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Need help with a problem involving planets and moons.

  1. Jan 27, 2009 #1
    1. The problem statement, all variables and given/known data
    While a planet P rotates in a circle about its sun, a moon M rotates in a circle about the planet, and both motions are in a plane. Let's call the distance between M and P one { lunar unit}. Suppose the distance of P from the sun is 2100 lunar units; the planet makes one revolution about the sun every 2 years, and the moon makes one rotation about the planet every 0.25 years. Choosing coordinates centered at the sun, so that, at time t=0 the planet is at (2100, 0), and the moon is at (2100, 1), then the location of the moon at time t, where t is measured in years, is (x(t), y(t)).

    Find equations for x(t) and y(t)


    2. Relevant equations
    Parametric equations of a circle:
    x = rcos(t)
    y = rsin(t)

    3. The attempt at a solution
    Seems like a fairly straightforward problem, except that it doesn't indicate whether the planets rotate counter-clockwise or clockwise. I've emailed my professor asking to clear up that point, but in the meantime, I'm assuming they both rotate clockwise.

    My professor says counter-clockwise. I'm adjusting the equations to make it that way.

    Using some intuition, I got the equations:
    x(t) = 2100*cos(-pi*t) + sin(-2*pi*t)

    y(t) = 2100*sin(-pi*t) + cos(-2*pi*t)

    in other words, x(t) = x-position of the planet + x-position of the moon. Same for y(t)

    I'm fairly sure these equations describe the motion of the moon correctly, but apparently, they are not the correct answers (it's an online submission process).

    Any thoughts?
     
    Last edited: Jan 28, 2009
  2. jcsd
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