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Help deriving this elliptical orbit equation?

  1. Apr 19, 2008 #1
    help deriving this elliptical orbit equation??

    Hi guys, this is my first post on these boards. just found out about this forum and im really happy because i often find i need a place like this to ask questions and my prayers are answered!

    im a physics/computer science major in my second year at the University of the Witwatersrand in Johannesburg, South Africa.

    any way.. enough history..

    i need help deriving this equation for an elliptical orbit :

    [tex]\frac{(x + ae)^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1[/tex]

    where e is the eccentricity and for an ellipse e < 1

    i cant find anything useful in my books and dont even know where to start.

    any help would be awesome! thanks!

    Last edited: Apr 19, 2008
  2. jcsd
  3. Apr 19, 2008 #2
    David Morin's book on mechanics explains very clearly on how to derive this equation
  4. Apr 19, 2008 #3
    hmm i dont have david morin's book on mechanics..

    any tips on how to go about deriving this? am i supposed to use the geometry of an ellipse?

  5. Apr 19, 2008 #4
    I assume that you are doing a course in Introductory Mechanics. The book by Kleppner & Kolenkow is really good for such a course. However in that book, the authors have begun from Law of conservation of energy and angular momentum and have derived the polar form of the equation. I believe that this is a good way to do this as it begins from conservation principles.
  6. Apr 19, 2008 #5


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    Welcome to PF!

    Hi skiz! Welcome to PF! :smile:

    Is this a mechanics question (find the orbit of a particle in an electric or gravitational field), or a geometry question (find the equation for an ellipse)?

    Assuming it's mechanics, start with Newton's second law, and remember that the force perpendicular to the "radius" vector is zero. :smile:
  7. Apr 20, 2008 #6
    hey tim, thanks for the welcome!

    yeah its a mechanics course. Our first 6 months are split between "Classical Mechanics" and "Modern Physics/Relativity"

    i find modern physics and relativity really interesting and easy to grasp but classical mechanics is kicking my ass...
  8. Apr 20, 2008 #7


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    Hi skiz! :smile:

    Just remember that nearly all classical mechanics boils down to good ol' Newton's second law …

    force in a particular direction = (rate of) change of momentum in that direction :smile:

    … and in each case you just have to work out which direction gives you the best information (in this case, it's the "transverse" direction).
  9. Dec 13, 2009 #8
    please any one help me??????

    please any one help me to find the equation of eccentricity of object moves in elliptical orbit
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