(adsbygoogle = window.adsbygoogle || []).push({}); 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???

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# Homework Help: Energy of Planetary Motion

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