Playing with Sun Burn

One of my resolutions (I forget which) is to play with physics - this was supposed to encourage me to do cutting edge astrophysics research rather than spending all my time messing about with astronomical data analysis, but instead it's turning out to mean something different (and perhaps just as much fun!).

I discovered a program today for calculating the elevations of astronomical objects - I needed it because I had to work out when during the night of June 29th our Keck targets would be visible. If the elevation is too low, the light is too heavily absorbed by the atmosphere (the "airmass" is too high) and so the object is too dim to observe.

This reminded me of a problem I was thinking about while getting sunburnt on a boat last summer: I claimed that it was unnecessary to put on sun cream at 4pm because the decreasing elevation of the Sun meant that the time to get sunburn was increasing exponentially fast. Well, now I have the plot that shows this to indeed be the case! I used the astronomy program to work out the airmass towards the Sun throughout the day in Palo Alto on 20th June 2006, and then calculated the time taken to absorb the same amount of energy as you would in 10 minutes (a typical burntime) at noon, as a function of the time of day. That's what the plot at the top of this post is.

You can see that at 4pm (240 minutes past noon) the burn time is still only a quarter of an hour but is climbing: by 5pm the burn time is about 25 minutes, and at 6pm it is much longer than the remaining daylight time (even though the Sun does not set until 8:30pm) and we are out of danger.

This does remind me that I must put cream on early though: by 9:30am the burn time is already only 18 minutes. All of this stuff has been confirmed experimentally of course - ouch.