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Homework Help: Orbital motion

  1. Aug 28, 2013 #1


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    I'm given the position vector as a function of time for a particle (b, c and ω are constants):

    [itex]\vec{r(t)} = \hat{x} b \cos(ωt) + \hat{y} c \sin(ωt)[/itex]

    To obtain it's velocity i differentiate [itex] \vec{r(t)} [/itex] with respect to time and i obtain:

    [itex]\vec{v(t)} = -\hat{x} ωb \sin(ωt) + \hat{y} ωc \cos(ωt)[/itex]

    Now i have to describe the orbit of this particle. I'm quite clear that if b=c the orbit is perfectly circular with constant tangential speed. But if b≠c (let's say b>c) is the motion elliptical with ±b as the semi-major axis?
  2. jcsd
  3. Aug 28, 2013 #2


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    Staff: Mentor

    Yes, the larger value will determine the semi-major axis, the smaller will determine the semi-minor axis of an elliptical trajectory. Your expression for r(t) is one form of the equation for an ellipse.
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