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Jan 23, 2020 at 18:44 answer added Phil Frost - W8II timeline score: 1
Jan 21, 2020 at 6:58 history edited pymekrolimus CC BY-SA 4.0
An ellipsoid is not coincident with a sphere.
Jan 21, 2020 at 6:52 comment added pymekrolimus You're right - an ellipsoid is not coincident with the sphere. I will remove that part. Instead the solid angle on the elliptical beam should be some fraction of the surface area of a hemisphere. How would I go about integrating this?
Jan 21, 2020 at 6:33 comment added tomnexus I think things are made worse by the addition of the sphere analogy. If you must project the beam onto a unit sphere, you'll find the area is the same as the solid angle. But there's no need to invoke a sphere to find solid angles. In your first case - there is no hemisphere, just a portion of the unit sphere. In the second case, there's definitely no ellipsoid; an ellipsoid isn't coimcident with a sphere at all (except in the trivial case). How about "just" integrating to find the solid angle of the elliptical beam itself, with your first formula?
Jan 21, 2020 at 4:54 history asked pymekrolimus CC BY-SA 4.0