1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Orbital motion

  1. Aug 28, 2013 #1


    User Avatar

    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


    User Avatar

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Orbital motion
  1. Orbital motion (Replies: 5)

  2. Orbital Motion (Replies: 17)

  3. Orbital motion (Replies: 10)