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Euler's Method and Planetary Motion

  1. Apr 24, 2015 #1
    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. :oldcool:
     
    Last edited: Apr 24, 2015
  2. jcsd
  3. Apr 25, 2015 #2

    haruspex

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    you've omitted centripetal acceleration.
     
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