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Ran into this differential equation, got stuck

  1. Aug 14, 2013 #1
    Trying to make a calculation and I ran into the following diff equation:

    r''=a+b/r^2

    And I can't seem to remember how one would go about solving it.

    b = 1355041.84
    r(0) = 1400
    r(t) = 239.6
    r'(o) = 0
    r'(t) = 75.2
    a = ?

    I'm specifically looking to find the value of the constant a. If someone could drop off a quick solution that would be great! :smile:

    (Note: this is part of an attempt to calculate the maximum acceleration of a starship from a video game cutscene as it approaches a small(is) object with a powerful gravity field)
     
  2. jcsd
  3. Aug 14, 2013 #2

    HallsofIvy

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    What do you mean by "r'(t)= 75.2"? What value of "t"? "a" is just a parameter in the problem that has to be determined by additional information. Perhaps "r'(t)= 75.2" is that "additional information" but I don't understand what it means.
     
  4. Aug 14, 2013 #3
    I don't know how long it took the ship to accelerate since the scene skips to the slingshot.

    All I know is the distance traveled (from a starting distance of 1400km to a distance of slightly over 239.6km), the velocity of the ship as it reached the closer radius, the fact that the ship wasn't moving at t=0 and the fact that the gravity acceleration of the miniature sun it was slingshotting around was about 1355041.84/r^2.

    That should be enough conditions to calculate a final answer, I just can't recall how to solve that kind of a differential equation.

    [EDIT] Note that I'm not calculating the gravity slingshot maneuver that was preformed right after that approach, only the approach itself.
     
  5. Aug 14, 2013 #4
    Nevermind, I just realized that I could calculate the whole thing via gravitational potential energy and hilariously enough the figure came out as higher than the speed of the ship itself...

    Thanks anyway! ^_^
     
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