So I was walking home last night, looking up at the stars shining. I wondered how much I'm shining back?
I started by assuming I'm a black body radiating at human body temperature.
T = 37 °C
I considered just my head i.e. a sphere with circumference of an average male human head.
C = 57 cm
I found the surface area of the idealized sphere representing my head.
A = 4πr2 = 0.103418882 m2
I plugged these into the Stefan-Boltzmann law to find the photon flux from my head.
N = (1.5205 * 1015 m-2 s-1 K-3) * T3 * A = 4.691 * 1021 photons per second
I looked up a number I'm comfortable with for the distance to the furthest naked-eye visible star.
D = 16308 light-years
And I assumed these stars have on average a similar diameter to our Sun.
d = 1.3914 billion meters
I found the angular diameter of this idealized far-away star.
𝛿 = (206265) * (d / D) = 3.03362676 * 10-7 arcseconds = 5.167 * 10-10 degrees
And converted this angle into square degrees.
Ω = πr2 = π * (𝛿/2)2 = 5.5771095 * 10-21
Finally I used this solid angle to find the average rate of photons intercepted by the idealized star.
N / (41253 / Ω) = 0.0238439 photons/s = one photon every 42 seconds
So spend a about a minute looking at the stars, and you're shining back at them. At least a little bit.