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B About the surface area of a prolate ellipsoid

  1. Feb 18, 2017 #1
    Is there any limit for which we can approximately write the surface area of a prolate ellipsoid to be 4piA*B comparing with the spherical 4piR*R??
     
    Last edited: Feb 18, 2017
  2. jcsd
  3. Feb 18, 2017 #2

    haruspex

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    Look at eqn 9 at http://mathworld.wolfram.com/ProlateSpheroid.html.
    You could substitute for a in terms of c and e using eqn 8, then make an approximation for small e.
     
  4. Feb 18, 2017 #3
    I don't know why but the link isnt working for me. However does it bring 4piAC as a result?
     
  5. Feb 18, 2017 #4

    haruspex

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    It can't be exactly that, of course, so it depends how good an approximation you want.
    The exact equations at that link are
    Area = ##2\pi a^2+2\pi ac\sin^{-1}(e)/e##, eqn (9), and ##a^2=c^2(1-e^2)##, eqn 8
    where the radii are a, a, c.
     
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