About the surface area of a prolate ellipsoid

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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??
 
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  • #2
haruspex
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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??
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.
 
  • #3
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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.
I don't know why but the link isnt working for me. However does it bring 4piAC as a result?
 
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haruspex
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I don't know why but the link isnt working for me. However does it bring 4piAC as a result?
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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