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Gravitation lab for online simulation-equation derivation help?

  1. May 12, 2010 #1
    gravitation lab for online simulation--equation derivation help?

    1. The problem statement, all variables and given/known data
    To start with, you can access the lab here: http://phet.colorado.edu/teacher_ideas/view-contribution.php?contribution_id=690" [Broken].
    I'm having trouble with the "Activity 4" part. It reads:
    "Change the number of bodies to 3. Notice that the position and velocity for Body 1 and Body 2 changed when you clicked by the 3. Change them back, then set Body 3’s mass to 0.001, its x position to 100, its y velocity to your value from Q7, and its y position and x velocity to 0. Using your equation from Q6, the fact that speed is the distance over time, and the equation for the circumference of a circle, derive an equation for the period of an object in a circular orbit. Show all of your work below."
    You can ignore all the stuff about changing bodies' masses and etc., unless you want to check out the simulation http://phet.colorado.edu/sims/my-solar-system/my-solar-system.swf" [Broken]. I'm more worried about the deriving the equation part of it.

    2. Relevant equations
    The equation from Q6 that it mentioned was derived by me like so (the point was to find what value the sim was using for G, universal gravitational constant): G=v2r / m
    centripetal a= 4pi2r / T2=v2/r
    Fnet = ma
    Circumference=2 *pi* r
    v=x/t

    3. The attempt at a solution
    I'm not sure how to start here! My attempt at a solution was putting the alternate equation for centripetal acceleration with period included in the section above--that truly is the extent of my thinking about it before I hit a brick wall. I don't know how to link velocity and position with period, as well. I'd like a verification that my previous derivation was correct.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. May 17, 2010 #2
    Re: gravitation lab for online simulation--equation derivation help?

    Okay, further attempts at a solution:

    Circumference=2*pi*r
    acentrip. =4pi2r / T2 = (circ)2 / T2

    or maybe ac = v2 / r = (x2/t2) / r = t2 / x2r

    How do I work G=v2r / M into it and make a comprehensive equation out of the whole thing? Any ideas?

    EDIT: maybe if I set t2 / x2r = 4pi2 / T2 and solve for T? would this be a useful direction to go in? Maybe then I can make substitutions.
     
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