> Even if it is 100%, it would have to be multiplied by the probability of photons from that star making it past all the interferences like nebulae, Oort cloud, and Earth's atmosphere along that exact vector.
You're missing the point that, given enough time, all those objects would be heated up by stellar radiation to the temperature of the originating star.
Consider the temperature over time of a body that is energetically coupled to a star, however far away. Because the star's temperature is relatively constant (a property of fusion reactions), it is the receiving body's temperature that changes, according to this equation:
All the bodies exposed to a star's energy radiation follow the above law. And given enough time and barring any other effects, all of them reach the star's surface temperature. Which leads us to Olbers' Paradox -- given billions of years and copious energy sources, why didn't this happen?
You're missing the point that, given enough time, all those objects would be heated up by stellar radiation to the temperature of the originating star.
Consider the temperature over time of a body that is energetically coupled to a star, however far away. Because the star's temperature is relatively constant (a property of fusion reactions), it is the receiving body's temperature that changes, according to this equation:
q = (e^(-t/k) - 1)*(a - b) + a
Where:
t = time
k = energy transfer factor
q = temperature at time t
a = temperature at time 0
b = temperature of source
The above expresses Newton's Law of Cooling:
https://www.dropbox.com/s/bt63bt59t9q76th/newtons_cooling_la...
All the bodies exposed to a star's energy radiation follow the above law. And given enough time and barring any other effects, all of them reach the star's surface temperature. Which leads us to Olbers' Paradox -- given billions of years and copious energy sources, why didn't this happen?