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Homework Help: Fortran - equation of motion, astronomical units

  1. Dec 14, 2014 #1
    1. The problem statement, all variables and given/known data
    Euler method : Plot the trajectory of a body moving under the influence of the suns gravity from initial conditions x=1, y=0, vx=0, vy=1.
    My trouble is figuring out my function.

    2. Relevant equations
    d2r / dt2 = -r/r3

    3. The attempt at a solution
    What I have been doing previously is breaking the function into x and y components, so for finding vx(i+1) I use Fx, as for vy and Fy.
    So for this case;
    Fx = -(x+0)/(SQRT(x2 + 0)3
    Fy = -(0+y)/(SQRT(0 + y2)3

    Is this right?
  2. jcsd
  3. Dec 14, 2014 #2


    Staff: Mentor

    What you wrote doesn't seem right.

    Are you familiar with polar coordinates?
  4. Dec 14, 2014 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    I wouldn't think so. Generally, for polar coordinates, r2 = x2 + y2, thus your definitions of Fx and Fy don't make sense.
  5. Dec 14, 2014 #4
    Im not here no, there is no mention on my handout but could you go on anyway? regarding polar that is
  6. Dec 14, 2014 #5


    Staff: Mentor

    Where is the sun, at (0, 0)?
    Does the plain 'r' denote the magnitude of ##\vec{r}##? To be clearer, you can write it as |r|.
    What does this part -- "so for finding vx(i+1) I use Fx, as for vy and Fy." -- mean?
    Last edited: Dec 14, 2014
  7. Dec 14, 2014 #6
    I assume the Sun must be at (0,0) yes. And yes r = |r|.
    Also, how do you do the vector notation?
    Regarding your edit to the code;
    I proceed as follows;
    x(i+1) = x(i) + vx(i).dt
    vx(i+1) = vx(i) + ax(i).dt where ax(i)=Fx i.e.; -r/|r|3
    It follows as with my trajectory problem you helped with previously.
    Last edited: Dec 14, 2014
  8. Dec 14, 2014 #7


    Staff: Mentor

    I had another question that I didn't get the quotes right, so you might have missed it.
    Since I don't know what the above means, I can't comment on what you have for vx below.

    # # \vec{r} # # - take out the spaces between the first and second pair of # characters.
  9. Dec 14, 2014 #8
    I've solved it now I just had to go from the beginning to understand things, no need for polar.
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