Let assume there is a unit sphere inside a oblate spheroid with minor axis 1 and major axis b. What is the surface area in the oblate spheroid surface produced from extending the subtended solid angle $\omega$ in the sphere?

  • 2
    $\begingroup$ It’s obviously going to depend on the location and shape of the patch of the sphere that comprises that solid angle. $\endgroup$ – amd Jan 10 at 3:11
  • $\begingroup$ Exactly, but is there a particular technique to described the relationship? $\endgroup$ – Jose E Calderon Jan 10 at 8:52
  • $\begingroup$ You could try inverting the computation of solid angle for a patch of the ellipsoid: project from the unit sphere onto the ellipsoid and compute the resulting surface integral. $\endgroup$ – amd Jan 10 at 9:13
  • $\begingroup$ @amd Thanks for pointing this out! It is Spheroid. Have corrected question. To be more specific- a Oblate Spheroid. $\endgroup$ – Jose E Calderon Jan 10 at 9:29
  • $\begingroup$ you can well reduce the problem to 2D $\endgroup$ – G Cab Jan 10 at 9:38

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