary Motion

  1. Feb 23, 2010 #1
    1. The problem statement, all variables and given/known data
    OK so here goes.

    I'm using an ODEsolver in java to plot the total energy over time of a planetary system. So I've been trying to calculate the rate of energy (per unit mass), [tex]\frac{E}{m}[/tex].

    2. Relevant equations
    The equation for total energy (per unit mass) of a planetary system is:
    [tex]\frac{E}{m}=1/2\cdot v^2-\frac{G\cdot M}{r}[/tex]

    G is the gravitational constant
    M is the mass of the sun (constant)
    v is the velocity of the planet, [tex]v^2=v^{2}_{x}+v^{2}_{y}[/tex]
    r is the distance of the planet from the sun, [tex]r^2=x^{2}+y^{2}[/tex]

    Essentially I need help finding [tex]\frac{dE}{dt}[/tex]

    3. The attempt at a solution
    The answer I got for the rate is:

    [tex]\frac{dE}{dt}=v\cdot\left(a+\frac{G\cdot M}{r}\right)[/tex]

    where a is the acceleration of the planet, [tex]a^2=a^{2}_{x}+a^{2}_{y}[/tex]

    The problem is that everytime I throw this equation into the ODEsolver, I get a plot of ever-increasing energy as time goes on which I know is not correct.

    Help anybody???
  2. jcsd
  3. Feb 23, 2010 #2


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    Isn't dE/dt = 0 because energy is conserved? Am I missing something here?
  4. Feb 23, 2010 #3
    YES!!! Of course it is.... what was I thinking. But this creates a whole problem... I've got to figure out how to plot E now inside the program without using the ODEsolver, which hasn't been mentioned in the book yet. *sigh*

    Thanks for clarifying :)
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