Chapter 22, Problem 55EAP

Daytime at “Night.” According to Olbers’ paradox, the entire sky would be as bright as the surface of a typical star if the universe were infinite in space, unchanging in time, and the same everywhere. However, conditions would not need to be quite that extreme for the “nighttime” sky to be as bright as the daytime sky.

1. Using the inverse square law for light from Mathematical Insight 15.1, determine the apparent brightness of the Sun in our sky.
2. Using the inverse square law for light, determine the apparent brightness our Sun would have if it were at a distance of 10 billion light-years.
3. From your answers to parts a and b, estimate how many stars like the Sun would need to exist at a distance of 10 billion light-years for their total apparent brightness to equal that of our Sun.
4. Compare your answer to part c with the estimate of the total number of stars in our observable universe from Mathematical Insight 1.3. Use your answer to explain why the night sky is much darker than the daytime sky. How much larger would the total number of stars need to be for “night” to be as bright as day?