# Formula for calculating if an object can cast a visible shadow on the ground or not

I know that we can see the shadow cast by the light of Venus on the ground. I also talk with one person who said they were able to see the shadow even from Jupiter.

Recently I've read something like this:

According to one calculation, Sirius should be just bright enough to cast shadows on white surfaces (snow or a white sheet spread on the ground) in near-ideal dark conditions.

http://www.noojum.com/images/stories/books/The-Brightest-Stars.pdf

So I am asking seriously about a formula based on a given object magnitude with which I could calculate if the shadow it cast could possibly be visible. Any live example will be also very helpful.

• Only for the Sun and Moon the penumbra will be important do to their extended source size. For all other natural sources one can quite reasonably assume parallel light (geometric) illumination, thus consider the contrast between direct light and the diffuse illumination caused by the scatter of that source within the atmosphere (and possibly the overall background brightness of the night sky) and possibly diffuse scatter on Earth's surface (especially visible in snowy conditions, thus at high albedo) Dec 9, 2021 at 9:28
• Yes, but is there any formula defining it or at least some examples provided? Dec 9, 2021 at 10:28
• @MKR, it's not simple, because you need the angular radiance from the source object as well as the distance to the receiver, background illumination in the spectral range of interest, sensor SNR, etc. Dec 9, 2021 at 13:22
• Ok, is there any publication/book/guide where I could find it with an explanation? Dec 9, 2021 at 14:31