# Euler's Method and Planetary Motion

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1. Apr 24, 2015

### antintheagora

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

2nd Law
F = m*a

Law of Universal Gravitation
F = -G*M1*M2/r^2

3. The attempt at a solution

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^2

I 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.

Last edited: Apr 24, 2015
2. Apr 25, 2015

### haruspex

you've omitted centripetal acceleration.