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antintheagora
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Homework Statement
Hi there,
I wish to use Newton's Laws in conjunction with Euler's Method to model the motion of a planet around a star.
Homework Equations
2nd Law
F = m*a
Law of Universal Gravitation
F = -G*M1*M2/r^2
The Attempt at a Solution
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First I combined the two laws above.
m*a = -G*M1*M2/r^2
Where M1 cancels out.
a = -G*m/r^2
Rewriting a as the second derivative of position gives:
d^2r/dt^2 = -G*m/r^2
Euler's method is incompatible with a second order differential equation, so I tried to write it as a system of coupled first order differential equations.
dr/dt = v
and
dv/dt = -G*m/r^2I guess this is where I'm a little stuck. Does everything appear correct so far? I tried Euler's method on these two but I think my results were incorrect. Any help would be greatly appreciated.
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