1. Feb 18, 2017 #1

   Tahmeed

   

   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

   Tahmeed, Feb 18, 2017
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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.

    

   haruspex, Feb 18, 2017
4. Feb 18, 2017 #3

   Tahmeed

   

   I don't know why but the link isnt working for me. However does it bring 4piAC as a result?

    

   Tahmeed, Feb 18, 2017
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.

    

   haruspex, Feb 18, 2017

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