How Bright Is The Daytime Sky?

OCT 20, 2010

A friend of mine recently bought a popular astronomer's toy---a gizmo called a Sky Quality Meter that measures light pollution. Point it at the nighttime sky and it tells you how bright the sky is in magnitudes per square arcsecond. Where he lives, the skies are pretty dark at night (at least for NJ). His gizmo tells him his skies are mag 19.5 per square arcsecond. He took his toy to a "dark-sky" site, also here in NJ, and it read 20.6. Not bad. Out of curiosity, I asked him: "How bright is the daytime sky?" He said he'd check. The other day he got back to me and said that the instrument was overloaded by the light and simply said that it is brighter than magnitude 0 per square arcsecond (i.e., a negative number). This made me wonder: is that right? That seems too bright to me. I've viewed Venus in the daytime through binoculars and small telescopes. Venus is brighter than the daytime sky. How bright is Venus? Well digging through old observing logs, I viewed (and photographed) Venus at noon on Oct 13, 2007 (the picture shown here was taken on a different day). At that time, Venus was magnitude -4.5, it was 29 arcseconds in diameter and its face (the face facing us) was 41.8 percent illuminated. Doing the math, Venus's illuminated face was 276 square arcseconds in apparent area. Hence, its "surface brightness" was -4.5 + 2.5*log(276) = 1.6. And, Venus was brighter than the daytime sky.

Using the picture shown here and consulting JL Hilton for the brightness of Venus in its crescent phase, I get that Venus had apparent magnitude of -0.75 and illuminated surface area of 65.2 square arcseconds so a surface brightness of -0.75 + 2.5*log(65.2) = 3.8. On this day, I would say that the daytime sky was brighter than Venus (the picture shown here is enhanced to make Venus appear brighter than it actually was relative to the sky). So, daytime skies are somewhere between 1.6 and 3.8 magnitudes per square arcsecond. I'm guessing about magnitude 3 but I don't know exactly.