[Physics] Why don’t flying birds have shadows


I saw a flock of birds flying around today, and noticed that they didn't cast any shadows on the ground. I thought this to be rather strange, so I tried to resolve this mystery.

My first idea was that the sun might actually be wide enough such that both 'ends' of the sun might cut underneath the birds, as the ground would still be illuminated by one or both sides of the sun as the bird flew in front. I calculated as follows:

enter image description here

I assumed the distance from the earth to the sun to be $d = 150\times 10^6 \text{km}$, and the radius of the sun to be $R = 6.957 \times 10^5 \text{km}$. The angle $\alpha$, as shown in my poorly drawn figure, is the half angle between the two sides of the sun, and can be easily calculated:
\alpha = \tan^{-1}\left(\frac{R}{d}\right) \approx 0.0046 \text{rad}
This means that the radius of an object flying at $20\rm m$ height must have
at least radius
r = 20\tan\alpha = 0.093\rm m
I assume the birds to have a wingspan greater than $20\rm cm$, so in this case they must cast a shadow.

I also considered the possible effects of diffraction, but aren't those effects too small to be observed on such a scale?

Does anybody have an explanation for why birds don't seem to cast shadows, or maybe where my attempt at explaining the phenomenon falls short?

Best Answer

In order to cast a discernible shadow, an object has to block the entire sun (or else some light rays from the unblocked parts will wash out whatever shadow was created from the blocked parts). Since birds tend to be relatively thin, irregular-shaped objects, whereas the sun is a circle with a diameter of about half a degree, it doesn't seem particularly likely that even a bird with sufficient wingspan would be able to block the entire sun at once.

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