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Integrating gravitational acceleration of particles for simulation

  1. Apr 9, 2013 #1
    I've tried out the two body problem and tried to work out the trajectories with respect to their center of mass frame(located at the origin) as follows (it worked!:smile:):

    particles = m1 and m2
    Fm1 = force of m2 on m1
    Fm2 = force of m1 on m2

    a = Gm2[itex]\hat{r}[/itex] / r2
    [itex]\hat{r}[/itex] is the unit vector
    [itex]\hat{r}[/itex] = r/|r|
    a m1 = Gm2 r / |r|^3
    r = √(x^2 + y^2)

    and did this for both a1 and a2 but my doubt is this:
    why is there a substitution for r vector only when the denominator term stays constant (magnitude).
    Wouldn't this imply that particles slows down when r vector decrease?!

    at each time intervals shouldn't the magnitude of vector connecting two particles change too? please help.
    also why can't type in complex equation forms (am1 = [itex]\frac{Gm2[itex]\hat{r}[/itex] }{r2}[/itex]). it shows the syntax instead of formatted text.
    Last edited: Apr 9, 2013
  2. jcsd
  3. Apr 9, 2013 #2


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    2017 Award

    Staff: Mentor

    What do you mean with that?
    The denominator stays constant for circular orbits only.
    In general, it does.

    Do not nest [itex] and BB-Code tags, that does not work.
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