Wednesday, July 24, 2013

Wave at Saturn


In case you missed it, there's a cool picture of the Earth and Moon taken from Saturn. Apparently a bunch of us earthly homebodies decided to wave at the Cassini spacecraft as it took pictures of us.

"Hi, Mom!"

On Earth, we're hit with a flux of about 1400 W/m2 of sunlight. Our bodies have an area of about one square meter, and I'll assume only 1/10 of the light that hits each of our bodies gets reflected out of the atmosphere. Since visible photons carry a few electron volts,1 we can estimate that 1020 photons leave each body every second.  These photons will be distributed over a sphere with a radius equal to the distance to Saturn, approximately 1.2 billion kilometers. A small fraction of this sphere coincides with the Cassini's camera lens. Assuming it's like most digital cameras, the area of Cassini's lens should be roughly 10 square centimeters. That's about one part in 1028 of the total area covered by the photons. Assuming a shutter speed of one second, the probability that one of your photons will appear in the "Wave at Saturn" picture is about one in one-hundred million. Since the world contains 7 billion people, there's a pretty good chance at least one of humanity's photons is in the picture.
[1] One electron volt is equivalent to 1.6×10-19 Joules.