1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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 :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook