How large would an airplane have to be from say 1,000 feet up to be able to block the sun completely
I'll take a slightly different approach: using measurements of the dimensions of a Boeing 747, from how far away can the plane, seen from below, completely block the Sun?
I found this image for the dimensions of the plane:
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[left]Performing pixel measurements in GIMP, I find the image scale to be .070m per pixel. Drawing in a full circle, let's find the maximum size of circle that can be 100% obscured by the plane:[/left]
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The diameter of this circle is about 224 pixels or 15.7 meters. The apparent angular diameter of the Sun or Moon in the sky is about 0.5 degrees. The distance at which a 15.7m diameter circle subtends 0.5 degrees is [/left]
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[left]I'm actually surprised by that! I did not expect a Boeing 747 over a mile in altitude to be able to block the Sun completely (given nearly perfect alignment). I think this easily explains how aircraft flying to/from your nearby airport are able to cause a brief noticeable dimming.

(Also, from the plane, you can clearly see the shadow on the ground, up to several thousands of feet.)[/left]
[left]Could an airplane be large enough to make the stars visible? Definitely no. Just like with trying to use a chimney, the sky itself is still too bright. Stars become visible in eclipses because not only is the Sun blocked, but also the sky brightness is reduced. And even then it is
still somewhat hard to see the stars (though planets are easy), because a lot of light is scattered into the shadow from outside of the totality. It's more like twilight than night time.[/left]
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But could the plane cause the Sun's corona to be visible? Actually, I think it could! If the plane completely blocks the Sun's photosphere without blocking too much of the surrounding corona, then it basically will act as a coronagraph, and for a brief moment, cause an artificial eclipse on the ground that could render at least the inner corona visible. But it's definitely not the best method, given both the brief duration of the totality and also the shape of the plane blocking most of the surrounding corona out as well.[/left]
[left]Not having any of the Sun's photosphere visible is
crucial to seeing the corona by eye. In the 2017 eclipse the re-appearing Sun made me unable (and unwilling) to see the corona within just a few seconds, which corresponds to a sliver of Sun only a few arcseconds wide, or still more than 99.9% of the Sun being covered! Really amazing that such a tiny bit of Sun is so bright.[/left]
[left]A camera can do better. By varying the exposure I was able to digitally capture the Sun's corona more than a minute before the totality:[/left]
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[center]The Sun, 64 seconds before totality (98.8% covered).[/center]
[left]This isn't the best idea to do to a camera, as the more Sun that is showing and the more the magnification, the more heating it will cause on the sensor or inside the camera optics. Smarter to use a filter. But for my level of zoom, and also not tracking the Sun, it turned out to be pretty safe during this period.[/left]