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Homework Help: Astrophysics - elliptical orbit proof help.

  1. Aug 29, 2010 #1
    A.)
    Assume a rectangular coord system has its origin at the center of an elliptical planetary orbit and that the coord system x axis lies along the major axis of the ellipse. Show that the equation for the ellipse is given by x^2/a^2 + y^2/b^2 =1.
    where a and b are the lengths if the semi-major axis and the semi-minor axis, respectively.

    b.)
    using the results from a, prove the area of an ellipse is given by A=(pi)ab.

    Im am completely lost right now. Any ideas?
     
  2. jcsd
  3. Aug 29, 2010 #2

    diazona

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    For starters, what facts do you know about an ellipse that you could use in the proof?
     
  4. Aug 29, 2010 #3
    (x-h)^2/a^2 + y-k)^2/b^2=1

    c^2= a^2 -b^2

    while a ≥b>0
     
  5. Aug 29, 2010 #4

    diazona

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    OK, well for part a, for the ellipse in question, what would h and k be?
     
  6. Aug 29, 2010 #5
    zero, so (x-h)^2 = x^2 and (y-k)^2= y^2 right?
     
  7. Aug 29, 2010 #6

    diazona

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    Right, so that part's done. (Although it seems really simple, are you sure you can use that equation as a starting point?)

    Now what about part b? How could you find area?
     
  8. Aug 29, 2010 #7
    thats what the text tell you to use. That does seem really simple, maybe thats why im so lost.

    B) i know the area A=piab
    so the way i was looking at it
    solve for y? then integrate it, with trig sub get pi ab?
     
  9. Aug 29, 2010 #8

    diazona

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    Yep, sounds like you're on the right track with that. (Obviously make sure you actually do it to verify that you get the right answer)
     
  10. Aug 29, 2010 #9
    Thank you so much for your help
     
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