- #1
jmtome2
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Homework Statement
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].
Homework 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]
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?