Why is there no Poisson spot in a solar eclipse?

Editor's Note: The question asked in this paper's title falls in the category of “Why didn't I think to ask that?” It is answered in just the way that you will want to answer it in a class: first with an experimental demonstration that larger objects result in smaller and dimmer Poisson spots, followed by a simple calculation, and then completed with a more careful calculation that is still not too hard to present in class. This seems to be appropriate for an introductory or intermediate optics course.