The daytime sky (the blue sky) is bright but transparent. That means that the stars are visible during the day. Very good visual astronomers I know have once or twice pointed out Venus to me during the day. I'm not so good as that!
I think it would be an interesting and valuable project for astronomy education, and maybe also image processing, to do the following: Take a large number of digital-camera images of the blue sky during some short period of one sunny day. Take these images and post-process them to detect the stars. That is, make an image of what you would have seen if the Sun had gone dark.
There was a time in my life that I thought this project was easy. I have made some superficial attempts and I no longer think that. One idea I have (but haven't pursued) is to do this on a day that the Moon is visible, and use the Moon as a stacking reference. It isn't a perfect reference (it's a wandering star) but it's probably good enough for a first guess at alignment. Because something about this project depends on the ratio of intensity (sky brightness) to flux (star brightness), which have different units (!), I think this project must be easier to do with a telephoto lens.
